Mathematics 4C

Prerequisite:

Mathematics 2 (X01MA2)

Grading of the course requires grading of the following courses:

Introduction to Algebra (X01ALG)
Mathematics 1 (X01MA1)

Lecturer:

Miroslav Dont

Tutor:

Miroslav Dont

Supervisor:

Department of Mathematics

Synopsis:

The course covers a necessary background from linear algebra and complex functions required for the study of cybernetics. In the first part linear maps in vector spaces and their description in terms of matrices are studied, then eigenvalues and eigenvectors, similar matrices, diagonalizability and Jordan canonical form of a matrix, including applications to systems of linear differential equations and matrix functions. The second part contains introduction to complex functions, holomorphic functions, Cauchy integral formula, Laurent series and residue theorem.

Requirements:

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

Syllabus of lectures:

1. Linear mappings and their properties.

2. Matrix of a linear mapping.

3. Eigenvalues and eigenvectors.

4. Similar matrices, diagonalizability.

5. Generalized eigenvectors.

6. Jordan canonical form of a matrix.

7. Applications.

8. Complex functions.

9. Holomorphic functions.

10. Complex integral.

11. Cauchy integral formula.

12. Laurent series.

13. Classification of singular points.

14. Residue theorem.

Syllabus of tutorials:

1. Linear mappings and their properties.

2. Matrix of a linear mapping.

3. Eigenvalues and eigenvectors.

4. Similar matrices, diagonalizability.

5. Generalized eigenvectors.

6. Jordan canonical form of a matrix.

7. Applications.

8. Complex functions.

9. Holomorphic functions.

10. Complex integral.

11. Cauchy integral formula.

12. Laurent series.

13. Classification of singular points.

14. Residue theorem.

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:

• Cybernetics and Measurements- structured studies (compulsory elective course)