Multidimensional Calculus
Code  Completion  Credits  Range 

QBMAM  Z,ZK  6  2+2 
 Lecturer:
 Tutor:
 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. Other part contains function series and power series with application to Taylor and Fourier series.
 Requirements:

The requirement for receiving the credit is an active participation in the tutorials.
 Syllabus of lectures:

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.Double and triple integral  Fubini theorem and theorem on substitution.
6.Path integral and its applications.
7.Surface integral and its applications.
8.The Gauss, Green, and Stokes theorem. Potential of a vector field.
9.Basic convergence tests for series of numbers.
10.Series of functions, the Weirstrasse test.
11.Power series, radius of convergence.
12.Standard expansions of elementary functions. Taylor series.
13.Fourier series.
 Syllabus of tutorials:

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.Double and triple integral  Fubini theorem and theorem on substitution.
6.Path integral and its applications.
7.Surface integral and its applications.
8.The Gauss, Green, and Stokes theorem. Potential of a vector field.
9.Basic convergence tests for series of numbers.
10.Series of functions, the Weirstrasse test.
11.Power series, radius of convergence.
12.Standard expansions of elementary functions. Taylor series.
13.Fourier series.
 Study Objective:
 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/tkadlec/ma3.htm
 No timetable has been prepared for this course
 The course is a part of the following study plans: