Mathematical Analysis 2
Code  Completion  Credits  Range  Language 

B0B01MA2  Z,ZK  7  4P+2S  Czech 
 Lecturer:
 Petr Hájek, Jaroslav Tišer (guarantor)
 Tutor:
 Petr Hájek, Jaroslav Tišer (guarantor), Josef Hekrdla, Miroslav Korbelář
 Supervisor:
 Department of Mathematics
 Synopsis:

The subject covers an introduction to the
differential and integral calculus in
several variables and basic relations between curve and surface integrals.
Other part contains function series and power series with application to Taylor and
Fourier series.
 Requirements:
 Syllabus of lectures:

1. Basic convergence tests for series.
2. Series of functions, the Weierstrass test. Power series.
3. Standard Taylor expansions. Fourier series.
4. Functions of more variables, limit, continuity.
5. Directional and partial derivatives  gradient.
6. Derivative of a composition of function, higher order derivatives.
7. Jacobiho matrix. Local extrema.
8. Extrema with constraints. Lagrange multipliers.
9. Double and triple integral  Fubini theorem and theorem on substitution.
10. Path integral and its applications.
11. Surface integral and its applications.
12. The Gauss, Green, and Stokes theorems.
13. Potential of vector fields.
 Syllabus of tutorials:

1. Basic convergence tests for series.
2. Series of functions, the Weierstrass test. Power series.
3. Standard Taylor expansions. Fourier series.
4. Functions of more variables, limit, continuity.
5. Directional and partial derivatives  gradient.
6. Derivative of a composition of function, higher order derivatives.
7. Jacobiho matrix. Local extrema.
8. Extrema with constraints. Lagrange multipliers.
9. Double and triple integral  Fubini theorem and theorem on substitution.
10. Path integral and its applications.
11. Surface integral and its applications.
12. The Gauss, Green, and Stokes theorems.
13. Potential of vector fields.
 Study Objective:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and theory of series.
 Study materials:

[1] Stewart J.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0538497815.
[2] L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
[3] S. Lang, Calculus of several variables, Springer Verlag, 1987
 Note:
 Further information:
 https://math.feld.cvut.cz/hajek/teaching.html
 Timetable for winter semester 2019/2020:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri  Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans:

 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering 2016 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (compulsory course in the program)
 Electronics and Communications 2016 (compulsory course in the program)
 Cybernetics and Robotics 2016 (compulsory course in the program)
 Open Informatics  Computer Science 2016 (compulsory course in the program)
 Open Informatics  Internet of Things 2016 (compulsory course in the program)
 Open Informatics  Software 2016 (compulsory course in the program)
 Open Informatics  Computer Games and Graphics 2016 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management (compulsory course in the program)
 Open Informatics (compulsory course in the program)
 Medical electronics and bioinformatics (compulsory course in the program)
 Open Informatics (compulsory course in the program)
 Open Informatics  Artificial Intelligence and Computer Science 2018 (compulsory course in the program)
 Open Informatics  Internet of Things 2018 (compulsory course in the program)
 Open Informatics  Software 2018 (compulsory course in the program)
 Open Informatics  Computer Games and Graphics 2018 (compulsory course in the program)