Linear Algebra and its Applications
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| AE0B01LAA | Z,ZK | 8 | 3+3s | Czech |
- Lecturer:
- Paola Vivi
- Tutor:
- Paola Vivi
- Supervisor:
- Department of Mathematics
- Synopsis:
-
The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (basis, dimension, inner product spaces, linear transformations) including eigenvalues and eigenvectors. Notions are illustrated in applications: matrices are used when solving systems of linear equations, eigenvalues are used for solving differential equations.
- Requirements:
- Syllabus of lectures:
-
1.Systems of linear equations. Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Rank of a matrix, the Frobenius theorem.
5. Linear mappings. Matrix of a linear mapping.
6. Matrix multiplication, inverse matrix. Determinants.
7.Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.
8. Eigenvalues and eigenvectors of matrices and linear mappings.
9. Differential equations. Method of separation of variables.
10. Linear differential equations, homogeneous and non-homogeneous. Variation of parameter.
11.Linear differential equations with constant coefficients. Basis of solutions. Solving
non-homogeneous differential equations.
12.Systems of linear differential equations with constant coefficients. Basis of solutions.Solving non-homogeneous systems.
13.Applications. Numerical aspects.
- Syllabus of tutorials:
-
1.Systems of linear equations. Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Rank of a matrix, the Frobenius theorem.
5. Linear mappings. Matrix of a linear mapping.
6. Matrix multiplication, inverse matrix. Determinants.
7.Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.
8. Eigenvalues and eigenvectors of matrices and linear mappings.
9. Differential equations. Method of separation of variables.
10. Linear differential equations, homogeneous and non-homogeneous. Variation of parameter.
11.Linear differential equations with constant coefficients. Basis of solutions. Solving
non-homogeneous differential equations.
12.Systems of linear differential equations with constant coefficients. Basis of solutions.Solving non-homogeneous systems.
13.Applications. Numerical aspects.
- Study Objective:
- Study materials:
-
1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997. ftp://math.feld.cvut.cz/pub/krajnik/vyuka/ua/linalgeb.pdf
- Note:
- Time-table for winter semester 2011/2012:
-
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 Fri Thu Fri - Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (compulsory course in the program)
- Communications, Multimedia and Electronics - Communication Technology (compulsory course in the program)
- Communications, Multimedia and Electronics - Multimedia Technology (compulsory course in the program)
- Communications, Multimedia and Electronics - Applied Electronics (compulsory course in the program)
- Communications, Multimedia and Electronics - Network and Information Technology (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management (compulsory course in the program)
- Communications, Multimedia and Electronics (compulsory course in the program)