Popis předmětu - BE5B01MA2
BE5B01MA2 | Calculus 2 | ||
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Role: | P | Rozsah výuky: | 4P+2S |
Katedra: | 13101 | Jazyk výuky: | EN |
Garanti: | Habala P. | Zakončení: | Z,ZK |
Přednášející: | Vivi P. | Kreditů: | 7 |
Cvičící: | Vivi P. | Semestr: | L |
Webová stránka:
https://math.fel.cvut.cz/en/people/vivipaol/BE5B01MA2.htmlAnotace:
The subject covers an introduction to the differential and integral calculus in several variables and basic relations between curve and surface integrals. Fourier series are also introduced.Výsledek studentské ankety předmětu je zde: AE3B01MA2
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.Osnovy přednášek:
1. | Real plane, three dimensional analytic geometry, vector functions. | |
2. | Functions of several variables: limits, continuity. | |
3. | Directional and partial derivative, tangent plane, gradient. | |
4. | Derivative of a composition of functions, higher order derivatives. | |
5. | Local extrema, Lagrange multipliers. | |
6. | Double integral, Fubini's Theorem. Polar coordinates. | |
7. | Triple integrals. Cylindrical and spherical coordinates. Change of variables in multiple integrals. | |
8. | Space curves. Line integrals. | |
9. | Potential of a vector field. Fundamental Theorem for line integrals. Green's Theorem. | |
10. | Parametric surfaces and their area. Surface integrals. | |
11. | Curl and divergence. Gauss, and Stokes theorem and their applications. | |
12. | Fourier series. | |
13. | Sine and cosine Fourier series. |
Osnovy cvičení:
1. | Real plane, three dimensional analytic geometry, vector functions. | |
2. | Functions of several variables: limits, continuity. | |
3. | Directional and partial derivative, tangent plane, gradient. | |
4. | Derivative of a composition of functions, higher order derivatives. | |
5. | Local extrema, Lagrange multipliers. | |
6. | Double integral, Fubini's Theorem. Polar coordinates. | |
7. | Triple integrals. Cylindrical and spherical coordinates. Change of variables in multiple integrals. | |
8. | Space curves. Line integrals. | |
9. | Potential of a vector field. Fundamental Theorem for line integrals. Green's Theorem. | |
10. | Parametric surfaces and their area. Surface integrals. | |
11. | Curl and divergence. Gauss, and Stokes theorem and their applications. | |
12. | Fourier series. | |
13. | Sine and cosine Fourier series. |
Literatura:
1. | L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973 | |
2. | S. Lang, Calculus of several variables, Springer Verlag, 1987 |
Požadavky:
https://math.fel.cvut.cz/en/people/vivipaol/BE5B01MA2%20-%20Calculus%202.pdfPoznámka:
Rozsah výuky v kombinované formě studia: 28p+6s |
Předmět je zahrnut do těchto studijních plánů:
Plán | Obor | Role | Dop. semestr |
BPEECS_2018 | Před zařazením do oboru | P | 2 |
BEECS | Před zařazením do oboru | P | 2 |
Stránka vytvořena 22.3.2025 17:50:39, semestry: Z/2024-5, Z/2025-6, L/2024-5, L/2025-6, připomínky k informační náplni zasílejte správci studijních plánů | Návrh a realizace: I. Halaška (K336), J. Novák (K336) |