310-2130/03 – Numerical Mathematics (NM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorMgr. Zuzana Morávková, Ph.D.Subject version guarantorMgr. Zuzana Morávková, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year3Semestersummer
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
MOR74 Mgr. Zuzana Morávková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Graded credit 2+2

Subject aims expressed by acquired skills and competences

The aim of this course is to acquaint students with the numerical solution of mathematical problems that arise in the other courses of their study and in the technical practice. The main accent lays in explanations of fundamental principles of numerical methods with emphases their general properties. It should lead to the ability in concrete situations to decide whether a numerical procedure is a suitable tool for solving a particular problem. An important ingredient of the course consists in the algorithmic implementation of methods and in the utilization of existing computer programs specialized for numerical computations. The graduate of this course should know: • to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method; • to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies; • to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The course is devoted to basic numerical methods of the linear algebra and mathematical analysis: iterative methods for solving of nonlinear equations, direct and iterative methods for solving of linear systems, eigenvalue problems, interpolation and approximation of functions, numerical computation of derivatives and integrals, solving of ordinary differential equations. The programming system Matlab is used during the course.

Compulsory literature:

1. Boháč, Z.: Numerical Methods and Statistics. VŠB-TU Ostrava, 2005. ISBN 80-248-0803-X

Recommended literature:

1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN 978-3-540-34658-6. 2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003, ISBN 0-521-00794-1. 3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999, ISBN-13: 9780139491573.

Way of continuous check of knowledge in the course of semester

Homeworks, tests.

E-learning

Další požadavky na studenta

Students have to know lessons Math I and Math II.

Prerequisities

Subject codeAbbreviationTitleRequirement
310-2111 MI Mathematics I Recommended
310-2112 MII Mathematics II Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Introduction (precisions, methods) 2. Interpolation and splines 3. Least square method 4. Roots finding (bisection method, Newton's .method) 5. Linear solver (Lu-factorization) 6. Iteratice methods for linear equations 7. Numerical intergrations 8. ODE solver

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Graded credit Graded credit 100  51
Mandatory attendence parzicipation: Lessons are obligatory, 20% absence can be excused.

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (B2341) Engineering (3902R001) Applied Informatics and Control P English Ostrava 3 Compulsory study plan
2019/2020 (B2341) Engineering (3907R009) Operation of Energy Equipment P English Ostrava 3 Compulsory study plan
2019/2020 (B2341) Engineering (2303R002) Mechanical Engineering Technology P English Ostrava 3 Compulsory study plan
2019/2020 (B2341) Engineering (2301R013) Robotics P English Ostrava 3 Compulsory study plan
2019/2020 (B2341) Engineering (3901R003) Applied Mechanics P English Ostrava 3 Compulsory study plan
2019/2020 (B0715A270012) Engineering P English Ostrava 3 Compulsory study plan
2019/2020 (B0713A070003) Energetics and Environments P English Ostrava 3 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner