Mathematics 3B

The course is a substitute for:

Mathematics 3B (X01M3B)

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Introduction to multivariable calculus. Functions of two and more variables - continuity, differentiation, gradient. Higher order derivatives and differentials, Taylor polynomial for multivariable functions, implicit functions. Maxima and minima of multivariable functions. Integration in plane and space, substitutions in integrals. Introduction to complex variables: holomorphic functions, line integral and Caychy's integral formula, power series expansions. Laurent series and residue theorem.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials. The final grading reflects the performance in both the written and oral part of the examination the student sits for at the end of the course.

Syllabus of lectures:

1. Functions of two and more variables, limit and continuity.

2. Partial and directional derivatives. Differential ind its applications.

3. Chain rule. Implicit functions.

4. Higher order derivatives. Local extrema.

5. Definite integral over plane and space regions. Fubini's theorem.

6. Computing integrals by substitution.

7. Complex numbers and functions.

8. Holomorphic functions, Cauchy-Riemann equations.

9. Elementary and multivalued holomorphic functions.

10. Path integral. Cauchy's integral formula.

11. Power expansions of holomorphic functions.

12. Laurent series.

13. Classification of singularities.

14. Residue theorem.

Syllabus of tutorials:

1. Functions of two and more variables, limit and continuity.

2. Partial and directional derivatives. Differential ind its applications.

3. Chain rule. Implicit functions.

4. Higher order derivatives. Local extrema.

5. Definite integral over plane and space regions. Fubini's theorem.

6. Computing integrals by substitution.

7. Complex numbers and functions.

8. Holomorphic functions, Cauchy-Riemann equations.

9. Elementary and multivalued holomorphic functions.

10. Path integral. Cauchy's integral formula.

11. Power expansions of holomorphic functions.

12. Laurent series.

13. Classification of singularities.

14. Residue theorem.

Study Objective:

Study materials:

1. P. Pták: Calculus II. ČVUT Praha, 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Electronics and Communication Technology - structured studies (compulsory elective course)