Calculus of functions of one or more real variables; linear algebra.

Algorithms and methods of approximate solution of algebraic and differential equations, with computer experiments.

The Students will reach the following objectives:

• Knowledge and understanding: partial differential equations and their origin as mathematical models for physics and engineering.

• Ability to apply knowledge and understanding: computational abilities for differential equations. The techniques will be tought during the lectures.

• Autonomy: all concepts will be based on computations that the Students can repeat or expand in an autonomous way, and can be used in a variety of situations.

• Communicating abilities: the course does not involve comminicative abilities in a significant way.

• Learning abiliites: the Students will learn that complex mathematical problems can be solved with computer.

Lectures and computer experiments.

Oral exam on the course program (as exposed during the lectures) and proof of knowledge of the Matlab language.

Matrix computations
Principles of numerical mathematics
Direct methods for the solution of linear systems
Iterative methods for the solution of linear systems
Iterative methods for eigenvalues and eigenvectors
Solution of non-linear algebraic equations
Polynomial interpolation of functions and data
Numerical integration
Orthogonal polynomials and Fourier transform
Numerical solution of ODEs

Introduction to PDEs for Engineers
Finite difference methods and finite element methods for PDEs.
 

Quarteroni, Sacco, Saleri: Numerical Mathematics, 2nd ed., Springer 2006.