SubjectsSubjects(version: 861)
Course, academic year 2019/2020
  
Applied Mathematics II - NCHF072
Title: Aplikovaná matematika II
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/3 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Artem Ryabov, Ph.D.
XP//In complex pre-requisite: MC260P01M, MZ370P19
XK//Is complex co-requisite for: MC260P112, MC260P28
Annotation -
Last update: Mgr. Kateřina Mikšová (14.05.2019)
Second semester of four-semester courses on Applied Mathematics. Introduction to linear algebra, matrix calculus. Derivatives and integrals in higher dimensions.
Literature - Czech
Last update: RNDr. Artem Ryabov, Ph.D. (14.06.2018)

[1] J. Bečvář, Lineární algebra (Matfyzpress, 2000).

[2] L. Motl, M. Zahradník, Pěstujeme lineární algebru (Karolinum, 2002).

[3] K. Výborný, M. Zahradník, Používáme lineární algebru (Karolinum, 2002).

[4] T.S. Blyth, E.F. Robertson, Basic Linear Algebra (Springer, 2002).

[5] J. Kopáček, Matematika pro fyziky I. II.,III. (Skripta MFF UK , Matfyzpress).

[6] J. Kopáček a kol., Příklady z matematiky pro fyziky I., II. (Skripta MFF UK , Matfyzpress).

[7] V. Jarník, Diferenciální počet I.,II (Academia)

[8] V. Jarník, Integrální počet I (Nakladatelství ČS AV)

[9] B.P. Děmidovič, Sbírka úloh a cvičení z matematické analýzy (Fragment, 2003)

Syllabus -
Last update: RNDr. Artem Ryabov, Ph.D. (13.05.2019)

Linear vector spaces.

Matrices and determinants, systems of linear equations, Gaussian elimination.

Bilinear and quadratic forms, positive and negative definiteness.

Basic theory of multivariate functions, metrics, limit, continuity.

Partial derivatives, total differential, operators grad, div, rot.

Multiple integrals. Interchange of a limit and integration, derivative and integration

Series, convergence and divergence, absolute and conditional convergence, Taylor series.

Ordinary differential equations and their systems, basic methods, Bernoulli and Euler equations, exact differential equations, series solution to differential equations.

 
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