NUMERICAL ANALYSIS

Introduction (discretization, error analysis), Numerical Differentiation (forward, backward and central differences), Numerical Integration (trapezoid rule, Simpson rule, Newton-Cotes formulae), Interpolation/Extrapolation (Taylor, Lagrange polynomials), Numerical solution of algebraic equations (trial & error, bisection, Newton-Raphson), Numerical solution of linear systems (Gauss, Jacobi, Gauss-Seidel), Numerical Integration of Ordinary Differential Equations (Euler, Runge-Kutta), Finite Differences.

Objectives

At the end of this course the student should have a good insight of the numerical methods and must be able to apply them in Engineering problems. At the end of the course the student will have further developed the following skills/competences: 1. Ability for deep understanding of the fundamental numerical methods. 2. Ability to recognize the advantages and disadvantages of each method in order to decide the most convenient in use on application basis. 3. Ability to use specific software in order to develop the necessary applications.

Prerequisites

There are no prerequisite courses. It is, however, recommended that students should have a good knowledge of Mathematics (Calculus, Linear Algebra, Differential Equations) as well as fundamental skills on Scientific Programming.

Syllabus

Introduction (discretization, error analysis), Numerical Differentiation (forward, backward and central differences), Numerical Integration (trapezoid rule, Simpson rule, Newton-Cotes formulae), Interpolation/Extrapolation (Taylor, Lagrange polynomials), Numerical solution of algebraic equations (trial & error, bisection, Newton-Raphson), Numerical solution of linear systems (Gauss, Jacobi, Gauss-Seidel), Numerical Integration of Ordinary Differential Equations (Euler, Runge-Kutta), Finite Differences, Special Topics, Non-linear systems.