Course detail

Numerical methods

FAST-HA52Acad. year: 2024/2025

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)

Entry knowledge

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).

Rules for evaluation and completion of the course

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

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.
Following the aim of the course, students will be able to apply numerical approaches to standard engineering problems.

Study aids

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)

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.