Course unit code: 
FSISPD 
Academic year: 
2016/2017 
Type of course unit: 
compulsory 
Level of course unit: 
Bachelor's (1st cycle) 
Year of study: 
3 
Semester: 
winter 
Number of ECTS credits: 
5 
Learning outcomes of the course unit:
Revision and deepening of the knowledge of Ordinary Differential Equations. Elements of the theory of Partial Differential Equations and survey of their application to the mathematical modelling. Ability to formulate mathematical model of the selected problems of mathematical physics and to compute the solution or propose an algorithm for numerical solution.


Mode of delivery:
90 % facetoface, 10 % distance learning


Prerequisites:
Solution of algebraic equations and system of linear equations, differential and integral calculus of functions of one and more variables, ordinary differential equations.


Corequisites:
Not applicable.


Recommended optional programme components:
Not applicable.


Course contents (annotation):
The course deals with the following topics: Ordinary differential equations  a brief survay of material studied within the 3rd semester subject and extending of the subject matter (stability of the solution, autonomous equations and systems, boundary value problems and trajectories).
Partial differential equations  basic concepts. The firstorder equations. The Cauchy problem for the kth order equation. Transformation, classification and canonical form of the secondorder equations. Derivation of selected equations of mathematical physics, formulation of initial and boundary value problems. The classical methods: method of characteristics, The Fourier series method, integral transform method, the Green function method. Maximum principles. Properties of the solutions to the elliptic, parabolic and hyperbolic equations.


Recommended or required reading:
V. J. Arsenin: Matematická fyzika, Alfa, Bratislava 1977 J. Franců: Parciální diferenciální rovnice, skripta FSI VUT, CERM 2011 (CS) J. Franců: Obyčejné diferenciální rovnice a Příklady z ODR, http://www.mat.fme.vutbr.cz/home/francu (CS) L. C. Evans: Partial Differential Equations, AMS, Providence 1998 W. E. Williams: Partial differential equations, V. J. Arsenin: Matematická fyzika, Alfa, Bratislava 1977. (SK) K. Rektorys: Přehled užité matematiky II., Prometheus 1995 (CS) J. Škrášek, Z. Tichý: Základy aplikované matematiky II, SNTL, Praha 1986 (CS)


Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.


Assesment methods and criteria linked to learning outcomes:
Courseunit credit is awarded on condition of having attended the seminars actively and passed two control tests:
Control test 1: O.D.E.: (a) solution of the 1st order equation, (b) solution of the 2nd order linear equation, (c) solution of a system of linear equations.
Control test 2: P.D.E.: (a) solution of the 1st order equation, (b) classification, and transformation of the 2nd order equation to its canonical form, (c) formulation of an initial boundary value problem related to the physical setting and finding its solution by means of the Fourier series method.
The examination consists of a practical and a theoretical part. Practical part: solving examples of P.D.E., see Control test 2. Theoretical part: theory of O.D.E. and P.D.E. (1 + 3 questions).


Language of instruction:
Czech


Work placements:
Not applicable.


Course curriculum:
Not applicable.


Aims:
After completing knowledge of ordinary differential equations the aim of the subject is to provide students with the basic knowledge of the partial differential equations, their basic properties, methods of solving them, and their application in mathematical modelling. Another goal is to teach the students to formulate and solve simple problems for mathematical physics equations.


Specification of controlled education, way of implementation and compensation for absences:
Absence has to be made up by selfstudy using lecture notes. Passing the control tests is required, in cases of bad result or absence in additional term.

