This course aims to introduce Scientific Computing through Matlab. Emphasis is placed on the capabilities offered by the Matlab environment for easily addressing problems of numerical methods, such as solving systems of equations, numerical interpolation, integration and differentiation, solving differential equations, etc.

Unit 1: Introduction to MATLAB
1. Basic Concepts – Getting Help – Numeric and Logical Expressions
2. Vectors and Matrices – Random Numbers
3. Procedural Programming – Scripts – Input – Output – Selection – Looping
4. Basic Plotting Commands
5. User-Defined Functions
6. Handling Character Strings
7. Complex Data Structures – Structures – Cell Arrays – Tables
8. Files
9. Advanced Topics in User-Defined Functions
10. More Plotting Functions
11. Live Scripts – Symbolic Variables – Expressions – Functions
Unit 2: Solving Mathematical Problems in MATLAB – Applications
12. Set Functions – Polynomials
13. Calculus, Series – Limits – Differentiation – Integration (Symbolic and Numeric)
14. Solving Equations and Systems Symbolically and Numerically
15. Linear Algebra, Sparse Matrices, Solving Linear Systems
16. Ordinary Differential Equations and ODE Systems, Initial and Boundary Value Problems,
Partial Differential Equations
17. Interpolation – Extrapolation – Approximation (Fitting)
18. Optimization – Linear and Integer Programming
19. Digital Signal Processing
20. Statistical Functions – Probabilities
21. Data Compression – SVD

Greek

Lectures, Practical Exercises