Mathematics for electronics

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The subject is devoted mainly to integral transforms like Laplace and Fourier transform. These transforms are applied to the solution of some boundary value problems for partial differential equations. The notion of partial differential equation is introduced briefly as well as physical interpretation of boundary value problems. Methods of complex variable are used in connection with inverse transforms. The Z-transform is used to solve some difference equations.

Requirements:

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

Syllabus of lectures:

1. Laplace transform, transform of impulses and periodic functions.

2. Inverse Laplace transform, Bromwich integral.

3. Inverse Laplace transforms and residua.

4. The notion of partial differential equation, some concrete equations.

5. Basic boundary value problems for PDE, physical interpretation.

6. Fourier method for boundary value problems.

7. Partial differential equations and Laplace transform.

8. The Fourier integral and Fourier transform.

9. Basic properties of the Fourier transform.

10. Further properties of the Fourier transform.

11. Partial differential equations and Fourier transform.

12. Z-transform, definition and basic properties.

13. Inverse Z-transform.

14. Difference equations and Z-transform.

Syllabus of tutorials:

1. Laplace transform, transform of impulses and periodic functions.

2. Inverse Laplace transform, Bromwich integral.

3. Inverse Laplace transforms and residua.

4. The notion of partial differential equation, some concrete equations.

5. Basic boundary value problems for PDE, physical interpretation.

6. Fourier method for boundary value problems.

7. Partial differential equations and Laplace transform.

8. The Fourier integral and Fourier transform.

9. Basic properties of the Fourier transform.

10. Further properties of the Fourier transform.

11. Partial differential equations and Fourier transform.

12. Z-transform, definition and basic properties.

13. Inverse Z-transform.

14. Difference equations and Z-transform.

Study Objective:

Study materials:

1. P. DuChateau, D. W. Zachmann: Partial Diffrential Equations (Schaum's Outline Series)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Electronics - Electronic Systems- structured studies (compulsory course)
• Electronics - Electronic Applications- structured studies (compulsory course)
• Electronics - Electronics and Photonics- structured studies (compulsory course)