


Politecnico di Torino  
Anno Accademico 2009/10  
02LSBJA Calculus III 

Corso di Laurea in Electronic And Computer Engineering  Vercelli 





Obiettivi dell'insegnamento
To provide the fundamental concepts about calculus in several variables and in the theory of Fourier series.

Competenze attese
At the end of the course the student is expected to be able to deal with problems in differential and integral calculus in several cariables, including continuity and differentiability of functions of several variables, the calculation of free and constrained extremals, multiple integration in several variables, analysis of vector fields, line and surface integrals, Fourier series

Prerequisiti
Analysis in one variable, as given in the courses of Calculus I and Calculus II, has to be known in order to deal with the topics of the present course.

Programma
Continuity of function of several variables. Differentiability. Partial derivatives and elementary calculus. Implicit functions. Extremals of functions of several variables. Lagrange multipliers. Multiple integration. Improper integrals. The formula of change of variables in multiple integrals, the Jacobian. Vector fields. The conservative case. Line integrals. Surface integrals Flux of a vector field through a surface. The gradient, curl, and divergence operators. Green formulas. The divergence Theorem. Stokes Theorem. Fourier series and their convergence. Orthonormal systems in functions spaces.

Laboratori e/o esercitazioni
There will be class exercises on each part of the course.

Bibliografia
R. Adams, Calculus, Pearson ed.

Controlli dell'apprendimento / Modalità d'esame
The exam will consist of a written examination on the topics indicated above. An oral examination can be required as well in addition.

Orario delle lezioni 
Statistiche superamento esami 
