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Introduction to Numerical Mathematics - NMNM211

Title:	Úvod do numerické matematiky
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	summer
E-Credits:	8
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:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vladimír Janovský, DrSc.
Class:	M Bc. FM M Bc. FM > Povinné M Bc. FM > 2. ročník
Classification:	Mathematics > Numerical Analysis
Pre-requisite :	{At least one 1st year Calculus course}
Incompatibility :	NNUM009
Interchangeability :	NNUM009
Is interchangeable with:	NNUM009

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: G_M (16.05.2012)

The first course of numerical analysis for students of Financial Mathematics.

Aim of the course -

Last update: G_M (27.04.2012)

a review of basic computational tools, practical excersises

Course completion requirements -

Last update: doc. RNDr. Václav Kučera, Ph.D. (29.10.2019)

Credit is obtained for participation in exercises and a computer test. The nature of the examination of the subject excludes repetition of the examination,

Literature -

Last update: doc. RNDr. Václav Kučera, Ph.D. (29.10.2019)

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

Quarteroni A., Sacco R. and Saleri F.: Numerical mathematics, Springer, 2000

Tebbens J., Hnětýnková I., Plešinger M., Strakoš Z. and Tichý P.: Analýza metod pro maticové výpočty. Základní metody. Matfyz press, Praha, 2012

Teaching methods -

Last update: G_M (27.04.2012)

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

Requirements to the exam -

Last update: G_M (27.04.2012)

Examination according to the syllabus.

Syllabus -

Last update: G_M (27.04.2012)

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: prof. RNDr. Vladimír Janovský, DrSc. (22.02.2019)

basic knowledge of calculus and linear algebra