Teacher

prof. Dario FASINO

Credits

6 CFU

Objectives

This course is specifically intended for engineering students who need to understand the fundamental principles of modern numerical analysis and key numerical methods for the computer solution of basic scientific problems.

Acquired skills:

- Analyze and solve numerically problems in continuum mathematics, appraise result reliability, and recognize restraints on accuracy and workload arising from computational resources.

Contents

Fundamentals in numerical computing (20 hours):
Basic concepts and tools in numerical analysis and computational mathematics. Computer arithmetics (floating-point computations). Error analysis. Conditioning of computational problems, algorithmic stability concepts, convergence of iterative methods.

Numerical linear algebra (20 hours):
Classical matrix factorizations. Direct methods for the solution of linear systems and least squares problems. Iterative methods based on matrix splittings, descent methods, Krylov methods.

Selected topics in computational mathematics (20 hours):
Nonlinear equations and systems. Numerical integration of functions by interpolatory and composite rules. Ordinary differential equations: numerical solutions of Cauchy problems.Finite difference method.

References:

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri. Numerical Mathematics. Springer.

Type of exam:

One final exam, written + oral.