


Politecnico di Torino  
Academic Year 2007/08  
01GRFGI Numerical methods 

Master of sciencelevel of the Bologna process in Physical Engineering  Torino 





Objectives of the course
The course is introductory to scientific computation.
The goal of the course is the description of basic numerical methods used in scientific computing. A simple mathematical derivation for each method is either given or outlined. Emphasis is placed on understanding why numerical methods work, their computational cost, efficiency and limitations. It is assumed that students are familiar with calculus and have taken a course on programming. MATLAB has become a fundamental and widespread tool for engineers and applied mathematicians to perform scientific computation. For this reason, we also present the main features of this software and experimentation of the MATLAB subroutines which implement the numerical methods described in the course. 
Prerequisites
Basic linear algebra, calculus and computer programming.

Syllabus
 Basic concepts of floatingpoint arithmetic. Conditioning of a problem. Numerical stability of an algorithm.
 Linear systems: direct methods (Gaussian eliminitation, LUdecomposition, Choleski) and iterative methods (Jacobi, GaussSeidel, SOR).  Approximation of functions and data: polynomial and piecewise polynomial interpolation, splines, discrete least squares.  Nonlinear equations: secant and Newton methods, fixedpoint iteration.  Numerical integration: NewtonCotes formulas, Gaussian quadrature rules, composite rules.  Initial value problems for ordinary differential equations: onestep methods (RungeKutta methods) and multistep (Adams) methods. Stiff problems.  Introduction to MATLAB  Scientific computing using MATLAB 
