


Politecnico di Torino  
Academic Year 2010/11  
23ACINX, 23ACIOD Mathematical analysis II 

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





Subject fundamentals
This course provides the basic notions of integral calculus in several variables and along curves. It also introduces the basic theory of numerical series and series of functions, in particular power series, Taylor expansions and Fourier series.
Finally, 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 obtained through this course will include basic tools of multivariate integral calculus and the theory of numerical series and series of functions. In particular, by the end of the course 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. Moreover, 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.
Concerning the part relating to numerical analysis, the knowledge obtained through this course will consist of essential concepts and methods commonly used to solve simple numerical problems. By the end of the course, the student will be able to identify the most efficient method for the solution of a given problem, to implement it by means of Matlab software and to interpret 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, differential calculus in several variables, and linear algebra.

Contents
Multiple integrals and integral calculus in several variables (10 hours).
Numerical series and series of functions (10 hours). Taylor expansions and power series (10 hours). Fourier series (8 hours). Generalities on numerical problems and algorithms (3 hours). Short description of basic numerical methods for the solution of linear systems (5 hours), for the approximation of functions and numerical data (6 hours), for the computation of roots of nonlinear equations (3 hours), and for the computation of integrals (3 hours). 
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 (10 hours) is also scheduled for the numerical simulation of some properties of the numerical methods presented in the lectures, using MATLAB software.

Texts, readings, handouts and other learning resources
C. Canuto, A. Tabacco, Analisi Matematica II, Springer 2008
G. Monegato, Metodi e algoritmi per il Calcolo Numerico, CLUT 2008. The exact texts, chosen from those in the following list, will be described by the teacher in class. C. Canuto, A. Tabacco, Mathematical Analysis II, Springer 2010. G. Monegato, Metodi e algoritmi per il Calcolo Numerico, CLUT 2008. 
Assessment and grading criteria
Written examination.

