Czech

2

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

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

Basic knowledge of linear algebra and of differential and integral calculus of functions of one and more variables.

Not applicable.

Not applicable.

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1.Numerical solution of 1 nonlinear algebraic equations – starting methods, method of successive approximations, methods of tangents and sesants. Rate of convergence.
2.Linear spaces and operators, norm of vectors and matrices. Contractive operators, Banach fixed point theorem.
3.Solution of systems of nonlinear algebraic equations – simple iteration, Newton method. Eigennumbers and eigenvectors of square matrices - direct calculation, power-law algorithm, iteration in a subspace.
4.Overview of methods for solution of systems of linear algebraic equations. Direct methods – Gauss elimination, LU-decomposition, Choleski decomposition. Quasidiagonal and sparse systems. System (pre-)conditioning. QR-decomposition. Construction of inverse and pseudoinverse matrices.
5.Iterative methods – Jacobi iteration, Gauss-Seidel iteration. Relaxation methods. Method of coupled gradients (CGM).
6.Function spaces. Function interpolation – Lagrange polynomials, Hermite polynomials.
7.Linear and cubic splines. Function approximation, method of least squares (LSM).
8.Numerical derivatives, extrapolation to a limit. Numerical integration – rectangular, trapezoidal and Simpson rule. Romberg method, Gauss quadrature.
9.Boundary and initial problems in the analysis of differential equations. Finite difference method (FDM).
10.Variational formulation. Ritz-Galerkin method, finite element method (FEM).

Not applicable.

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.

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

Not applicable.

Not applicable.

Not applicable.

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

26 hours, compulsory