


Politecnico di Torino  
Academic Year 2012/13  
01NKIMC Numerical and statistical methods for engineering 

1st degree and Bachelorlevel of the Bologna process in Civil Engineering  Torino 





Subject fundamentals
In the section devoted to the differential equations, the course deepens, by means of the analysis of some models, two main notions particularly useful in the applications: the stability of the equilibrium configurations and the oscillations.
The basic notions concerning the elementary probability are given, as well as those instruments used to represent the random behavior of physical quantities in ingeneering phenomena. Moreover, the course provides the foundation for those methods that are considered essential for scientific computation and that generally occur as intermediate steps in the solution of more complex mathematical models for engineering problems. 
Expected learning outcomes
The student acquires and deepens the fundamental notions of the theory of the dynamical systems.
In particular, by the end of the course, the student will be able to recognize a configuration of equilibrium, to determine the stability and to draw the phase portraits for some kind of second order differential equations. Concerning the part relating to numerical analysis, essential concepts and methods commonly used to solve simple numerical problems will be acquired. By the end of the course, the student will be able to identify an efficient method for the solution of a given problem, to implement it by means of MATLAB/OCTAVE software and to give a critical interpretation of the numerical results obtained. 
Prerequisites / Assumed knowledge
Working knowledge is required of mathematical notions and tools introduced during the first year courses. In particular, this course relies upon the basic notions of differential and integral calculus in one variable, linear
algebra, elementary mechanics. 
Contents
Differential equations as flows. Onedimensional case (Malthus, Verhulst), equilibrium, stability, impossibility of oscillations. Twodimensional case (equations of Mechanics, LotkaVolterra), closed orbits, limit cicles, PoincaréBendixson's Theorem. Non linear oscillations, equations of superior order (3cfu).
Elementary probability: axioms, conditional probability, Bayes' Theorem. The use of continuous distributions, such as the normal (gaussian) and the lognormal, to represent the random behavior of physical engineering quantities (2cfu). Generalities on numerical problems and algorithms. Short description of basic numerical methods for the solution of linear systems, for the approximation of functions, for the computation of integrals and for the solution of ordinary differential equations (3cfu). 
Delivery modes
Exercises will cover the topics of the lectures. Some will be carried out by the teacher at the blackboard, others will actively involve the students. Moreover, computer room activity (1 cfu) is also scheduled,
where the numerical algorithms presented in the lectures will be implemented by using MATLAB/OCTAVE software. The application of these algorithms to very simple problems, allows to study some properties of the numerical methods presented and to give a critical analysis of the numerical results obtained. 
Texts, readings, handouts and other learning resources
S. Strogatz, "Nonlinear dynamics and Chaos", AddisonWesley, 1994,
Chap. I – VIII G. Monegato, Metodi e algoritmi per il Calcolo Numerico, CLUT 2008. L. Scuderi, Laboratorio di Calcolo Numerico. Esercizi di Calcolo Numerico risolti con Matlab, CLUT 2005. Ulteriore materiale didattico quale lezioni online, dispense, esercizi proposti ed esercizi svolti sarà reso disponibile sul Portale della Didattica. 
Assessment and grading criteria
The final exam consists of a two hour written test. At the discretion of the teacher, an additional colloquium concerning the written exam might be required. The exam includes theoretical and/or practical questions.
The minimum mark to pass the exam is 18; at least 5 points must come from the exercises concerning the differential equations, at least 5 points from exercises on numerical methods and at least 4 points from exercises on statistics. During the exam, no course material is allowed. It is forbidden to use electronic devices, mobile phones and scientific calculators. 
