Mathematics 2
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| A3B01MA2 | Z,ZK | 7 | 4+2s | Czech |
- Enrollement in the course requires an successful completion of the following courses:
- Mathematics 1 (A3B01MA1)
- Lecturer:
- Jaroslav Tišer (gar.)
- Tutor:
- Jaroslav Tišer (gar.), Vojtěch Bartík, Tomáš Bílek, Miroslav Dont, Ladislav Průcha, Dušan Valášek
- 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. Basic convergence tests for series.
2. Series of functions, the Weierstrass test. Power series.
3. Standard Taylor expansions. Fourier series.
4. Functions of more variables, limit, continuity.
5. Directional and partial derivatives - gradient.
6. Derivative of a composition of function, higher order derivatives.
7. Jacobiho matrix. Local extrema.
8. Extrema with constraints. Lagrange multipliers.
9. Double and triple integral - Fubini theorem and theorem on substitution.
10. Path integral and its applications.
11. Surface integral and its applications.
12. The Gauss, Green, and Stokes theorems.
13. Potential of vector fields.
- Syllabus of tutorials:
-
1. Basic convergence tests for series.
2. Series of functions, the Weierstrass test. Power series.
3. Standard Taylor expansions. Fourier series.
4. Functions of more variables, limit, continuity.
5. Directional and partial derivatives - gradient.
6. Derivative of a composition of function, higher order derivatives.
7. Jacobiho matrix. Local extrema.
8. Extrema with constraints. Lagrange multipliers.
9. Double and triple integral - Fubini theorem and theorem on substitution.
10. Path integral and its applications.
11. Surface integral and its applications.
12. The Gauss, Green, and Stokes theorems.
13. Potential of vector fields.
- 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:
-
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:
-
- Kybernetika a robotika - Robotika (compulsory course in the program)
- Kybernetika a robotika - Senzory a přístrojová technika (compulsory course in the program)
- Kybernetika a robotika - Systémy a řízení (compulsory course in the program)
- Kybernetika a robotika - před rozřazením do oborů (compulsory course in the program)