Multidimensional Analysis
Code  Completion  Credits  Range  Language 

AE1B01MA2  Z,ZK  6  2+2 
 Prerequisite:
 Linear Algebra and its Applications (AE0B01LAA)
Introduction to Calculus (AE0B01MA1)  Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and to basics of series of numbers and functions.
 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.Extrema with constraints, Lagrange multipliers.
6.Double and triple integral  Fubini theorem and theorem on substitution.
7.Path integral and its applications.
8.Surface integral and its applications.
9.The Gauss, Green, and Stokes theorem. Potential of a vector field.
10.Basic convergence tests for series of numbers.
11.Series of functions, the Weirstrasse test.
12.Power series, radius of convergence. 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.Extrema with constraints, Lagrange multipliers.
6.Double and triple integral  Fubini theorem and theorem on substitution.
7.Path integral and its applications.
8.Surface integral and its applications.
9.The Gauss, Green, and Stokes theorem. Potential of a vector field.
10.Basic convergence tests for series of numbers.
11.Series of functions, the Weirstrasse test.
12.Power series, radius of convergence. 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/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 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (compulsory course in the program)
 Communications, Multimedia and Electronics  Communication Technology (elective course)
 Communications, Multimedia and Electronics  Multimedia Technology (elective course)
 Communications, Multimedia and Electronics  Applied Electronics (elective course)
 Communications, Multimedia and Electronics  Network and Information Technology (elective course)
 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 (compulsory course in the program)
 Communications, Multimedia and Electronics (elective course)
 Cybernetics and Robotics (elective course)
 Open Informatics (elective course)
 Communications, Multimedia and Electronics  Communications and Electronics (elective course)