CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics 2

The course is not on the list Without time-table
Code Completion Credits Range Language
A3B01MA2 Z,ZK 7 4+2 Czech
The course cannot be taken simultaneously with:
Multidimensional Analysis (A1B01MA2)
Multidimensional Calculus (A2B01MA3)
Enrollement in the course requires an assessment of the following courses:
Lecturer:
Tutor:
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.

2. L. Gillman, R. H. McDowell, Calculus, W.W.Norton &amp; Co.,New York, 1973

3. S. Lang, Calculus of several variables, Springer Verlag, 1987

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2020-01-25
For updated information see http://bilakniha.cvut.cz/en/predmet12561804.html