# 310-2304/01 – Numerical Methods (NumMeth)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor prof. RNDr. Radek Kučera, Ph.D. Subject version guarantor prof. RNDr. Radek Kučera, Ph.D. Study level undergraduate or graduate Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties FAST, HGF, FMT, FEI, FBI, FS, USP Intended for study types Bachelor
Instruction secured by
KUC14 prof. RNDr. Radek Kučera, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 2+2

### Subject aims expressed by acquired skills and competences

The course is an introduction to the numerical methods. The main goal consists in explanations of fundamental numerical principles so that students should be able to decide about an appropriate method for problems arising in the other courses or in the technical practice. An important ingredient is the algorithmic implementation of numerical methods and the usage of the standard numerical software. 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. It is necessary to complete Mathematics 1 and Mathematics 2 courses or their equivalents.

### Teaching methods

Lectures
Individual consultations
Tutorials

### Summary

The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis. The following topics are presented: direct and iterative methods for solving systems of linear equations; eigenvalue problems; iterative solving of nonlinear equations; interpolation and approximation of the function data; numerical computation of integrals and derivatives; numerical solving of initial value problems for ordinary differential equations; using MATLAB in numerical computations.

### Compulsory literature:

1. Burden, R. L., Faires, J. D.: Numerical Analysis. Cengage Learning, 2011 2. Chapra, S., Canale, R.: Numerical Methods for Engineers. McGraw-Hill Education, 2009.

### Recommended literature:

1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. 2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. 3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999.

### Way of continuous check of knowledge in the course of semester

Tests and credits ================= Exercises --------- Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize - completion of three written tests, 0-20 CP Exam ---- - written exam 0-60 CP, successful completion at least 25 CP - oral exam 0-20 CP, successful completion at least 5 CP

### Other requirements

The requirements are analogous to the program of the course.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Program of lectures =================== Week. Lecture ------------- 1st Course contents, the issue of errors, stability calculations. 2nd Solution of nonlinear equations, separation of roots, the simplest method. 3rd Newton's method and simple iterations. 4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition. 5th Eigenvalues and eigenvectors, numerical calculation. 6th Iterative methods for solving linear equations. 7th Interpolation by polynomials and splines. 8th Least squares approximation. 9th Numerical differentiation and integration. 10th Extrapolation in the calculation of integrals. Gaussian integration formulas. 11th One-step method for solving initial value problems for ordinary differential equations. 12th Multistep methods. 13th Ordinary differential equations of higher order. 14th Systems of differential equations. Program of the excercises and the exam questions are analogous. Matalb program is used in the excersises.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of pointsMax. počet pokusů
Examination Examination 100  51 3
Mandatory attendence participation: 80%

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Conditions for subject completion and attendance at the exercises within ISP:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng - Bachelor Studies 2022/2023 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FMT + Nanotechnology 2022/2023 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block
ECTS Bc.-Mgr. 2022/2023 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FMT+9360 2021/2022 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2021/2022 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS Bc.-Mgr. 2021/2022 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS FCE Bc-Mgr 2020/2021 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2020/2021 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FMT+9360 2020/2021 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block
ECTS FCE Bc-Mgr 2019/2020 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
Additional Subjects 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FMST 2019/2020 Full-time English Compulsory 601 - Study Office stu. block

### Assessment of instruction

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