Mathematics 6A

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Heat equation as an example of a boundary value problem. Variational from of boundary value problems, Ritz and Galerkin approximation. One-dimensional finite elements method. Basic partial differential equations. Boundary value problems and their physical interpretation. One-dimensional wave equation, d'Alembert method. Variation methods for elliptic problms, minimum of energy functional. Ritz and Galerkin method, finite elements method. Constructing finite elements. Random variables, elementary statistics. Simle tests on parameters. Empirical distribution function, histogram. Testing hypotheses.

Requirements:

Syllabus of lectures:

1. Heat equation as an example of a boundary value problem

2. Variational from of boundary value problems, Ritz and Galerkin approximation

3. One-dimensional finite elements method

4. Basic partial differential equations

5. Boundary value problems and their physical interpretation

6. One-dimensional wave equation, d'Alembert method

7. Variation methods for elliptic problms, minimum of energy functional

8. Ritz and Galerkin method, finite elements method

9. Constructing finite elements

10. Random variables, elementary statistics

11. Simle tests on parameters

12. Empirical distribution function, histogram

13. Testing hypotheses

Syllabus of tutorials:

1. Heat equation as an example of a boundary value problem

2. Variational from of boundary value problems, Ritz and Galerkin approximation

3. One-dimensional finite elements method

4. Basic partial differential equations

5. Boundary value problems and their physical interpretation

6. One-dimensional wabe equation, d'Alembert method

7. Variation methods for elliptic problems, minimum of energy functional

8. Ritz and Galerkin method, finite elements method

9. Constructing finite elements

10. Random variables, elementary statistics

11. Simle tests on parameters

12. Empirical distribution function, histogram

13. Testing hypotheses

Study Objective:

Study materials:

[1] M. K. Ochi: Applied Probability & Stochastic Processes in Engineering. Wiley 1989.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Technologické systémy -inženýrský blok (compulsory course)
• Elektrické stroje, přístroje a pohony-inženýrský blok (compulsory course)
• Elektroenergetika-inženýrský blok (compulsory course)
• Elektrické stroje, přístroje a pohony-inženýrský blok (compulsory course)
• Elektroenergetika-inženýrský blok (compulsory course)
• Technologické systémy -inženýrský blok (compulsory course)