Calculus 2
Code  Completion  Credits  Range  Language 

BE5B01MA2  Z,ZK  7  4+2 
 Lecturer:
 Paola Vivi
 Tutor:
 Paola Vivi
 Supervisor:
 Department of Mathematics
 Synopsis:

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.
 Requirements:
 Syllabus of lectures:

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.
 Syllabus of tutorials:

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.
 Study Objective:

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.
 Study materials:

1. L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
2. S. Lang, Calculus of several variables, Springer Verlag, 1987
 Note:
 Further information:
 http://math.feld.cvut.cz/vivi/
 Timetable for winter semester 2016/2017:
 Timetable is not available yet
 Timetable for summer semester 2016/2017:

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
Mon Tue Fri Thu Fri  The course is a part of the following study plans:

 Electrical Engineering and Computer Science (EECS) (compulsory course in the program)