ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ V PRAZE
STUDIJNÍ PLÁNY
2018/2019

# Linear Algebra and its Applications

Předmět není vypsán Nerozvrhuje se
Kód Zakončení Kredity Rozsah Jazyk výuky
AE0B01LAA Z,ZK 8 3+3
Přednášející:
Cvičící:
Předmět zajišťuje:
katedra matematiky
Anotace:

The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (linear space,basis, dimension, euclidean 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 systems of linear differential equations.

Výsledek studentské ankety předmětu je zde: http://www.fel.cvut.cz/anketa/aktualni/courses/AE0B01LAA

In order to obtain the certificate of attendance,

students are required to actively participate in the laboratory class, hand in the assigned

homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate („zapocet“) are allowed to take the exam.

http://math.feld.cvut.cz/vivi/AE0B01LAA2010.pdf

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

Další informace:
http://math.feld.cvut.cz/vivi/
Pro tento předmět se rozvrh nepřipravuje
Předmět je součástí následujících studijních plánů:
Platnost dat k 23. 4. 2019
Aktualizace výše uvedených informací naleznete na adrese http://bilakniha.cvut.cz/cs/predmet12773104.html