• Pravděpodobně máte vypnutý JavaScript. Některé funkce portálu nebudou funkční.

# Course detail

## Applied mathematics

Course unit code: FAST-CA57
Type of course unit: optional
Level of course unit: Master's (2nd cycle)
Year of study: 1
Semester: summer
Number of ECTS credits:
 Learning outcomes of the course unit: The students manage the subject to the level of understanding foundation of the modern methods of ordinary and partial differential equations in the engineering applications.
 Mode of delivery: 90 % face-to-face, 10 % distance learning
 Prerequisites: Basics of the theory of one- and more-functions. Differentiation and intgration of functions.
 Co-requisites: n. a.
 Recommended optional programme components: n. a.
 Course contents (annotation): Basics of ordinary fifferential equations focussing on engineering applications – classic solution, Cauchy problem and boundary problems (their classification). Analytical methods for solving boudary problems in ordinary secod and fourth order differential equations. Methods of solution of non-homogeneous boundary problems – Fourier method, Green´s function, variation of constants method. Solutions of non-linear differential equations with given boundary conditions. Sobolev spaces and generalized solutions and reason for using such notions. Variational methods of solutions. Introduction to the theory of partial differential equations of two variables – classes and basic notions. Classic solution of a boundary problem (classes), properties of solutions. Laplace and Fourier transform – basic properties. Fourier method of solution of evolution equations, difussion problems, wave equation. Laplace method used to solve evolution equations - heat transfer equation. Equations used in the theory of elasticity.
 Recommended or required reading: FARLOW, S. J.: Partial Differential Equations. John Wiley&Sons, 1982. MÍKA, S., KUFNER, A.: Okrajové úlohy pro obyčejné diferenciální rovnice.. SNTL, 1983. BARTÁK, J., HERRMANN, L., LOVICAR, V., VEJVODA, O.: Partial Differential Equations. Ellis Horwood and SNTL, 1991.
 Planned learning activities and teaching methods: n. a.
 Assesment methods and criteria linked to learning outcomes: Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.
 Language of instruction: Czech
 Work placements: n. a.

Type of course unit:
Lecture: 26 hours, optionally prof. RNDr. Josef Daněček, CSc. 26 hours, compulsory prof. RNDr. Josef Daněček, CSc.