Courses

Numerical Analysis

General

Course Contents

Introduction to Numerical Analysis,
Numerical Calculations and Errors,
Numerical Solution of Nonlinear Equations (Bisection Method, String Method, Newton Method)
Numerical solution of systems of equations
Numerical Solution of Systems of Linear Equations. Immediate Methods: Gaussian deletion,
Gauss-Jordan, LU factorization.
Repetitive Methods: Jacobi, Gauss-Seidel, sequential hyperelaxation.
Numerical Solution of Systems of Nonlinear Equations, Newton-Raphson method
Interpolation (Polynomial approach, Lagrange interpolation etc)
Approach (Minimum Squares)
Numerical Integration (Table Rule, Complex Table Rule, Simpson 1/3 & 3/8, Romberg Algorithm,
Integration by Gauss)
Numerical Solution of Ordinary Differential Equations (Euler Method. Improved Euler Method.
Runge-Kutta Methods: 2nd, 3rd and 4th order,Finite difference method.)
Systems of Ordinary Differential Equations.
Laboratory Exercises and applications in MATLAB

Educational Goals

The aim of this course is to teach the student the necessary tools for the numerical solution of mathematical problems, the application of numerical methods and the implementation of these solutions with programs on PC. For this reason in the course laboratory the MATLAB software package is used, which makes it possible to implement and study the methods presented in theory. Upon successful completion of the course the student will be able to:
– understands the effect of truncation – rounding errors and method errors on numerical results as well as number systems and their representation
– selects the appropriate arithmetic method to use in each problem,
– implements algorithms for solving nonlinear equations
– implements algorithms for solving linear systems with direct and iterative methods,
-recognizes and implements basic data interpolation methods
-recognizes and implements basic regression methods
-knows and implements basic methods of arithmetic integration
– knows and implements basic methods for solving differential equations and systems of differential equations
-recognizes and uses MATLAB software and its tools with ease.

General Skills

Research, analysis and synthesis of data and information, using corresponding technologies, Adaptation to new situations, Independent work, Teamwork – distribution of responsibilities, Intellectual competences, Societal competence.

Teaching Methods

Lectures, Exercises, Online guidance, Projected Presentations, E-mail communication, Online Synchronous and Asynchronous Teaching Platform (moodle).

Students Evaluation

Assessment Language: English / Greek
The final grade of the course is formed by 70% by the grade of the theoretical part and by 30% by the grade of the laboratory part.
1. The grade of the theoretical part is formed by a written final examination.
The written final examination of the theoretical part may include:
Solving problems of application of the acquired knowledge, Short answer questions etc
2. The examination of the Laboratory Exercises is carried out with the continuous evaluation of the laboratory skills and the theoretical knowledge that were acquired in the course by the method of continuous evaluation and submission of weekly assignments

Recommended Bibliography

Numerical Methods for Engineers 7th Edition by Steven Chapra, Raymond Canale, Boston: McGraw-Hill Higher Education.
Numerical Analysis, Tenth Edition, Richard L. Burden, J. Douglas Faires, Annette M. Burden, Cengage Learning Boston, USA
Numerical Analysis Using MATLAB® and Excel®, Third Edition, Steven T. Karris, Orchard Publications