Mathematics 3C

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, derivatives for composite functions. Maxima and minima of multivariable functions. Integration plane and space, substitutions in integrals. Probability and statistics - random phenomena and variables, density and distribution functions, expectation and variance. Correlation and independance of random variables.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Functions of two and more variables.

2. Partial and directional derivatives, Gradient.

3. Differential, higher order derivatives.

4. Derivatives for composite functions. Local extrema.

5. Integration over plane and space regions.

6. Computing integrals by substitutions.

7. Random phenomena, probability.

8. Conditional probability, Bayes formula.

9. Random variables.

10. Density and distribution functions.

11. Expected value and variance.

12. Basic types of random variables and their distributions.

13. Random vectors, joint probability functions.

14. Correlation, independence of random variables.

Syllabus of tutorials:

1. Functions of two and more variables.

2. Partial and directional derivatives, Gradient.

3. Differential, higher order derivatives.

4. Derivatives for composite functions. Local extrema.

5. Integration over plane and space regions.

6. Computing integrals by substitutions.

7. Random phenomena, probability.

8. Conditional probability, Bayes formula.

9. Random variables.

10. Density and distribution functions.

11. Expected value and variance.

12. Basic types of random variables and their distributions.

13. Random vectors, joint probability functions.

14. Correlation, independence of random variables.

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:

• Cybernetics and Measurements- structured studies (compulsory course)