Politecnico di Torino
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Politecnico di Torino
Academic Year 2007/08
01GRFGI
Numerical methods
Master of science-level of the Bologna process in Physical Engineering - Torino
Teacher Status SSD Les Ex Lab Tut Years teaching
Monegato Giovanni ORARIO RICEVIMENTO     3 1 1 0 7
SSD CFU Activities Area context
MAT/08 5 C - Affini o integrative Cultura scientifica, umanistica, giuridica, economica, socio-politica
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 floating-point arithmetic. Conditioning of a problem. Numerical stability of an algorithm.
- Linear systems: direct methods (Gaussian eliminitation, LU-decomposition, Choleski) and iterative methods (Jacobi, Gauss-Seidel, SOR).
- Approximation of functions and data: polynomial and piecewise polynomial interpolation, splines, discrete least squares.
- Nonlinear equations: secant and Newton methods, fixed-point iteration.
- Numerical integration: Newton-Cotes formulas, Gaussian quadrature rules, composite rules.
- Initial value problems for ordinary differential equations: one-step methods (Runge-Kutta methods) and multistep (Adams) methods. Stiff problems.
- Introduction to MATLAB
- Scientific computing using MATLAB

Programma definitivo per l'A.A.2008/09
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