Mathematics 3
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
01MAT3 | Z,ZK | 4 | 2+2 | Czech |
- Course guarantor:
- David Krejčiřík
- Lecturer:
- Miroslav Kolář, David Krejčiřík, Severin Pošta
- Tutor:
- Miroslav Kolář, David Krejčiřík, Severin Pošta
- Supervisor:
- Department of Mathematics
- Synopsis:
-
The subject summarises the most important notions and theorems related to the study of finite-dimensional vector spaces.
- Requirements:
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Basic high school mathematics.
- Syllabus of lectures:
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1. Vector spaces;
2. Linear span and independence;
3. Basis and dimension;
4. Linear transformations;
5. Operator equations;
6. Scalar product and orthogonality;
7. Linear functionals and adjoint;
8. Matrices;
9. Determinants;
10. Spectrum;
11. Matrix exponential;
12. Quadratic forms.
- Syllabus of tutorials:
-
0. Complex numbers;
1. Examples of vector spaces and subspaces;
2. Linear dependence of vectors - problem with parametres.
3. Selection of basis vectors from a set of generators, completing a basis;
4. Injectivity and kernel of a linear mapping;
5. Examples of scalar products and orthogonalization process;
6. Examples of linear functionals and construction of adjoint mappings;
7. Operations with matrices and construction of the matrix of a linear mapping;
8. Working with determinants, computation of the inverse matrix;
9. Eigenvalues and eigenfunctions of matrices;
10. Construction of matrix exponential;
11. Properties of quadratic forms.
- Study Objective:
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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:
[1] S. Axler: Linear algebra done right, Springer, New York 2014
Recommended references:
[2] J. Kopáček, Matematika pro fyziky II, UK, Praha, 1989.
[3] Lecture notes on the hompeage of the lecturer.
- Note:
- Time-table for winter semester 2024/2025:
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06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri - Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans:
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- Aplikovaná informatika (compulsory course in the program)
- Jaderná chemie (compulsory course in the program)
- Radiologická technika (compulsory course in the program)