


Politecnico di Torino  
Academic Year 2007/08  
02ACIBK Mathematical analysis II 

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





Objectives of the course
This course gives the students the skills to use basics of differential and integral calculus with many variables, of equations and of differential systems, of functions series.

Expected skills
The student must be able to use the knowledge acquired in applicative situations.

Prerequisites
A good knowledge of differential and integral calculus in a variable and of some basics of liner algebra is required.

Syllabus
Elements of applicative geometry in the space.
Functions of many variables: partial and directional derivatives, gradients. Multiple integration applied to calculus of areas and volumes and to geometry of masses. Integration on curves and surfaces and linear and flux integrals. Systems of differential equations with constant coefficients. Numerical series, introduction to series of functions. Series of powers and Fourier's series with applications. Tutorship: Professros are available to explain the students some topics of the program and of practicals, and to check, in an informal way, the learning of the students. Students are divided into two groups. 
Laboratories and/or exercises
Practicals are on lectures' themes; they are carried out at the blackboard or at the PC and they are held by professors and carried out by students at their own PCs. Students are divided into two groups.
Didactic Material The didactic material is made up partly of reference books and partly of material prepared by the lecturer. Supplementary texts available at the library: Apostol T., Calcolo. Volume III, Bollati Boringhieri Bacciotti A., Ricci F., Analisi Matematica II, Liguori Ed. Bacciotti A., Boieri P., Farina D. Chiti G., Esercizi di Analisi Matematica II, Soc. Ed. Esculapio Conti F., Calcolo: Teoria e applicazioni, McGraw Hill Exam Procedure The exam may not be taken by anyone who has not previously passed the exams for Mathematical Analysis I. The exam consists of a written paper which may be supplemented by an oral test. The consultation of texts is not permitted during the written test. 
