


Politecnico di Torino  
Academic Year 2017/18  
26AGIMW Numerical methods 

Master of sciencelevel of the Bologna process in Chemical And Sustainable Processes Engineering  Torino 





Subject fundamentals
This course provides an introduction to basic tools for the numerical solution of mathematical problems arising from applications. In particular the course focuses on reliability of algorithms and evaluation of their cost both in terms of computational complexity and of memory occupancy, to prepare students to a critic usage of commercial software.

Expected learning outcomes
The students should acquire the capability to solve a simple mathematical model: to choose an appropriate method, to derive an efficient algorithm and to implement it in MATLAB language. Reliability of the results obtained should also be evaluated.

Prerequisites / Assumed knowledge
Students are intended to be familiar with contents of the courses of Mathematical Analysis and Geometry.

Contents
Computer arithmetic. Well/Badly conditioned problems. Stable/Unstable algorithms.
Linear systems: Direct methods (Gauss elimination, LU Factorization, Choleski Factorization), Iterative methods (Jacobi, gaussSeidel, methods for solving large systems). Approximation of data and functions (Polynomial and piecewise polynomial interpolation, splines, leastsquares approximation). Solution of nonlinear equations and systems of nonlinear equations (Newton's method, fixed point method). Numerical Integration: NewtonCotes formulas, Gaussian Quadrature, Composite rules. Ordinary differential equations with initialvalue conditions: onestep methods (RungeKutta) and multistep methods (Adams), Stiff problems. Ordinary differential equations with boundary conditions: Collocation method, Galerkin method. Partial differential equations: classification of quasilinear second order equations, finite difference method for hyperbolic and parabolic equations, stability and convergence, finite difference method for elliptic equations; collocation method, Galerkin method, finite element method. 
Delivery modes
Exercises at the LAIB's developed by using MATLAB.
Examples of use of the methods and solution of test problems. Engineering applications mostly in chemical engineering field. 
Texts, readings, handouts and other learning resources
Giovanni Monegato, Metodi e Algoritmi per il Calcolo Numerico, CLUT, 2008.
Letizia Scuderi, Laboratorio di Calcolo Numerico, CLUT, 2005. Texts and solutions of many exercises are available in the section Materiale Didattico on the portal. Engineering applications proposed during the lectures are available on the portal. 
Assessment and grading criteria
Assessment consists of a written 2 hours examination on theory and applications. One question is devoted to MATLAB and requires a short program. Books or notes are not admitted. A pocket calculator may be used. On student's request an oral test may follow, if the written examination mark is at least equal to 17/30.

