Fundamentals of Numerical Mathematics - NNUM105
Title: Základy numerické matematiky
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 9
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Vít Dolejší, Ph.D., DSc.
prof. RNDr. Jaroslav Haslinger, DrSc.
Classification: Mathematics > Numerical Analysis
Pre-requisite : {Aspoň jedna analýza 1. roč. na M nebo F}
Incompatibility : NNUM009
Interchangeability : NMNM201
Is incompatible with: NMNM201
Is interchangeable with: NMNM201, NNUM009
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Annotation -
The first course of numerical analysis for students of mathematics. Basic numerical methods for interpolation, approximation of functions, solving systems of linear algebraic equations, solving nonlinear equations and their systems. Initial value problem for ordinary differential equtions. Difference equations. Optimization.
Last update: T_KNM (19.05.2008)
Aim of the course -

To give a basic knowledge in numerical mathematics

Last update: FEIST/MFF.CUNI.CZ (28.04.2008)
Literature -

Stoer J., Bullirsch R.: Introduction to Numerical Analysis, Springer, l978

Last update: T_KNM (19.05.2008)
Teaching methods -

Lectures and tutorials in a lecture hall.

Last update: T_KNM (19.05.2008)
Requirements to the exam -

Examination according to the syllabus.

Last update: T_KNM (19.05.2008)
Syllabus -

Numerical methods of linear algebra. LU decomposition, elimination method, matrix iterative methods, power method .

Interpolation of functions. Lagrange and Hermite polynomials. Spline functions. Least-square approximation.

Qudrature formulas. Gaussian and Newton-Cotes formulas.

Solution of Nonlinear Equations.

Systems of linear difference equations, homogeneous, nohomogeneous systems, fundamental system of solutions, systems with constant coefficients.

Numerical solution of ordinary differential equations. a) One-step methods: Examples, general one-step methods, local discretization error, accumulated discretization error, convergence, consistency, error estimates, round-off errors, aposteriori error estimate, derivation of some formulae, Runge-Kutta methods. b) Multi-step methods, general framework, convergence, stability, consistency, order of the method, error estimates, derivation of some multi-step schemes.

Some optimization methods. Elements of convex analysis, steepest descent methods with constant and optimal step, convergence.

Last update: T_KNM (19.05.2008)
Entry requirements -

basic knowledge of calculus and linear algebra

Last update: FEIST/MFF.CUNI.CZ (28.04.2008)