# ΜΥ03 - Numerical Analysis

## General Information

School: Digital Technology

Department: Informatics and Telematics

Course Title: Numerical Analysis

Course id: ΜΥ03

Type: Core Course

Semester: 2

Teaching and Examination Language: Greek

Is the course offered in Erasmus: Yes

Course web-page: https://eclass.hua.gr/courses/DIT154/

## Activities

Lectures (Theory): 3,0

Lab lectures: 0,0

ECTS credits: 5,0

## Learning Outcomes

The course belongs to the wider area of ​​Scientific Computing. Scientific calculations are the basis for many fields and an important tool for the study of scientific problems arising from many sciences such as Physics, Chemistry, Biology, Economics etc. Most of these problems lead to the solution of a mathematical problem, for which either there is not always an analytical solution, or if there is it requires complex calculations. The course also includes the implementation of algorithms in a laboratory environment, based on the programming language Python.

## General Skills

"●        Search, analysis and synthesis of data and information with the use of the assorted technologies
●        Decision Making
●        Independent work
●        Team work
●        Promoting free, creative and deductive reasoning

## Course Content

Errors in numerical calculaitons
-Representation of numbers in memory, rounding error,s propagating error.

Numerical solution of nonlinear equations
- Dividing method
- Fixed point problem
- Newton Rapshon method
- Cutting method
- Horner shape

Numerical methods for solving linear systems
- Gaussian elimination method
- Jordan elimination method
- Three-diagonal system solution
- Basic iterative methods

Numerical calculation of eigenvalues ​​and eigenvectors
- Method of forces
- Reverse method of forces.

Approximation of functions
- Finite differences
- Interpolation polynomial

Numerical derivation and integration
- Types of numerical derivation for equidistant points
- Numerical derivation by the method of determinable factors
- Error in arithmetic derivation

Numerical solution of ordinary differential equations
- Euler method
- Taylor series method
- Numerical solution of ordinary differential equations with boundary conditions

## Learning and Teaching Methods - Evaluation

Teaching methods: face-to-face

Use of ICT:

### Course Organization

 Activity Semester work load Lectures 39,0 Lab exercises 0,0 Individual of group projects Lab report preparation Thesis Independent Study 86,0 Total 125

## Literature

-Applied numerical analysis - 3rd edition, P. Giannopoulou, A. Dimitriadis Δημητριάδης, S. Doukakis, C. Kilias, N. Matzakos Νίκος
-Numerical methods and applications for engineers, 4th edition, Sarris, I. - Karakasidis T.
-Numerical methods for engineers, 7th edition, Chapra S. - Canale R., F. Koutelieris (editing)