M3100 Mathematical Analysis III

Faculty of Science
Autumn 2024
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
In-person direct teaching
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16:00–17:50 M1,01017, Tue 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Tue 16:00–17:50 M5,01013, J. Jekl
M3100/02: Tue 18:00–19:50 M5,01013, J. Jekl
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series and transformation. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals. IV. Curvilinear integral. V. Surface integral. VI. Introduction to complex analysis
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Adjustment for pandemic period (onsite/online teaching):
Lectures and seminars are NOT compulsory.
The exam will be probably online. Specific course according to the situation at the time.
If possible, other standard rules will be maintained.

Standard rules for regular semesters:
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
5 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2023
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18:00–19:50 A,01026, Tue 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Thu 18:00–19:50 M6,01011, J. Jekl
M3100/02: Thu 16:00–17:50 M6,01011, J. Jekl
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series and transformation. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals. IV. Curvilinear integral. V. Surface integral. VI. Introduction to complex analysis
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Adjustment for pandemic period (onsite/online teaching):
Lectures and seminars are NOT compulsory.
The exam will be probably online. Specific course according to the situation at the time.
If possible, other standard rules will be maintained.

Standard rules for regular semesters:
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
5 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2022
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 A,01026, Wed 18:00–19:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Tue 16:00–17:50 M6,01011, J. Jekl
M3100/02: Thu 18:00–19:50 M3,01023, J. Jekl
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series and transformation. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals. IV. Curvilinear integral. V. Surface integral. VI. Introduction to complex analysis
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Adjustment for pandemic period (onsite/online teaching):
Lectures and seminars are NOT compulsory.
The exam will be probably online. Specific course according to the situation at the time.
If possible, other standard rules will be maintained.

Standard rules for regular semesters:
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
5 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
autumn 2021
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18:00–19:50 A,01026, Wed 18:00–19:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Tue 18:00–19:50 M2,01021, J. Jekl
M3100/02: Wed 16:00–17:50 M3,01023, J. Jekl
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series and transformation. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals. IV. Curvilinear integral. V. Surface integral. VI. Introduction to complex analysis
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Adjustment for pandemic period (onsite/online teaching):
Lectures and seminars are NOT compulsory.
The exam will be probably online. Specific course according to the situation at the time.
If possible, other standard rules will be maintained.

Standard rules for regular semesters:
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
5 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2020
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 prace doma, Tue 18:00–19:50 prace doma
  • Timetable of Seminar Groups:
M3100/01: Wed 18:00–19:50 M2,01021, P. Šepitka
M3100/02: Mon 16:00–17:50 M4,01024, J. Jekl
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series and transformation. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals. IV. Curvilinear integral. V. Surface integral. VI. Introduction to complex analysis
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Adjustment for autumn semester 2020 (pandemic, online teaching):
Lectures and seminars are NOT compulsory.
5 written intrasemestral tests in seminars (10% of the overall evaluations).
The exam will be probably online. Specific course according to the situation at the time.
If possible, other standard rules will be maintained.

Standard rules for regular semesters:
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
3 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2019
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
RNDr. Iva Dřímalová, Ph.D. (seminar tutor)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18:00–19:50 A,01026, Tue 18:00–19:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Tue 12:00–13:50 M4,01024, I. Dřímalová
M3100/02: Tue 16:00–17:50 M1,01017, J. Jekl
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series and transformation. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals. IV. Curvilinear integral. V. Surface integral. VI. Introduction to complex analysis
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
3 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2018
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17. 9. to Fri 14. 12. Mon 16:00–17:50 A,01026, Tue 16:00–17:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Mon 17. 9. to Fri 14. 12. Mon 8:00–9:50 M6,01011, P. Šepitka
M3100/02: Mon 17. 9. to Fri 14. 12. Tue 18:00–19:50 M2,01021, P. Šepitka
M3100/51: Mon 17. 9. to Fri 14. 12. Wed 14:00–15:50 F4,03017, P. Musilová
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series.
  • II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series.
  • III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
3 written intrasemestral tests in seminars (30% of the overall evaluations).
Final exam: Written test (40%) and oral exam (30%).
To pass: at least 1/3 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
autumn 2017
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Mon 18:00–19:50 A,01026, Tue 11:00–12:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Mon 18. 9. to Fri 15. 12. Wed 18:00–19:50 M1,01017, P. Šepitka
M3100/51: Mon 18. 9. to Fri 15. 12. Thu 14:00–15:50 F3,03015, L. Czudková
Prerequisites
M2100 Mathematical Analysis II
The knowledge from courses Mathematical Analysis I, II is assumed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Learning outcomes
At the end of the course students will be able to:
define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;
apply the methods of mathematical analysis to concrete problems.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • BUCK, R. Creighton. Advanced calculus. 3d ed. Long Grove: Waveland Press, 2003, x, 622. ISBN 1577663020. info
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
3 written intrasemestral tests in seminars (30% of the overall evaluations).
Final exam: Written test (40%) and oral exam (30%).
To pass: at least 1/3 points from intrasemestral tests, then 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2016
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Mon 18:00–19:50 A,01026, Tue 11:00–12:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Mon 19. 9. to Sun 18. 12. Tue 16:00–17:50 M2,01021, P. Šepitka
M3100/02: Mon 19. 9. to Sun 18. 12. Thu 8:00–9:50 M1,01017, P. Šepitka
M3100/51: Mon 19. 9. to Sun 18. 12. Fri 8:00–9:50 F4,03017, L. Czudková
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompanying seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previous courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2015
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
RNDr. Iva Dřímalová, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M1,01017, Wed 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Tue 18:00–19:50 M5,01013, I. Dřímalová
M3100/02: Tue 16:00–17:50 M5,01013, P. Šepitka
M3100/51: Wed 16:00–17:50 F4,03017, L. Czudková
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompanying seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previous courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2014
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
RNDr. Iva Dřímalová, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 10:00–11:50 M1,01017, Tue 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Tue 8:00–9:50 M4,01024, I. Dřímalová
M3100/02: Wed 14:00–15:50 M3,01023, P. Šepitka
M3100/03: Wed 8:00–9:50 M3,01023, P. Šepitka
M3100/51: Wed 10:00–11:50 F4,03017
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompanying seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previous courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2013
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
Mgr. Kateřina Hanžlová (seminar tutor)
Ing. Mgr. Petr Valenta (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 A,01026, Fri 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M3100/F1: Thu 13:00–14:50 F1 6/1014, L. Czudková
M3100/01: Mon 13:00–14:50 M4,01024, K. Hanžlová
M3100/02: Mon 15:00–16:50 M1,01017, K. Hanžlová
M3100/03: Tue 18:00–19:50 M5,01013, P. Valenta
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompanying seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previous courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2012
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
Mgr. Kateřina Hanžlová (seminar tutor)
Ing. Mgr. Petr Valenta (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M1,01017, Fri 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Tue 12:00–13:50 M4,01024, K. Hanžlová
M3100/02: Tue 10:00–11:50 M5,01013, K. Hanžlová
M3100/03: Thu 18:00–19:50 M6,01011, P. Valenta
M3100/04: Tue 12:00–13:50 F4,03017, L. Czudková
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of Mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2011
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
RNDr. Mgr. Hana Haladová, Ph.D. (seminar tutor)
Mgr. Kateřina Hanžlová (seminar tutor)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 A,01026, Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Wed 15:00–16:50 M1,01017, K. Hanžlová
M3100/02: Wed 12:00–13:50 M4,01024, K. Hanžlová
M3100/03: Thu 10:00–11:50 M4,01024, B. Půža
M3100/04: Thu 12:00–13:50 M4,01024, H. Haladová
M3100/05: Mon 18:00–19:50 M4,01024, H. Haladová
M3100/06: Wed 15:00–16:50 F1 6/1014
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of Mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2010
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Michaela Benešová (seminar tutor)
RNDr. Mgr. Hana Haladová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 M1,01017, Wed 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Wed 18:00–19:50 M4,01024, M. Benešová
M3100/02: Tue 18:00–19:50 M2,01021, M. Benešová
M3100/03: Mon 18:00–19:50 M5,01013, H. Haladová
M3100/04: Mon 16:00–17:50 M4,01024, H. Haladová
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of Mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2009
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
doc. RNDr. Ladislav Adamec, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 M1,01017, Thu 15:00–16:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Wed 8:00–9:50 M4,01024, B. Půža
M3100/02: Tue 18:00–19:50 M2,01021, L. Adamec
M3100/03: Tue 16:00–17:50 M2,01021, L. Adamec
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of Mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2008
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
doc. RNDr. Martin Kolář, Ph.D. (seminar tutor)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Jan Orava (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 11:00–12:50 A,01026, Fri 10:00–11:50 A,01026
  • Timetable of Seminar Groups:
M3100/01: Mon 8:00–9:50 M5,01013, M. Kolář
M3100/02: Mon 16:00–17:50 M4,01024, J. Orava
M3100/03: Mon 13:00–14:50 M3,01023, J. Orava
M3100/04: Fri 13:00–14:50 F1 6/1014, M. Krbek
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2007
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
doc. RNDr. Ladislav Adamec, CSc. (seminar tutor)
Mgr. Jan Orava (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 N21, Wed 8:00–9:50 N21
  • Timetable of Seminar Groups:
M3100/01: Thu 8:00–9:50 UP2, L. Adamec
M3100/02: Tue 18:00–19:50 UP2, J. Orava
M3100/03: Tue 16:00–17:50 UP1, J. Orava
M3100/04: Mon 8:00–9:50 UM, B. Půža
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2006
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Josef Rebenda, Ph.D. (seminar tutor)
Mgr. Jiří Vítovec, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable
Mon 16:00–17:50 N21, Tue 14:00–15:50 N21
  • Timetable of Seminar Groups:
M3100/01: Mon 14:00–15:50 UP1, J. Vítovec
M3100/02: Mon 10:00–11:50 U1, J. Rebenda
M3100/03: Thu 8:00–9:50 UP2, J. Vítovec
M3100/04: Tue 16:00–17:50 F3,03015, M. Krbek
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2005
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
doc. RNDr. Ladislav Adamec, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable
Tue 16:00–17:50 N21, Thu 15:00–16:50 N21
  • Timetable of Seminar Groups:
M3100/01: Thu 10:00–11:50 UM, L. Adamec
M3100/02: Thu 12:00–13:50 UP1, L. Adamec
M3100/03: Thu 17:00–18:50 N21, B. Půža
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2004
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Viera Růžičková, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable
Tue 8:00–9:50 N21, Thu 10:00–11:50 N21
  • Timetable of Seminar Groups:
M3100/01: Thu 8:00–9:50 N21, V. Růžičková, Rozvrhově doporučeno: 2.r. Me,Mf
M3100/02: Tue 10:00–11:50 N21, V. Růžičková, Rozvrhově doporučeno: 2.r. Mo.Ms
M3100/03: Mon 17:00–18:50 F1 6/1014, M. Krbek
M3100/04: Wed 18:00–19:50 F2 6/2012, M. Krbek
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 8 fields of study the course is directly associated with, display
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2003
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
Mgr. Martina Bobalová, Ph.D. (seminar tutor)
Mgr. Ladislav Polák (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable of Seminar Groups
M3100/01: No timetable has been entered into IS. M. Bobalová
M3100/02: No timetable has been entered into IS. L. Polák
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2002
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Simona Fišnarová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable of Seminar Groups
M3100/01: No timetable has been entered into IS. S. Fišnarová
M3100/02: No timetable has been entered into IS. S. Fišnarová
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2001
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Bedřich Půža, CSc.
Prerequisites (in Czech)
M2100 Mathematical Analysis II
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Diferenciální počet v Rn (parciální a směrové derivace, slabý a silný diferenciál, Taylorova věta, extrémy) Zobrazení mezi euklidovskými prostory (derivace a diferenciály zobrazení, derivování složených zobrazení, implicitní funkce, regulární zobrazení, variety, extrémy na varietách) Přímé metody řešení obyčejných diferenciálních rovnic (rovnice se separovanými proměnnými, homogenní dif.rovnice, lineární a Bernoulliova diferenciální rovnice, rovnice nerozřešené vzhledem k derivaci, lineární diferenciální rovnice vyšších řádů) Základy integrálního počtu v Rn (Fubiniova věta, substituce, aplikace) Základy teorie funkcí komplexní proměnné (holomorfní funkce, singularity, Cauchyova věta)
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2000
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
prof. RNDr. Zdeněk Pospíšil, Dr. (seminar tutor)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Bedřich Půža, CSc.
Prerequisites (in Czech)
M2100 Mathematical Analysis II
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Diferenciální počet v Rn (parciální a směrové derivace, slabý a silný diferenciál, Taylorova věta, extrémy) Zobrazení mezi euklidovskými prostory (derivace a diferenciály zobrazení, derivování složených zobrazení, implicitní funkce, regulární zobrazení, variety, extrémy na varietách) Přímé metody řešení obyčejných diferenciálních rovnic (rovnice se separovanými proměnnými, homogenní dif.rovnice, lineární a Bernoulliova diferenciální rovnice, rovnice nerozřešené vzhledem k derivaci, lineární diferenciální rovnice vyšších řádů) Základy integrálního počtu v Rn (Fubiniova věta, substituce, aplikace) Základy teorie funkcí komplexní proměnné (holomorfní funkce, singularity, Cauchyova věta)
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 1999
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Bedřich Půža, CSc.
Prerequisites (in Czech)
M2100 Mathematical Analysis II
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus (in Czech)
  • Diferenciální počet v Rn (parciální a směrové derivace, slabý a silný diferenciál, Taylorova věta, extrémy) Zobrazení mezi euklidovskými prostory (derivace a diferenciály zobrazení, derivování složených zobrazení, implicitní funkce, regulární zobrazení, variety, extrémy na varietách) Přímé metody řešení obyčejných diferenciálních rovnic (rovnice se separovanými proměnnými, homogenní dif.rovnice, lineární a Bernoulliova diferenciální rovnice, rovnice nerozřešené vzhledem k derivaci, lineární diferenciální rovnice vyšších řádů) Základy integrálního počtu v Rn (Fubiniova věta, substituce, aplikace) Základy teorie funkcí komplexní proměnné (holomorfní funkce, singularity, Cauchyova věta)
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
Mgr. Michaela Benešová (seminar tutor)
RNDr. Mgr. Hana Haladová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of Mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Michaela Benešová (seminar tutor)
RNDr. Mgr. Hana Haladová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of Mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompaning seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previo0us courses Mathematical Analysis I,II
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3100 Mathematical Analysis III

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Bedřich Půža, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
Mgr. Josef Rebenda, Ph.D. (seminar tutor)
Mgr. Jiří Vítovec, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the tree semestrs basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, oprations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Standardní přednáška a cvičení, stejný způsob zakonční jako u předchozích kursů Matematická analýza I,II.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (recent)