Mathematics 2
Code  Completion  Credits  Range  Language 

AE3B01MA2  Z,ZK  7  4+2 
 Enrollement in the course requires an assessment of the following courses:
 Mathematics 1 (AE3B01MA1)
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

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.
 Requirements:
 Syllabus of lectures:

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.
 Syllabus of tutorials:

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.
 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. 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
 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 (compulsory course in the program)
 Cybernetics and Robotics  Senzors and Instrumention (compulsory course in the program)
 Cybernetics and Robotics  Systems and Control (compulsory course in the program)
 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 (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 (elective course)
 Communications, Multimedia and Electronics (elective course)
 Cybernetics and Robotics (compulsory course in the program)
 Open Informatics (elective course)
 Communications, Multimedia and Electronics  Communications and Electronics (elective course)