MA002 Calculus

Faculty of Informatics
Autumn 2021
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14. 9. to Tue 7. 12. Tue 14:00–15:50 B204
  • Timetable of Seminar Groups:
MA002/01: Thu 16. 9. to Thu 9. 12. Thu 10:00–11:50 B204, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 25 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations.
Learning outcomes
At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Written intrasemestral tests in seminars (30 points).
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
The conditions for final evaluation may be specified later depending on the pandemic situation and legal regulations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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.

MA002 Calculus

Faculty of Informatics
Autumn 2020
Extent and Intensity
2/2. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 16:00–17:50 B204
  • Timetable of Seminar Groups:
MA002/01: Wed 10:00–11:50 C416, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 25 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations.
Learning outcomes
At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Written intrasemestral tests in seminars (30 points).
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
The conditions for final evaluation may be specified later depending on the pandemic situation and legal regulations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2019
Extent and Intensity
2/2. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 10:00–11:50 B204
  • Timetable of Seminar Groups:
MA002/01: Thu 14:00–15:50 A320, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 25 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations.
Learning outcomes
At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2020, Autumn 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2018
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 10:00–11:50 B204
  • Timetable of Seminar Groups:
MA002/01: Thu 8:00–9:50 B204, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 23 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2019, Autumn 2020, Autumn 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2017
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Thu 14:00–15:50 A320
  • Timetable of Seminar Groups:
MA002/01: Thu 16:00–17:50 A320, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 23 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2016
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 8:00–9:50 A320
  • Timetable of Seminar Groups:
MA002/01: Thu 12:00–13:50 A320, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 23 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2015
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 8:00–9:50 C525
  • Timetable of Seminar Groups:
MA002/01: Thu 18:00–19:50 A320, P. Šepitka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 23 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2014
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Mgr. Milan Bačík (seminar tutor)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 14:00–15:50 B204
  • Timetable of Seminar Groups:
MA002/01: Fri 8:00–9:50 A320, M. Bačík
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 22 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms 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 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus

Faculty of Informatics
Autumn 2013
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Mgr. Bc. Tomáš Hebelka (seminar tutor)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 10:00–11:50 G125
  • Timetable of Seminar Groups:
MA002/01: Wed 8:00–9:50 G125, T. Hebelka
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 22 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus III

Faculty of Informatics
Autumn 2012
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Mgr. Bc. Tomáš Hebelka (assistant)
doc. RNDr. Michal Veselý, Ph.D. (assistant)
RNDr. Jan Vondra, Ph.D. (alternate examiner)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 11:00–13:50 G124
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 22 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Teaching methods
lectures (3 hours per week); it is recommended to enrol also MA019 Practicing Calculus III
Assessment methods
Exam: written (theory test + practical part), it takes 120 minutes.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus III

Faculty of Informatics
Autumn 2011
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
doc. Mgr. Petr Zemánek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Timetable
Mon 17:00–19:50 G123
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 22 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Teaching methods
lectures
Assessment methods
Teaching: lecture 3 hours a week. Exam: written.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus III

Faculty of Informatics
Autumn 2010
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Tue 8:00–10:50 B003
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 26 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Teaching methods
lectures
Assessment methods
Teaching: lecture 3 hours a week. Exam: written.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus III

Faculty of Informatics
Autumn 2009
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 9:00–11:50 B011
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 26 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Teaching methods
lectures
Assessment methods
Teaching: lecture 3 hours a week. Exam: written.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.

MA002 Calculus III

Faculty of Informatics
Autumn 2008
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 9:00–11:50 B011
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 19 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods
Teaching: lecture 3 hours a week
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, 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.

MA002 Calculus III

Faculty of Informatics
Autumn 2007
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
prof. RNDr. Miroslav Bartušek, DrSc.
Faculty of Informatics
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 16:00–18:50 B011
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 19 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Písemná zkouška, zamereni prakticke a teoreticke, reseni praktickych prikladu a znalost definici a zakladnich vet a souvislosti mezi nimi. Zadne povolene materialy.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, 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.

MA002 Calculus III

Faculty of Informatics
Autumn 2006
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Miroslav Bartušek, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
prof. RNDr. Miroslav Bartušek, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Miroslav Bartušek, DrSc.
Timetable
Mon 9:00–11:50 A107
Prerequisites
! M002 Calculus III || MB001 Calculus II || M001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 7 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Písemná zkouška, zamereni prakticke a teoreticke, reseni praktickych prikladu a znalost definici a zakladnich vet a souvislosti mezi nimi. Zadne povolene materialy.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, 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.

MA002 Calculus III

Faculty of Informatics
Autumn 2005
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Miroslav Bartušek, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
prof. RNDr. Miroslav Bartušek, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Miroslav Bartušek, DrSc.
Timetable
Mon 9:00–11:50 A107
Prerequisites
! M002 Calculus III || MB001 Calculus II || M001 Calculus II
Completion of courses Mathematical Analysis I and 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
there are 7 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Písemná zkouška, zamereni prakticke a teoreticke, reseni praktickych prikladu a znalost definici a zakladnich vet a souvislosti mezi nimi. Zadne povolene materialy.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, 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.

MA002 Calculus III

Faculty of Informatics
Autumn 2004
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Miroslav Bartušek, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. RNDr. Miroslav Bartušek, DrSc.
Timetable
Wed 8:00–10:50 B003
Prerequisites
M002 Calculus III || MB001 Calculus II || M001 Calculus II
Completion of courses Mathematical Analysis I and Mathematical Analysis II.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Písemná zkouška, zamereni prakticke a teoreticke, reseni praktickych prikladu a znalost definici a zakladnich vet a souvislosti mezi nimi. Zadne povolene materialy.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, 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.

MA002 Calculus III

Faculty of Informatics
Autumn 2003
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Miroslav Bartušek, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. RNDr. Miroslav Bartušek, DrSc.
Timetable
Thu 15:00–17:50 B011
Prerequisites (in Czech)
M002 Calculus III || MB001 Calculus II || M001 Calculus II
Znalosti v rozsahu bakalářských předmětů Matematická analýza I, Matematická analýza II.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives (in Czech)
Magisterský kurz, který prezentuje nepovinnou část matematické analýzy. Jsou probírány posloupnosti a řady funkcí a jejich aplikace. Dále je pozornost věnována křivkovému integrálu, základům komplexní analýzy a elementárním metodám řešení diferenciálních rovnic.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Písemná zkouška, zamereni prakticke a teoreticke, reseni praktickych prikladu a znalost definici a zakladnich vet a souvislosti mezi nimi. Zadne povolene materialy.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2002, 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.

MA002 Calculus III

Faculty of Informatics
Autumn 2002
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Miroslav Bartušek, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. RNDr. Miroslav Bartušek, DrSc.
Timetable
Thu 7:00–9:50 A107
Prerequisites (in Czech)
! M002 Calculus III
Znalosti v rozsahu bakalářských předmětů Matematická analýza I, Matematická analýza II.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives (in Czech)
Magisterský kurz, který prezentuje nepovinnou část matematické analýzy. Jsou probírány posloupnosti a řady funkcí a jejich aplikace. Dále je pozornost věnována křivkovému integrálu, základům komplexní analýzy a elementárním metodám řešení diferenciálních rovnic.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Assessment methods (in Czech)
Písemná zkouška.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms 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.

MA002 Calculus

Faculty of Informatics
Autumn 2023

The course is not taught in Autumn 2023

Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 25 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations.
Learning outcomes
At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Written intrasemestral tests in seminars (30 points).
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
The conditions for final evaluation may be specified later depending on the pandemic situation and legal regulations.
Language of instruction
Czech
Further Comments
Course is no more offered.
The course is taught: every week.
The course is also listed under the following terms 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.

MA002 Calculus

Faculty of Informatics
Autumn 2022

The course is not taught in Autumn 2022

Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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 25 fields of study the course is directly associated with, display
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations.
Learning outcomes
At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
  • https://www.math.muni.cz/~dosly/varpoc.pdf
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Written intrasemestral tests in seminars (30 points).
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
The conditions for final evaluation may be specified later depending on the pandemic situation and legal regulations.
Language of instruction
Czech
Further Comments
Course is no more offered.
The course is taught: every week.
The course is also listed under the following terms 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.
  • Enrolment Statistics (recent)