Multidimensional Calculus
| Kód | Zakončení | Kredity | Rozsah | Jazyk výuky |
|---|---|---|---|---|
| AE2B01MA3 | Z,ZK | 6 | 2+2s | česky |
- Podmínkou zápisu předmětu je, že student získal v předchozích semestrech zápočet z následujících předmětů:
- Linear Algebra and its Applications (AE0B01LAA)
Introduction to Calculus (AE0B01MA1) - Přednášející:
- Paola Vivi (gar.)
- Cvičící:
- Paola Vivi (gar.)
- Předmět zajišťuje:
- katedra matematiky
- Anotace:
-
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.
- Požadavky:
-
The requirement for receiving the credit is an active participation in the tutorials.
- Osnova přednášek:
-
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.
- Osnova cvičení:
-
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.
- Cíle studia:
-
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.
- Studijní materiály:
-
1. L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
2. S. Lang, Calculus of several variables, Springer Verlag, 1987
- Poznámka:
-
Rozsah výuky v kombinované formě studia: 14p+6s
- Rozvrh na zimní semestr 2011/2012:
- Rozvrh není připraven
- Rozvrh na letní semestr 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
Po Út St Čt Pá - Předmět je součástí následujících studijních plánů:
-
- Communications, Multimedia and Electronics - Communication Technology (povinný předmět programu)
- Communications, Multimedia and Electronics - Multimedia Technology (povinný předmět programu)
- Communications, Multimedia and Electronics - Applied Electronics (povinný předmět programu)
- Communications, Multimedia and Electronics - Network and Information Technology (povinný předmět programu)
- Communications, Multimedia and Electronics (povinný předmět programu)