Description:

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.

Contents:

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.

Seminar contents:

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.

Recommended 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/

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar