Přehled studia |
Přehled oborů |
Všechny skupiny předmětů |
Všechny předměty |
Seznam rolí |
Vysvětlivky
Návod
| AE0B01LAG |
Linear Algebra |
Rozsah výuky: | 4+2 |
| Garanti: | |
Role: | P,V |
Zakončení: | Z,ZK |
| Vyučující: | |
| Zodpovědná katedra: | 13101 |
Kreditů: | 7 |
Semestr: | Z |
Anotace:
This course covers introductory topics of linear algebra. The main focus
is on
the related notions of linear spaces and linear transformations (linear
independence, bases and coordinates) and matrices (determinants, inverse
matrix, matrix of a linear mapping, eigenvalues). Applications include
solving systems of linear equations, geometry in 3-space (including dot
product and cross product), and solving linear differential equations.
Výsledek studentské ankety předmětu je zde:
AE0B01LAG
Osnovy přednášek:
| 1. | | Introduction, polynomials. |
| 2. | | Linear spaces, linear dependence and independence. |
| 3. | | Basis, dimension, coordinates of vectors. |
| 4. | | Matrices, operations, determinants. Inverse matrix. |
| 5. | | Systems of linear equations. |
| 6. | | Linear mappings. Matrix of a linear mapping. |
| 7. | | Free vectors. Dot product and cross product. |
| 8. | | Lines and planes in 3-dimensional Euclidean space. |
| 9. | | Eigenvalues and eigenvectors of matrices and linear mappings. |
| 10. | | Similarity of matrices, matrices similar to diagonal matrices. |
| 11. | | Generalized eigenvectors. |
| 12. | | Systems of linear differential equations of 1st order with constant |
coefficients.
| 13. | | Linear differential equations of order n with constant coefficients. |
| 14. | | Back-up class. |
Osnovy cvičení:
| 1. | | Polynomials. |
| 2. | | Examples of linear spaces, linear independence. |
| 3. | | Basis, coordinates of vectors. |
| 4. | | Operations with matrices, determinants. Finding inverse matrix. |
| 5. | | Systems of linear equations. |
| 6. | | Examples of linear mappings. |
| 7. | | Matrix of a linear mapping, change of basis. |
| 8. | | Dot product and cross product in geometry. Lines and planes. |
| 9. | | Eigenvalues and eigenvectors of matrices. |
| 10. | | Diagonalization of matrices. |
| 11. | | Generalized eigenvectors and applications. |
| 12. | | Systems of linear differential equations. |
| 13. | | Linear differential equations of order n. |
| 14. | | Back-up class. |
Literatura:
| [1] | | P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005. |
Požadavky:
http://math.feld.cvut.cz/0educ/pozad/a0b01lag.htm
Poznámka:
| Rozsah výuky v kombinované formě studia: 28p+6s |
Webová stránka:
http://math.feld.cvut.cz/vivi/
Předmět je zahrnut do těchto studijních plánů:
| Stránka vytvořena 23.8.2017 07:47:15, semestry: L/2016-7, Z,L/2017-8, Z/2018-9, připomínky k informační náplni zasílejte správci studijních plánů |
Návrh a realizace: I. Halaška (K336), J. Novák (K336) |
