# Subject description - AD3B01MA2

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 AD3B01MA2 Mathematics 2 Extent of teaching: 28+6 Guarantors: Roles: P,V Language ofteaching: CS 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:

Webpage:

Subject is included into these academic programs:

 Program Branch Role Recommended semester BKOI1 Computer Systems V 2 BKOI_BO Common courses V 2 BKOI3 Software Systems V 2 BKOI2 Computer and Information Science V 2 BKEEM1 Applied Electrical Engineering V 2 BKEEM_BO Common courses V 2 BKEEM2 Electrical Engineering and Management V 2 BKKYR1 Robotics P 2 BKKYR_BO Common courses P 2 BKKYR3 Systems and Control P 2 BKKYR2 Sensors and Instrumentation P 2 BKKME1 Communication Technology V 2 BKKME_BO Common courses V 2 BKKME4 Network and Information Technology V 2 BKKME3 Applied Electronics V 2 BKKME2 Multimedia Technology V 2 BIS(ECTS)-D Intelligent Systems V 2 BKSTMWM Web and Multimedia V 2 BKSTMSI Software Engineering V 2 BKSTMMI Manager Informatics V 2 BKSTMIS Intelligent Systems V 2 BKSTM_BO Common courses V 2 BSI(ECTS)-D Software Engineering V 2 BWM(ECTS)-D Web and Multimedia V 2 BMI(ECTS)-D Manager Informatics V 2

 Page updated 26.6.2019 17:52:50, 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)