MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2019
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Mgr. Jakub Juránek, Ph.D. (seminar tutor)
Mgr. Jiřina Šišoláková, Ph.D. (assistant)
prof. Mgr. Petr Hasil, Ph.D. (alternate examiner)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Wed 12:00–15:50 A217
  • Timetable of Seminar Groups:
MB202/01: Tue 19. 2. to Tue 14. 5. Tue 12:00–13:50 B204, J. Juránek
MB202/02: Tue 19. 2. to Tue 14. 5. Tue 14:00–15:50 B204, J. Juránek
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Learning outcomes
At the end of the course students will be able to:
work both practically and theoretically with the derivative and (indefinite and definite) integral ;
use calculus for solving various applied problems;
analyse the behavior of functions of one real variable;
understand the theory and use of infinite number series and power series;
use some integral transforms and Fourier series.
Syllabus
  • 1. Creating the ZOO – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1st ed. Brno: Masarykova univerzita, 2013, 773 pp. ISBN 978-80-210-6307-5. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018.

MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2018
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jakub Juránek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 16:00–19:50 A320
  • Timetable of Seminar Groups:
MB202/01: Wed 16:00–17:50 A320, J. Juránek
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Learning outcomes
At the end of the course students will be able to:
work both practically and theoretically with the derivative and (indefinite and definite) integral ;
use calculus for solving various applied problems;
analyse the behavior of functions of one real variable;
understand the theory and use of infinite number series and power series;
use some integral transforms and Fourier series.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1st ed. Brno: Masarykova univerzita, 2013, 773 pp. ISBN 978-80-210-6307-5. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019.

MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2017
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (alternate examiner)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 16:00–19:50 A218
  • Timetable of Seminar Groups:
MB202/01: Wed 14:00–15:50 A320, M. Veselý
MB202/02: Wed 16:00–17:50 A320, M. Veselý
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1st ed. Brno: Masarykova univerzita, 2013, 773 pp. ISBN 978-80-210-6307-5. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
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 Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2018, Spring 2019.

MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2016
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Bc. Martin Chvátal, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Wed 12:00–15:50 A217
  • Timetable of Seminar Groups:
MB202/01: Mon 8:00–9:50 A320, M. Chvátal
MB202/02: Mon 10:00–11:50 A320, M. Chvátal
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1st ed. Brno: Masarykova univerzita, 2013, 773 pp. ISBN 978-80-210-6307-5. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
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 Spring 2013, Spring 2014, Spring 2015, Spring 2017, Spring 2018, Spring 2019.

MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2015
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Eva Janoušková, Ph.D. (seminar tutor)
Mgr. Marek Sas (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Fri 8:00–11:50 A217
  • Timetable of Seminar Groups:
MB202/T01: Mon 16. 2. to Fri 15. 5. Mon 9:40–11:15 116, E. Janoušková, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB202/01: Mon 8:00–9:50 A320, M. Sas
MB202/02: Mon 10:00–11:50 A320, M. Sas
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
  • J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
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 Spring 2013, Spring 2014, Spring 2016, Spring 2017, Spring 2018, Spring 2019.

MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2014
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Milan Bačík (seminar tutor)
Mgr. Marek Sas (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Thu 14:00–15:50 D3, Fri 12:00–13:50 G101
  • Timetable of Seminar Groups:
MB202/01: Tue 8:00–9:50 G125, M. Bačík
MB202/02: Tue 10:00–11:50 G125, M. Bačík
MB202/03: Thu 8:00–9:50 M2,01021, M. Sas
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
  • J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
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 Spring 2013, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019.

MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2013
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Martin Panák, Ph.D. (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 G101, Wed 8:00–9:50 G101
  • Timetable of Seminar Groups:
MB202/01: Thu 8:00–9:50 G124, J. Šilhan
MB202/02: Thu 10:00–11:50 G124, J. Šilhan
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses
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 Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019.
  • Enrolment Statistics (recent)