Multidimensional Calculus
Code  Completion  Credits  Range  Language 

AE2B01MA3  Z,ZK  6  2+2 
 Enrollement in the course requires an assessment of the following courses:
 Linear Algebra and its Applications (AE0B01LAA)
Introduction to Calculus (AE0B01MA1)  Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

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.
 Requirements:
 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:

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/
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Cybernetics and Robotics  Robotics (elective course)
 Cybernetics and Robotics  Senzors and Instrumention (elective course)
 Cybernetics and Robotics  Systems and Control (elective course)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering (elective course)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (elective course)
 Communications, Multimedia and Electronics  Communication Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Multimedia Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Applied Electronics (compulsory course in the program)
 Communications, Multimedia and Electronics  Network and Information Technology (compulsory course in the program)
 Open Informatics  Computer Systems (elective course)
 Open Informatics  Computer and Information Science (elective course)
 Open Informatics  Software Systems (elective course)
 Electrical Engineering, Power Engineering and Management (elective course)
 Communications, Multimedia and Electronics (compulsory course in the program)
 Cybernetics and Robotics (elective course)
 Open Informatics (elective course)
 Communications, Multimedia and Electronics  Communications and Electronics (compulsory course in the program)