Subject description - AE0B01LAA

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 AE0B01LAA Linear Algebra and its Applications Extent of teaching: 3+3 Guarantors: Roles: P,V Language ofteaching: 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)