Mathematical Analysis 2
Code  Completion  Credits  Range  Language 

B0B01MA2A  Z,ZK  6  4+2  Czech 
 Lecturer:
 Petr Hájek (guarantor)
 Tutor:
 Petr Hájek (guarantor), Jaroslav Tišer (guarantor), Josef Hekrdla, Natalie Žukovec
 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. J. Stewart.: 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 2018/2019:
 Timetable is not available yet
 Timetable for summer semester 2018/2019:

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  The course is a part of the following study plans:

 Electronics and Communications 2018 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering 2018 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (compulsory course in the program)