 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Multidimensional Calculus

The course is not on the list Without time-table
Code Completion Credits Range
QB-MAM Z,ZK 6 2+2
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:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1.Functions of more variables: Limit, continuity.

2.Directional and partial derivative - gradient.

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

4.Jacobi matrix. Local extrema.

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

6.Path integral and its applications.

7.Surface integral and its applications.

8.The Gauss, Green, and Stokes theorem. Potential of a vector field.

9.Basic convergence tests for series of numbers.

10.Series of functions, the Weirstrasse test.

12.Standard expansions of elementary functions. Taylor series.

13.Fourier series.

Syllabus of tutorials:

1.Functions of more variables: Limit, continuity.

2.Directional and partial derivative - gradient.

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

4.Jacobi matrix. Local extrema.

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

6.Path integral and its applications.

7.Surface integral and its applications.

8.The Gauss, Green, and Stokes theorem. Potential of a vector field.

9.Basic convergence tests for series of numbers.

10.Series of functions, the Weirstrasse test.

12.Standard expansions of elementary functions. Taylor series.

13.Fourier series.

Study Objective:
Study materials:

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

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

Note:
Further information: