Multidimensional Analysis

Lecturer:

Tomáš Bílek, Josef Hekrdla

Tutor:

Tomáš Bílek, Josef Hekrdla

Supervisor:

Department of Mathematics

Synopsis:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and to basics of series of numbers and functions.

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.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 theorem. Potential of a vector field.

10.Basic convergence tests for series of numbers.

11.Series of functions, the Weirstrasse test.

12.Power series, radius of convergence. 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.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 theorem. Potential of a vector field.

10.Basic convergence tests for series of numbers.

11.Series of functions, the Weirstrasse test.

12.Power series, radius of convergence. Taylor series.

13.Fourier series.

Study Objective:

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:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri	roomJ5:347a Bílek T. 14:30–16:00 ODD WEEK (lecture parallel1) Dejvice Cvicebna
Thu
Fri

The course is a part of the following study plans:

• Elektrotechnika, energetika a management - Aplikovaná elektrotechnika_162957 (compulsory course in the program)
• Elektrotechnika, energetika a management - Elektrotechnika a management_163134 (compulsory course in the program)
• Elektrotechnika, energetika a management, před rozřazením do oborů (compulsory course in the program)