Mathematics-Calculus m-D

Vztahy:

It is not possible to register for the course A8B01MCM if the student is concurrently registered for or has already completed the course A3B01MA2 (mutually exclusive courses).

Garant předmětu:

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:

https://moodle.fel.cvut.cz/course/view.php?id=6317

Syllabus of lectures:

1. Functions of more variables, limit, continuity.

2. Directional and partial derivatives - gradient.

3. Derivative of a composition of function, higher order derivatives.

4. Jacobiho matrix. Local extrema.

5. Extrema with constraints. Lagrange multipliers.

6. Double and triple integral - Fubini theorem and theorem on substitution.

7. Path integral and its applications.

8. Surface integral and its applications.

9. The Gauss, Green, and Stokes theorems.

10. Potential of vector fields.

11. Basic convergence tests for series.

12. Series of functions, the Weierstrass test. Power series.

13. Standard Taylor expansions. Fourier series.

Syllabus of tutorials:

1. Functions of more variables, limit, continuity.

2. Directional and partial derivatives - gradient.

3. Derivative of a composition of function, higher order derivatives.

4. Jacobiho matrix. Local extrema.

5. Extrema with constraints. Lagrange multipliers.

6. Double and triple integral - Fubini theorem and theorem on substitution.

7. Path integral and its applications.

8. Surface integral and its applications.

9. The Gauss, Green, and Stokes theorems.

10. Potential of vector fields.

11. Basic convergence tests for series.

12. Series of functions, the Weierstrass test. Power series.

13. Standard Taylor expansions. Fourier series.

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 0-538-49781-5.

[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://moodle.fel.cvut.cz/course/view.php?id=6317

No time-table has been prepared for this course

The course is a part of the following study plans:

• Open Electronic Systems (compulsory course in the program)
• Open Electronic Systems (compulsory course in the program)