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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Multidimensional Calculus

The course is not on the list Without time-table
Code Completion Credits Range Language
AE2B01MA3 Z,ZK 6 2+2
Enrollement in the course requires an assessment of the following courses:
Linear Algebra and its Applications (AE0B01LAA)
Introduction to Calculus (AE0B01MA1)
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The course covers an introduction to differential and integral calculus in several variables and basic relations between curve and surface integrals. We also introduce function series and power series with application to Taylor and Fourier series.

Requirements:
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.

11.Power series, radius of convergence.

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.

11.Power series, radius of convergence.

12.Standard expansions of elementary functions. Taylor series.

13.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. L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973

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

Note:
Further information:
http://math.feld.cvut.cz/vivi/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-09-18
For updated information see http://bilakniha.cvut.cz/en/predmet12804404.html