Finite precision computation. Numerical solution of linear systems and ordinary differential equations. Data and function approximation. Fundamentals of image analysis.
Numerical methods for engineers - Chapra, S., Canale, R., Mc-Graw Hill.
Numerical methods and software - Kahaner, D., Moler, C.; Nash, S., Prentice Hall
Introduction to Matlab for engineers, W. Palm III, Mc-Graw Hill, 2005.
Learning Objectives
Knowledge of the most used numerical methods for solving linear equations, approximating data and functions
and solving differential problems.
Ability to apply the methods studied to application oriented problems.
Prerequisites
Fundamentals of linear algebra and calculus
Teaching Methods
Lectures (34 hours) and Matlab laboratory (14 hours)
Type of Assessment
Oral exam
Course program
Algorithms. Floating point arithmetic. Finite precision. Norms of matrices and vectors. Conditioning of a problem.
Stability of an algorithm.
Direct methods for linear systems: Gauss method and pivoting strategies.
Data and function approximation: interpolation and least-squares data fitting.
Approximate solution of initial value problems and boundary value problems for ordinary differential equations: Runge-Kutta methods and finite difference methods.
MATLAB: Handling matrices, operations between matrices. Function and script files. If, while and for commands.
2D e 3D plots. Built-in functions for linear systems, basic fitting, ordinary differential equations.
Introduction to the use of tools for image analysis.