Course detail

Numerical methods

FAST-HA52Acad. year: 2014/2015

a) Development of errors in numerical calculations. Numerical solution of algebraic equations and their systems.
b) Direct and iterative methods of solution of linear algebraic equations. Eigennumbers and eigenvectors of matrices. Construction of inverse and pseudoinverse matrices.
c) Interpolation polynoms and splines. Approximation of functions using the least square method.
d) Numerical evaluation of derivatives and integrals. Numerical solution of selected differential equations.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Vala, CSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

To understand fundamentals of numerical methods for the interpolation and approximation of functions and for the solution of algebraic and differential equations, reqiured in the technical practice.

Prerequisites

Basic knowledge of linear algebra and of differential and integral calculus of functions of one and more variables. Ability to study mathematical textbooks (no lectures are included).

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - seminars.

Assesment methods and criteria linked to learning outcomes

Successful completion of the scheduled tests and submission of solutions to problems assigned by the teacher for home work. Unless properly excused, students must attend all the workshops. Successful result of the test is required (13th weak).

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

To understand fundamentals of numerical methods for the interpolation and approximation of functions and for the solution of algebraic and differential equations, reqiured in the technical practice.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

J. Dalík: Numerické metody. CERM Brno, 1997. (CS)
Jiří Vala: Lineární prostory a operátory. elektronický učební materiál pro kombinované studium na FAST, 2004. (CS)
R. W. Hamming: Numerical Methods for Scientists and Engineers. Dover Publications, 1987. 978-0486652412. (CS)

Classification of course in study plans

  • Programme N-P-C-GK Master's

    branch G , 1 year of study, summer semester, elective
    branch GD , 1 year of study, summer semester, compulsory

Type of course unit

 

Exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Jiří Vala, CSc.

Syllabus

1.-3. Development of errors in numerical calculations. Numerical solution of algebraic equations and their systems.
4.-6. Direct and iterative methods of solution of linear algebraic equations. Eigennumbers and eigenvectors of matrices. Construction of inverse and pseudoinverse matrices.
7.-9. Interpolation polynoms and splines. Approximation of functions using the least square method.
10.-12. Numerical evaluation of derivatives and integrals. Numerical solution of selected differential equations.
13. Conclusions, test.