


Politecnico di Torino  
Academic Year 2016/17  
03KXULP, 04KXULM, 04KXUOD, 04KXUPC Mathematical analysis II 

1st degree and Bachelorlevel of the Bologna process in Electronic And Communications Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Computer Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Physical Engineering  Torino Espandi... 





Subject fundamentals
The teaching 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 teaching provides the foundation for some numerical methods that are considered essential for scientific computation, and for the MATLAB programming language, which is widely used in the engineering field.

Expected learning outcomes
The knowledge that will be obtained through this teaching 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 planar and solid figures.
Concerning the part relating to numerical analysis, the student will be able to solve simple numerical problems, that generally occur as intermediate steps in the solution of more complex mathematical problems and that can not be solved analytically. 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 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 teaching. In particular, this teaching 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. Moreover, the knowledge of the primary programming syntax is required.

Contents
• Numerical series (6 hours)
• Sequences and series of functions (4 hours) • Taylor expansions and power series (10 hours) • Fourier series (10 hours) • Multiple integrals and integral calculus in several variables (20 hours) • Computer arithmetic, errors (3 hours) • Numerical solution of linear systems (6 hours) • Approximation of functions and data (5 hours) • Computation of roots of non linear equations (3 hours) • Computation of integrals of one variable functions (3 hours) 
Delivery modes
The teaching consists of 50 hours of theoretical lectures and 30 hours of exercises. Among the lasts, 20 hours are carried out at the blackboard, and 10 in the computer room, where the numerical algorithms presented in the lectures are implemented by using MATLAB software.

Texts, readings, handouts and other learning resources
C. Canuto, A. Tabacco, Mathematical Analysis II, Springer 2015.
A. Quarteroni, F. Saleri, Scientific Computing with MATLAB and OCTAVE, Springer, 2006. 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 hours written test. At the discretion of the teacher, an additional colloquium concerning the written exam might be required. The exam includes theoretical and practical questions. The minimum mark to pass the exam is 18; at least 10 points must come from exercises on 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.

