Lecturer: Luisa Donatella Marini  

Course name: Numerical Methods for Engineering Sciences
Course code: 502946
Degree course: Ingegneria Elettrica, Ingegneria Informatica
Disciplinary field of science: MAT/08
L'insegnamento costituisce attività di base per: Ingegneria Elettrica
The course relates to:
University credits: CFU 6
Course website: http://www.imati.cnr.it/marini

Specific course objectives

Aim: to enable students to classify real-life problems and choose the best suited algorithms for dealing with them, in terms of costs/benefits and convergence properties. At the same time, the course is meant to make students well acquainted with the use of software and with the practical implementation of some algorithms

Course programme

The course is divided in two parts, devoted essentially to boundary value problems for Partial Differential Equations (Pde's), and to initial value problems for Ordinary Differential Equations (Ode's). The basic common and necessary instruments to deal with both classes of problems are also developed.

Pde's

• Linear elliptic equations: various examples of applications
• Variational formulations (Lax-Milgram lemma)
• Approximation: Conforming finite element methods (error estimates)
• Comparison with finite differences
• Applications to various problems

Ode's

• Concept of stability
• Classical one-step methods (convergence properties)
• Multistep methods (Adams' family, convergence properties)
• Runge-Kutta methods
• Stiff systems

Common arguments
The following arguments are necessary instruments to tackle the two above classes of problems

• Solution of linear systems of equations (direct and iterative methods, stability analysis, condition number)
• Approximation of functions/data: Lagrange interpolation, least-squares
• Numerical integration: interpolatory and gaussian formulae in 1D, 2D formulae on rectangles and triangles
• Solution of nonlinear equations (bisection and Newton' method)

Course entry requirements

Differential and integral calculus for real functions; complex numbers; linear algebra; computer programming experience

Course structure and teaching

Lectures (hours/year in lecture theatre): 36
Practical class (hours/year in lecture theatre): 16
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

A. Quarteroni, R. Sacco, F. Saleri. Matematica Numerica - III edition. Springer-Verlag Italia, Milano 2008.

Testing and exams

Written dissertation on a couple of arguments developed during the semester. To access to the final exam it is compulsory to take part to the Matlab Laboratory, and to produce a written discussion. Admission to the exam upon a sufficient grade in the Laboratory work.