# 714-0886/01 – 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 2009/2010 Year of cancellation 2019/2020 Intended for the faculties FAST, USP, FEI, FBI, FS, FMT, HGF Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, 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

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng - Bachelor Studies 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Bachelor Studies 2018/2019 Full-time English Choice-compulsory 301 - Study and International Office stu. block
V - ECTS - VSB 2018/2019 Full-time English Optional 401 - Study Office stu. block
FBI_ECTS 2018/2019 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
FMMI 2018/2019 Full-time English Compulsory 601 - Study Office stu. block
ECTS FCE Bc-Mgr 2018/2019 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2017/2018 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FBI_ECTS 2017/2018 Full-time English Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
USP 2017/2018 Full-time English Optional USP - University Study Programmes stu. block
FBI_ECTS 2017/2018 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
ECTS FCE Bc-Mgr 2017/2018 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FMMI 2017/2018 Full-time English Compulsory 601 - Study Office stu. block
V - ECTS - VSB 2017/2018 Full-time English Optional 401 - Study Office stu. block
ECTS FMG-VSB 2017/2018 Full-time English Optional 501 - Study Office stu. block
V - ECTS - VSB 2016/2017 Full-time English Optional 401 - Study Office stu. block
FMMI 2016/2017 Full-time English Compulsory 601 - Study Office stu. block
ECTS FCE Bc-Mgr 2016/2017 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FBI_ECTS 2016/2017 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
USP 2016/2017 Full-time English Optional USP - University Study Programmes stu. block
ECTS FMG-VSB 2016/2017 Full-time English Optional 501 - Study Office stu. block
ECTS - MechEng - Bachelor Studies 2016/2017 Full-time English Choice-compulsory 301 - Study and International Office stu. block
USP 2015/2016 Full-time English Optional USP - University Study Programmes stu. block
V - ECTS - VSB 2015/2016 Full-time English Optional 401 - Study Office stu. block
FMMI 2015/2016 Full-time English Compulsory 601 - Study Office stu. block
ECTS - MechEng - Bachelor Studies 2015/2016 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FBI_ECTS 2015/2016 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
ECTS FMG - VSB 2015/2016 Full-time Czech Optional 501 - Study Office stu. block
V - ECTS - VSB 2014/2015 Full-time Czech Optional 401 - Study Office stu. block
FBI_ECTS 2014/2015 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
FMMI_N 2014/2015 Full-time Czech Compulsory 601 - Study Office stu. block
USP 2014/2015 Full-time Czech Optional USP - University Study Programmes stu. block
O - ECTS FMG - Bc. 2014/2015 Full-time Czech Optional 501 - Study Office stu. block
ECTS - MechEng 2014/2015 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
V - ECTS - VSB 2013/2014 Full-time Czech Optional 401 - Study Office stu. block
O - ECTS FMG - Bc. 2013/2014 Full-time Czech Optional 501 - Study Office stu. block
ECTS FCE Bc-Mgr 2013/2014 Full-time Czech Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
USP 2013/2014 Full-time Czech Optional USP - University Study Programmes stu. block
FMMI 2013/2014 Full-time Czech Compulsory 601 - Study Office stu. block
ECTS - MechEng 2013/2014 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng 2012/2013 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
O - ECTS FMG - Bc. 2012/2013 Full-time Czech Optional 501 - Study Office stu. block
FMMI 2012/2013 Full-time Czech Compulsory 601 - Study Office stu. block
USP 2012/2013 Full-time Czech Optional USP - University Study Programmes stu. block
ECTS FCE Bc-Mgr 2012/2013 Full-time Czech Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block

### Assessment of instruction

Předmět neobsahuje žádné hodnocení.