Multidimensional Analysis

Prerekvizita:

Linear Algebra and its Applications (AE0B01LAA)
Introduction to Calculus (AE0B01MA1)

Přednášející:

Paola Vivi

Cvičící:

Paola Vivi

Předmět zajišťuje:

katedra matematiky

Anotace:

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.

Požadavky:

Požadavky viz http://math.feld.cvut.cz/0educ/pozad/a1b01ma2.htm

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.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.

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.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.

Cíle studia:

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	místnost T2:C4-363 Vivi P. 09:15–10:45 (přednášková par. 1) Dejvice Cvicebnamístnost T2:C3-51 Vivi P. 11:00–12:30 (přednášková par. 1 paralelka 101) Dejvice Posluchárna
Pá

Předmět je součástí následujících studijních plánů:

• Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering (povinný předmět programu)
• Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (povinný předmět programu)
• Electrical Engineering, Power Engineering and Management (povinný předmět programu)