Mathematics 5A

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Vector space, basis, dimension, examples. Matrices, matrix algebra. Eigenvalues and eigenvectors. Similar matrices, diagonalizable matrices. Systems of linear diferential equations. Using eigenvectors to solve systems of linear differential equations. Systems with diagonalizable matrices. Generalized eigenvectors. Generalized eigenvectors and systems of linear differential equations. Series, Laurent series, Z-transforms. Inverse Z-transforms. Z-transforms and difference equations. Minimal polynomial of a matrix, functions of matrices. Applications to systems of linear differential equations.

Requirements:

Syllabus of lectures:

1. Vector space, basis, dimension, examples

2. Matrices, matrix algebra

3. Eigenvalues and eigenvectors

4. Similar matrices, diagonalizable matrices

5. Systems of linear diferential equations

6. Using eigenvectors to solve systems of linear differential equations

7. Systems with diagonalizable matrices

8. Generalized eigenvectors

9. Generalized eigenvectors and systems of linear differential equations

10. Series, Laurent series, Z-transforms

11. Inverse Z-transforms

12. Z-transforms and difference equations

13. Minimal polynomial of a matrix, functions of matrices

14. Applications to systems of linear differential equations

Syllabus of tutorials:

1. Vector space, basis, dimension, examples

2. Matrices, matrix algebra

3. Eigenvalues and eigenvectors

4. Similar matrices, diagonalizable matrices

5. Systems of linear diferential equations

6. Using eigenvectors to solve systems of linear differential equations

7. Systems with diagonalizable matrices

8. Generalized eigenvectors

9. Generalized eigenvectors and systems of linear differential equations

10. Series, Laurent series, Z-transforms

11. Inverse Z-transforms

12. Z-transforms and difference equations

13. Minimal polynomial of a matrix, functions of matrices

14. Applications to systems of linear differential equations

Study Objective:

Study materials:

[1] C. D. Meyer: Matrix Analysis and Applied Linear Algebra. SIAM, 2000.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Silnoproudá elektrotechnika-bakalářský blok (compulsory course)
• Silnoproudá elektrotechnika-bakalářský blok (compulsory course)