Multidimensional Calculus

Lecturer:

Josef Tkadlec (gar.)

Tutor:

Josef Tkadlec (gar.)

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.

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:

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	roomT2:D3-209 Tkadlec J. 14:30–16:00 (lecture parallel1) Dejvice Posluchárna
Tue
Fri
Thu	roomT2:A4-203a Tkadlec J. 14:30–16:00 (lecture parallel1 parallel nr.101) Dejvice Učebna
Fri

The course is a part of the following study plans: