# Faculty of Mechanical Engineering

VŠB-TUO - Students' Mobility > Courses for exchange students

## Description of individual course units

### IMPORTANT NOTE!!!

#### Following fields are not relevant for Exchange students:

• Type of Course Unit
• Level of Course Unit
• Year of Study

Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit CodeCourse Unit TitleNumber of ECTS Credits Allocated
714-0886/01Numerical Methods5 ECTS credits
Type of Course UnitCompulsory
Level of Course UnitFirst Cycle
Year of Study
Semester when the Course Unit is deliveredWinter, Summer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
Learning Outcomes of the Course Unit
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.
Recommended Optional Programme Components
Common optional components are not offered, students of special interest can participate in departmental activities or can arrange consulting hours with lecturer.
Course Contents
Program of lectures
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Week. Lecture
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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.
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.
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.