Lecturer: Carlo Lovadina  

Course name: Complementi di analisi matematica
Course code: 064003
Degree course: Ingegneria per l'Ambiente e il Territorio
Disciplinary field of science: MAT/05
L'insegnamento costituisce attività di base per: Ingegneria per l'Ambiente e il Territorio
University credits: CFU 3
Course website: n.d.

Specific course objectives

The Course aims at proving the very basic tools to study linear elliptic, parabolic and hyperbolic PDEs.

Course programme

The following topics will be addressed.

First order PDEs.
The linear case with constant coefficients. The Cauchy problem.

Second order PDEs.
Homogeneous linear equations with constant coefficients. Characteristic curves. Classification of second order PDEs. Elliptic equations: the Poisson problem; variational formulations. Parabolic equations: the initial-boundary problem; variational formulations. Hyperbolic equations: wave propagation, initial-boundary problem; variational formulations.

Course entry requirements

Basic Calculus for one and several variable real functions. Complex numbers. Fundamentals of linear algebra.

Course structure and teaching

Lectures (hours/year in lecture theatre): 17
Practical class (hours/year in lecture theatre): 11
Practicals / Workshops (hours/year in lecture theatre): 0
Project work (hours/year in lecture theatre): 0

Suggested reading materials

S. Salsa. Equazioni a derivate parziali. Metodi, modelli e applicazioni. Springer Italia, 2004.

A. Quarteroni. Numerical models for differential problems. Springer, 2009.

Testing and exams

Oral final exam