# Subject description - AE3B01MA2

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 AE3B01MA2 Mathematics 2 Extent of teaching: 4+2 Guarantors: Roles: P,V Language ofteaching: EN Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 7 Semester: L

Anotation:

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.

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 Basic convergence tests for series. 2 Series of functions, the Weierstrass test. Power series. 3 Standard Taylor expansions. Fourier series. 4 Functions of more variables, limit, continuity. 5 Directional and partial derivatives - gradient. 6 Derivative of a composition of function, higher order derivatives. 7 Jacobiho matrix. Local extrema. 8 Extrema with constraints. Lagrange multipliers. 9 Double and triple integral - Fubini theorem and theorem on substitution. 10 Path integral and its applications. 11 Surface integral and its applications. 12 The Gauss, Green, and Stokes theorems. 13 Potential of vector fields.

Exercises outline:

 1 Basic convergence tests for series. 2 Series of functions, the Weierstrass test. Power series. 3 Standard Taylor expansions. Fourier series. 4 Functions of more variables, limit, continuity. 5 Directional and partial derivatives - gradient. 6 Derivative of a composition of function, higher order derivatives. 7 Jacobiho matrix. Local extrema. 8 Extrema with constraints. Lagrange multipliers. 9 Double and triple integral - Fubini theorem and theorem on substitution. 10 Path integral and its applications. 11 Surface integral and its applications. 12 The Gauss, Green, and Stokes theorems. 13 Potential of vector fields.

Literature:

 1 J. Stewart.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p. 2 L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973 3 S. Lang, Calculus of several variables, Springer Verlag, 1987

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Webpage:

http://math.feld.cvut.cz/vivi/

Subject is included into these academic programs:

 Program Branch Role Recommended semester BEKME1 Communication Technology V 2 BEKME5 Komunikace a elektronika V 2 BEKME_BO Common courses V 2 BEKME4 Network and Information Technology V 2 BEKME3 Applied Electronics V 2 BEKME2 Multimedia Technology V 2 BEKYR1 Robotics P 2 BEKYR_BO Common courses P 2 BEKYR3 Systems and Control P 2 BEKYR2 Sensors and Instrumentation P 2 BEEEM1 Applied Electrical Engineering V 2 BEEEM_BO Common courses V 2 BEEEM2 Electrical Engineering and Management V 2 BEOI1 Computer Systems V 2 BEOI_BO Common courses V 2 BEOI3 Software Systems V 2 BEOI2 Computer and Information Science V 2

 Page updated 24.6.2019 17:52:59, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)