


Politecnico di Torino  
Academic Year 2008/09  
19ACIES Mathematical analysis II 

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





Objectives of the course
Main goal of this course is to complete the introduction of the basic topics of mathematical analysis of functions of several variables. In particular, the theory of multiple integration and of surface integration is developed. Furthermore, numerical series and series of functions (power series and Fourier series in particular) and systems of ordinary differential equations are studied.

Expected skills
Familiarity with the subjects of the course and computational ability. Ability to read a technical text.

Prerequisites
The topics of the courses Analisi Matematica 1 and Geometria.

Syllabus
Differential calculus of functions of several variables; implicit functions; Lagrange multipliers; inverse function theorem and transformations of coordinate systems.
Integral calculus: multiple integration. Length of a curve and area of a surface. Curve and surface integration. Green, Gauss and Stokes Theorems. Conservative fields and differential forms. Numerical series and series of functions: definition and criteria for convergence. Power series and Taylor series. Series solutions of ordinary differential equations of the first order. Fourier series in real and complex form: computation of the coefficients and convergence properties. Systems of differential equations: solutions of linear systems. Qualitative behaviour of the solutions. 
Bibliography
The following texts are used in the courses of Analisi Matematica 2. Ask your teacher or look at the WEB page of your course for specific information.
A. Bacciotti, F. Ricci: Lezioni di Analisi Matematica 2, Levrotto&Bella J. P. Cecconi, G. Stampacchia, Analisi Matematica 2, Liguori N.Fusco, F. Marcellini, C. Sbordone, Elementi di Analisi Matematica due, versione semplificata per i nuovi corsi di laurea, Liguori Ed. M. Bramanti, C.D. Pagani, S. Salsa: Matematica, Calcolo infinitesimale e algebra lineare, seconda edizione, Zanichelli A. Bacciotti, P. Boieri, D. Farina: Esercizi di calcolo differenziale e integrale in pił variabili, Societą editrice Esculapio. F. Marcellini, C. Sbordone, Esercitazioni di matematica, secondo volume prima e seconda parte, Liguori Ed. S. Salsa  A. Squellati: Esercizi di Analisi Matematica 2, Parte prima, seconda, terza, Masson. V. Demidovich, Esercizi e problemi di Analisi Matematica, Editori Riuniti 
Check availability at the library 
Revisions / Exam
The exam consists of a written and of an oral part. The written part ascertains the familiarity of the student with the arguments of the course while the oral part is mostly concerned with the theory.
In order to be admitted to the oral part of the exam, students should score 15/30 or higher in the written part. 
