Lecturer: Ugo Pietro Gianazza  

Course name: Analisi matematica C
Course code: 062249
Degree course: Ingegneria Meccanica
Disciplinary field of science: MAT/05
L'insegnamento costituisce attività di base per: Ingegneria Meccanica
University credits: CFU 6
Course website: http://www.imati.cnr.it/~gianazza/comp_anmat.html

Specific course objectives

The course complements the previous ones Analisi Matematica A and B. It gives an introduction of advanced topics such as optimization of functionals with or without contraints, ordinary and partial differential equations, calculus of variation, Fourier series and transform.

Course programme

Differential calculus and applications
Differential calculus for function of several variables. Dini theorem. Constrained extrema. Lagrange multipliers.

Systems of ordinary differential equations
Introduction to O.D.E.s. Cauchy problem and boundary value problems. Nonlinear equations in normal form. Systems of O.D.E.s. Higher order differential equations. Partial differential equations: Laplace problem, wave problem, heat problem.

Calculus of variation
Minima and maxima of functionals, Euler-Lagrange equation. Extremal and extremant lines. Applications.

Fourier series
Trigonometric polynomials and series. Fourier series: definition, uniform, L2, and point-wise convergence. Application to P.D.E.s. Fourier tranform

Course entry requirements

Analisi Matematica A, Analisi Matematica B, Geometria e Algebra.

Course structure and teaching

Lectures (hours/year in lecture theatre): 30
Practical class (hours/year in lecture theatre): 30
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

R.A. Adams. Calcolo differenziale 2. Casa Editrice Ambrosiana. (per il punto 1 del programma del corso).

C. Citrini. Analisi matematica 2. Editrice Bollati Boringhieri. (per i punti 2,3,4 del programma del corso).

C.D. Pagani - S. Salsa. Analisi Matematica 2. Masson. (per i punti 2,3,4 del programma del corso).

Testing and exams

The exam consists in a written test and an oral examination: they have to be taken in the same exam session.