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MU:MU20010 Numerical Methods - Course Information

## MU20010 Numerical Methods

**Mathematical Institute in Opava**

Summer 2021

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- RNDr. Petra Nábělková, Ph.D. (lecturer)

Mgr. Vojtěch Pravec, Ph.D. (seminar tutor) **Guaranteed by**- RNDr. Petra Nábělková, Ph.D.

Mathematical Institute in Opava **Timetable**- Wed 11:25–13:00 R2
- Timetable of Seminar Groups:

*V. Pravec* **Prerequisites**(in Czech)-
**MU20002**Mathematical Analysis II && TYP_STUDIA ( B ) **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Mathematical Methods and Modelling (programme MU, Bc-M)
- Mathematical Methods in Economics (programme MU, Bc-M)
- Mathematical Methods in Risk Management (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)

**Course objectives**- The aim of this course is to acquaint students with the basic numerical approaches to solving the problems they encountered in mathematical analysis and algebra.
**Syllabus**- 1. Numerical representation: representation of numbers, origin and classification of errors, errors of arithmetic operations, conditionality of tasks and numerical stability of algorithms.

2. Interpolation: Algebraic polynomial interpolation-existence and uniqueness of polynomial interpolation, estimation of interpolation error, Lagrange, Newton and Hermit interpolating polynomials, interpolation on equidistant nodes. Spline interpolation.

3. Approximation: choosing the class of approximating functions, least squares method.

4. Numerical solution of nonlinear equations: roots separation, simple iteration method, bisection method, tangent method, secant methods, regula falsi.

5. Numerical solution of systems of equations: Gauss elimination with control column, LU-decomposition, Jacobi method, Gauss-Seidel method.

6. Numerical integration: Newton-Cotes quadrature formulas, error estimates.

- 1. Numerical representation: representation of numbers, origin and classification of errors, errors of arithmetic operations, conditionality of tasks and numerical stability of algorithms.
**Literature**- R. L. Burden, J. D. Faires.
*Numerical Analysis*. Boston, 2010. ISBN 978-0538733519. info - I. Horová, J. Zelinka.
*Numerické metody řešení okrajových úloh pro diferenciální rovnice*. Brno, 2004. ISBN 80-210-3317-7. info

*required literature*- R, Kučera.
*Numerické metody*. Ostrava. ISBN 80-248-1198-7. info - J. Segethová.
*Základy numerické matematiky*. Karolinum, Praha, 1998. ISBN 80-7184-596-5. info - E. Vitásek.
*Numerické metody*. SNTL, Praha, 1987. info - Z. Riečanová a kol.
*Numerické metody a matematická štatistika*. Alfa, Bratislava, 1987. ISBN 063-559-87. info

*recommended literature*- A. Ralston.
*Základy numerické matematiky*. Praha, 1978. info

*not specified*- R. L. Burden, J. D. Faires.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course can also be completed outside the examination period. **Teacher's information**- Attendance at lectures is desirable. During the first lecture, students will be introduced to the requirements of the lecturer for graduation.

Assignment of the credit is conditioned by active participation in seminars, completion of partial credit test on the sum of at least 60% points or 70% points from the correctional credit test. The tutor determines the exact conditions of the credit and the date of credit tests.

The exam consists of two parts - written and oral. The written part of the exam is focused on the numerical handling of the curriculum. Upon successful completion of the written part, the oral part is followed by an examination of the basic terms and assertions of the theory and their mutual relation.

The student should orient himself in the numerical approaches discussed and recognize the suitability of their choice where the relevant problems can not be solved analytically, or the obtaining of solutions in this way is extremely difficult.

- Enrolment Statistics (recent)

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