Basics of Nummerical Mathematics

Course guarantor:

Milan Bořík

Lecturer:

Milan Bořík

Tutor:

Milan Bořík

Supervisor:

Department of Mathematics

Synopsis:

Basics of Nummerical Mathematics follows on from algorithms in courses Mathematics 1G and Mathematics 2G.

Requirements:

Project.

Syllabus of lectures:

Number systems. Float arithmetics. Errors in number representation.

Errors sources. Absolute and relative error.

Basic algorithms. Cycles.

Algebraic operations. Polynomial division algorithm.

Interpolation polynomials. Extrapolation.

Nummerical solution of the equation f(x)=0. Bisection. Regula falsi. Newton metod. Combination of methods.

Modification of Newton method.

Taylor polynomial. Lagrange theorem.

Problems with the definitions of a function, e.g. exp(x).

Algorithms for solution of systems of linear equations. Cramer rule. Inverse matrix by an adjoint matrix. LU decomposition.

Matrix and vector norms.

Regression methods. The least square method.

Nummerical methods for solution of integrals.

Syllabus of tutorials:

Number systems. Float arithmetics. Errors in number representation.

Errors sources. Absolute and relative error.

Basic algorithms. Cycles.

Algebraic operations. Polynomial division algorithm.

Interpolation polynomials. Extrapolation.

Nummerical solution of the equation f(x)=0. Bisection. Regula falsi. Newton metod. Combination of methods.

Modification of Newton method.

Taylor polynomial. Lagrange theorem.

Problems with the definitions of a function, e.g. exp(x).

Algorithms for solution of systems of linear equations. Cramer rule. Inverse matrix by an adjoint matrix. LU decomposition.

Matrix and vector norms.

Regression methods. The least square method.

Nummerical methods for solution of integrals.

Study Objective:

Basics of Nummerical Mathematics follows on from algorithms in courses Mathematics 1G and Mathematics 2G.

Study materials:

[1] K. Rektorys a spolupracovníci: Přehled užité matematiky I, Prometheus Praha, 2000.

[2] Pultarová, I., Novák, J., Novák, P.: Základy informatiky. Počítačové modelování v Matlabu, skripta FSv ČVUT v Praze, 2005.

[3] Kočandrlová, M., Černý, J.: Geo-matematika I, skripta FSv ČVUT v Praze, 2007.

Note:

Further information:

https://mat.fsv.cvut.cz/aznm

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: