


Politecnico di Torino  
Academic Year 2015/16  
24ACIOA, 24ACIPC Mathematical analysis II 

1st degree and Bachelorlevel of the Bologna process in Computer Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Cinema And Media Engineering  Torino 





Subject fundamentals
This course provides the basic theory of numerical series and series of functions, in particular power series, Taylor expansions and Fourier series. It also introduces the basic notions of integral calculus in several variables. 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 knowledge that will be obtained through this course includes basic tools of theory of numerical series and series of functions and of the multivariate integral calculus. In particular, by the end of the course, the student will be able to handle series of numbers and functions, and will be familiar with the basic tools of Fourier analysis with discrete frequencies. Moreover, the student will be able to set out (and, in some cases, also carry out explicitly) the computation of quantities such as areas and volumes, moments of inertia and centroids of complex planar and solid figures.
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, geometry of curves and surfaces, differential calculus in several variables. 
Contents
Numerical series and series of functions (1 cfu).
Taylor expansions and power series (1 cfu). Fourier series (1 cfu). Multiple integrals and integral calculus in several variables (2 cfu). Generalities on numerical problems and algorithms. Short description of basic numerical methods for the solution of linear systems, for the approximation of functions and numerical data, for the computation of roots of nonlinear equations, and for the computation of integrals (3cfu). 
Delivery modes
Exercises (2 cfu) 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
C. Canuto, A. Tabacco, Mathematical Analysis II, Springer 2010.
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. Further course material as lectures online, lecture notes, proposed and solved exercises will be given through the ‘portale della didattica’ website. 
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 10 points must come from series and multiple integrals and at least 5 points must come from exercises on numerical methods. During the exam, no course material is allowed. It is forbidden to use electronic devices, mobile phones and scientific calculators. 
