Mathematics 3

Lecturer:

Emil Humhal (gar.)

Tutor:

Emil Humhal (gar.)

Supervisor:

Department of Mathematics

Synopsis:

The subject summarizes the most important notions and theorems related to the study of vector spaces.

Requirements:

Basic high school mathematics

Syllabus of lectures:

1. A vector space, 2. linear dependence and independence, 3. basis and dimension, 4. subspaces of a vector space, 5. linear transformations, 6. matrices, 7. matrices of linear transformations, 8. systems of linear equations, 9. determinants, 10. orthogonality, 11. eigenvalues and eigenvectors, 12. quadratic form.

Syllabus of tutorials:

1. Examples of vector spaces.

2. Investigation of linear dependence/independence - problem with parametres.

3. Selection of basis vectors from a set of generators, completing a basis.

4. Intersection and sum of subspaces - their basis and dimension.

5. Assembling matrices of linear mappings.

6. Systems of linear algebraic equations including systems with parametres.

7. Gauss method of evaluation of inverse matrix.

8. Different methods of determinant calculation.

9. Examples scalar products, Gram-Schmidt orthogonalization.

10. Evaluation of eigen values and eigen vectors, diagonalizability.

Study Objective:

Knowledge: Learning basic concepts of linear algebra necessary for a proper understanding of related subjects, such as analysis of functions of several variables, numerical mathematics, and so on. Skills: Applications of theoretical concepts and theorems in continuing subjects.

Study materials:

Key references:

[4] C. W. Curtis: Linear Algebra, An Introductory Approach. Springer-Verlag 1984

Recommended references:

[5] Faddeev D. K., Faddeeva V. N.: Computional Methods of Linear Algebra. Freeman, San Francisko, London 1963

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: