Calculus 2
Login to access the course.Calculus 2 (Main course) BE5B01MA2
Credits | 7 |
Semesters | Summer |
Completion | Assessment + Examination |
Language of teaching | English |
Extent of teaching | 4P+2S |
Annotation
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.
Study targets
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.
Course outlines
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.
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.
Exercises outlines
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.
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.
Literature
1. L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
2. S. Lang, Calculus of several variables, Springer Verlag, 1987
http://math.feld.cvut.cz/vivi/
2. S. Lang, Calculus of several variables, Springer Verlag, 1987
http://math.feld.cvut.cz/vivi/
Requirements
http://math.feld.cvut.cz/vivi/BE5B01MA2.pdf