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 AD2B01MA3 Multidimensional Calculus Extent of teaching: 14+6 Guarantors: Roles: P,V Language ofteaching: CS Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 6 Semester: L

Anotation:

The course covers an introduction to differential and integral calculus in several variables and basic relations between curve and surface integrals. We also introduce function series and power series with application to Taylor and Fourier series.

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 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.

Exercises outline:

 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.

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

Requirements: