Linear Algebra and its Applications
| Kód | Zakončení | Kredity | Rozsah | Jazyk výuky |
|---|---|---|---|---|
| AE0B01LAA | Z,ZK | 8 | 3+3s | česky |
- Přednášející:
- Paola Vivi
- Cvičící:
- Paola Vivi
- Předmět zajišťuje:
- katedra matematiky
- Anotace:
-
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.
- Požadavky:
- Osnova přednášek:
-
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.
- Osnova cvičení:
-
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.
- Cíle studia:
- Studijní materiály:
-
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
- Poznámka:
-
Rozsah výuky v kombinované formě studia: 21p+9s
- Rozvrh na zimní semestr 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
Po Út St Čt Pá - Rozvrh na letní semestr 2011/2012:
- Rozvrh není připraven
- Předmět je součástí následujících studijních plánů:
-
- Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering (povinný předmět programu)
- Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (povinný předmět programu)
- Communications, Multimedia and Electronics - Communication Technology (povinný předmět programu)
- Communications, Multimedia and Electronics - Multimedia Technology (povinný předmět programu)
- Communications, Multimedia and Electronics - Applied Electronics (povinný předmět programu)
- Communications, Multimedia and Electronics - Network and Information Technology (povinný předmět programu)
- Electrical Engineering, Power Engineering and Management (povinný předmět programu)
- Communications, Multimedia and Electronics (povinný předmět programu)