Subject description - AE0B01LAA

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AE0B01LAA Linear Algebra and its Applications Extent of teaching:3+3
Guarantors:  Roles:P,V Language of
teaching:
EN
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:8 Semester:Z

Anotation:

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.

Course outlines:

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.

Exercises outline:

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.

Literature:

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

Requirements:

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

Webpage:

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

Subject is included into these academic programs:

Program Branch Role Recommended semester
BEEEM1 Applied Electrical Engineering P 1
BEEEM_BO Common courses P 1
BEEEM2 Electrical Engineering and Management P 1
BEKME1 Communication Technology P 1
BEKME5 Komunikace a elektronika P 1
BEKME_BO Common courses P 1
BEKME4 Network and Information Technology P 1
BEKME3 Applied Electronics P 1
BEKME2 Multimedia Technology P 1
BEKYR1 Robotics V 1
BEKYR_BO Common courses V 1
BEKYR3 Systems and Control V 1
BEKYR2 Sensors and Instrumentation V 1
BEOI1 Computer Systems V 1
BEOI_BO Common courses V 1
BEOI3 Software Systems V 1
BEOI2 Computer and Information Science V 1


Page updated 24.6.2019 17:52:59, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)