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Fundamentals of Numerical Mathematics - NNUM009

Title:	Základy numerické matematiky
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	9
Hours per week, examination:	summer 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
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vladimír Janovský, DrSc.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNM211, NNUM105
Is incompatible with:	NNUM105, NMNM211
Is interchangeable with:	NMNM211

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Annotation -

Last update: T_KNM (19.05.2008)

The first course of numerical analysis for bachelor study of mathematics. Topics: systems of linear equations, least squares, nonlinear systems, function minimalization, interpolation, ordinary differential equations, eigenvalue problems.

Aim of the course -

Last update: JANOVSKY/MFF.CUNI.CZ (30.04.2008)

a review of basic computational tools, practical excersises

Literature - Czech

Last update: JANOVSKY (20.04.2006)

Segethová J.: Základy numerické matematiky, MFF UK, 2002

Deuflhard P. and Hohmann A.: Introduction to Scientific Computing, 2nd edition, Springer, 2002

Teaching methods -

Last update: T_KNM (19.05.2008)

The course consists of lectures in a lecture hall and exercises in a computer laboratory.

Requirements to the exam -

Last update: T_KNM (19.05.2008)

Examination according to the syllabus.

Syllabus -

Last update: T_KNM (19.05.2008)

Solving liner systems, direct methods: Gauss elimination, LU-decomposition, pivoting, Cholesky decompositon.

Least Squares: data fitting, linear least squares, normal equation, pseudoinverse, QR-decomposition.

Nonlinear systems: Fixed Point Theorem (contraction mapping), Newton's Method, Newton-like methods.

Function minimization: Nelder-Mead Method, Method of Steepest Descent, Conjugate Gradient Method.

Interpolation: Lagrange Interpolating Polynomial, Chebyshev Polynomial, splines.

Ordinary Differential Equations: initial value problem, Euler Method, implicit Euler Method, Runge-Kutta Method.

Eigenvalue problems: a primer (eigenvalue, eigenvector, Characteristic Polynomial, multiplicity, Similar Matrices, Jordan canonical form), Power Method, Inverse iteration, QR algoritmus.

Iterative Methods (linear systems): large sparse matrices, Gauss-Seidel Method, Successive Overrelaxation Method, Conjugate Gradient Method, preconditioning.

Entry requirements -

Last update: T_KNM (19.05.2008)

basic knowledge of calculus and linear algebra