Multidimensional Calculus

Prerequisite:

Linear Algebra and its Applications (AD0B01LAA)
Introduction to Calculus (AD0B01MA1)

Lecturer:

Tomáš Bílek

Tutor:

Tomáš Bílek

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:

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

http://math.feld.cvut.cz/vivi/AE2B01MA3.pdf

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:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Komunikace, multimedia a elektronika - Komunikační technika_163439 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Multimediální technika_163458 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Aplikovaná elektronika_163524 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Síťové a informační technologie_163540 (compulsory course in the program)
• Komunikace, multimedia a elektronika, před rozřazením do oborů (compulsory course in the program)
• Komunikace, multimédia a elektronika (compulsory course in the program)