Lecturer: Ugo Pietro Gianazza  

Course name: Basic tools for partial differential equations
Course code: 502939
Degree course: Ingegneria Civile
Disciplinary field of science: MAT/05
The course relates to:
University credits: CFU 6
Course website: http://www.imati.cnr.it/~gianazza/comp_anmat.html

Specific course objectives

The course complements the previous one Analisi Matematica. 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.

Differential Equations
Introduction to Ordinary Differentail Equations. Cauchy problem and boundary value problems. Nonlinear equations in normal form. Systems of Ordinary Differentail Equations. Higher order differential equations. An introduction to 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 Analysis
Trigonometric polynomials and series. Fourier series: definition, uniform, L2, and point-wise convergence. Applications to Partial Differential Equations. An introduction to Fourier tranform

Course entry requirements

Analisi Matematica, Geometria e Algebra.

Course structure and teaching

Lectures (hours/year in lecture theatre): 22
Practical class (hours/year in lecture theatre): 43
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

R.A. Adams. Calcolo differenziale 2. Casa Editrice Ambrosiana. (for topic 1 of the course syllabus).

C. Citrini. Analisi matematica 2. Editrice Bollati Boringhieri. (for topics 2,3,4 of the course syllabus).

C.D. Pagani - S. Salsa. Analisi Matematica 2. Masson. (for topics 2,3,4 of the course syllabus).

Testing and exams

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