Numerical Analysis

• Introduction to Numerical Analysis, Numerical Systems, Representation of Numbers,
Conversions, Floating – point numbers, Errors, Absolute and relative error, Propagation of
uncertainty, Accuracy.
• Linear Systems, Linear System Solving, Cramer’s Rule, Gauss Method, Gauss – Jordan
Method, Thomas’ algorithm, LU decomposition, Cholesky decomposition
• Iterative Methods for Solving Linear Systems, Convergence Conditions, Jacobi method,
Gauss – Seidel method.
• Solving nonlinear equations and systems, Roots of nonlinear equations, Long Division,
Bisection method, Newton Raphson method, Intersection method, Nonlinear System
Solving.
• Numerical integration, Rectangle method, Simpson’s 1/3 rule, Simpson’s 3/8 rule,
Composite functions.
• Interpolation and Extrapolation, Numerical Approach, Polynomial interpolation, Lagrange
polynomial, Newton polynomial, Least squares.
• Solving first order linear differential equations, Euler Method, Runge – Kutta Method.

Upon successful completion of this course, students will be able:
• to understand the basic arithmetic methods.
• to estimate the advantages and disadvantages of the methods.
• to distinguish the differences between the methods in order to choose the most
appropriate one for the problem they are called to solve.
• to design and develop mathematical modeling and numerical analysis algorithms.
• to compose and / or use appropriate software to implement the required application.
• to explain the results of different methods based on absolute and relative errors.
• to evaluate and compare Numerical Analysis methods.
• to judge the appropriateness of each arithmetic method in specific problems.

Mathematical Analysis I , II, Applied Mathematics,
Introduction to Structured Programming

Assessment methods: Two mandatory sets of assignments (30%)
and a final written exam (70%).
Assessment criteria: They are explicitly mentioned in the first
lesson and are announced on the course website.

- Recommended Book Resources:
1. Sarris I.- Karakasidis Th., Numerical Methods and Applications
for Engineers, A. TZIOLA PUBLICATIONS, Edition: 4th/ 2019.
2. Papageorgiou G. Tsitouras Ch., Numerical Analysis with applications
in MATHEMATICA and MATLAB, TSOTRAS AN
ATHANASIOS, Edition: 1st / 2015.
3. Chapra S. - Canale R., Numerical Methods for Engineers, A.
TZIOLA PUBLICATIONS, Edition: 7th / 2016.
4. AKRIVIS GD, DOUGALIS BA, INTRODUCTION TO NUMERICAL
ANALYSIS, UNIVERSITY EDITION. CRETE, Edition: 4th / 2015.