Multidimensional Analysis
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| A1B01MA2 | Z,ZK | 6 | 2+2s | Czech |
- The course cannot be taken simultaneously with:
- Multidimensional Calculus (A2B01MA3)
- Prerequisite:
- Linear Algebra and its Applications (A0B01LAA)
- Enrollement in the course requires an assessment of the following courses:
- Introduction to Calculus (A0B01MA1)
- Lecturer:
- Josef Tkadlec (gar.), Josef Hekrdla
- Tutor:
- Josef Tkadlec (gar.), Vojtěch Bartík, Josef Hekrdla, Eva Nováková, Karel Pospíšil
- 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 Thu Fri - The course is a part of the following study plans:
-
- Elektrotechnika, energetika a management - Aplikovaná elektrotechnika (compulsory course in the program)
- Elektrotechnika, energetika a management - Elektrotechnika a management (compulsory course in the program)
- Elektrotechnika, energetika a management - před rozřazením do oborů (compulsory course in the program)