Mathematics 4

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Functions of a complex variable. Holomorphic functions, Cauchy integral formula. Elementary probability. Conditional probability. Bayes formula. Random variables. Distribution function. Transformations of random variables. Mean and variance. Tschebyschev inequality. Binomial, Poisson, normal and exponential distributions. Random vectors, joint distribution function. Independent random variables. Functions of random vectors. Conditional probability. Systems of differential equations. Systems with constant coefficients. Structure of systems solutions.

Requirements:

Syllabus of lectures:

1. Functions of complex variable

2. Holomorphic functions. Cauchy integral formula

3. Elementary probability

4. Conditional probability. Bayes formula

5. Random variables. Distribution function

6. Transformations of random variables

7. Mean and variance. Tschebyschev inequality

8. Binomial, Poisson, normal and exponential distributions

9. Random vectors, joint distribution function

10. Independent random variables

11. Functions of random vectors. Conditional probability

12. Systems of differential equations

13. Systems with constant coefficients

14. Structure of systems solutions

Syllabus of tutorials:

1. Functions of complex variable

2. Holomorphic functions. Cauchy integral formula

3. Elementary probability

4. Conditional probability. Bayes formula

5. Random variables. Distribution function

6. Transformations of random variables

7. Mean and variance. Tschebyschev inequality

8. Binomial, Poisson, normal and exponential distributions

9. Random vectors, joint distribution function

10. Independent random variables

11. Functions of random vectors. Conditional probability

12. Systems of differential equations

13. Systems with constant coefficients

14. Structure of systems solutions

Study Objective:

Study materials:

[1] Pták, P.: Calculus II. Skripta 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: