Lecturer: Daniele Boffi   Claudio Cusano   Raffaella Guglielmann  

Course name: Numerical Analysis And Programming
Course code: 502525
Degree course: Ingegneria Civile e Ambientale
Disciplinary field of science: MAT/08,ING-INF/05
L'insegnamento costituisce attività di base per: Ingegneria Civile e Ambientale
University credits: ECTS 12
Course website: n.d.

Specific course objectives

The course provides an introduction to the basic tools of Numerical Analysis and Programming. In particular, the course aims at showing the most commonly used algorithms for the solution of practical problems. The algorithms are presented with the help of Matlab software.

Course programme

The course is split into two parts: Numerical computing and Computing. The first part is taught in the first semester, the second part in the second one. Both parts contains theoretical and practical lectures.

Argomento da modificare
Numerical analysis: here is the list of subjects.

• Nonlinear equations: bisection method, Newton method. Convergence and convergence order. Stopping criteria.
• Approximation of functions and data: Lagrange interpolation, piecewise polynomial interpolation; least square method and data fitting: linear regression.
• Numerical integration and differentiation: Approximation of the derivative. Quadrature rules: midpoint, trapezoidal, and Simpson rules. Gauss formulae.
• Direct solvers for linear system: condition number and eigenvalue problems. Gaussian elimination and LU factorization; implementation and complexity of LU factorization; symmetric and positive definitive matrices: Cholesky factorization.
• Iterative solvers for linear systems: Jacobi, Gauss-Seidel, and relaxation; implementation and convergence; stopping criteria.
• Numerical solution of ordinary differential equations: one-step methods: forward and backward Euler, Crank-Nicolson, Heun; stability and A-stability, consistency, convergence and convergence order; computational aspects.

Principles of computer science and programming

• Representation of the information: integers and rational numbers; representation of negative numbers; fixed and floating point representations. Encoding of text and multimedia.
• Computer architecture: Von Neumann's architecture; machine language; instruction execution cycle; memory devices and input/output devices.
• Algorithms: definitions and properties; analysis of their correctness and complexity. Search and sorting algorithms.
• The Matlab programming language: variables and expressions; control structures; functions and recursion.

Course entry requirements

Real differential and integral calculus. Complex numbers. Vector and matrix calculus. Practical computer skills.

Course structure and teaching

Lectures (hours/year in lecture theatre): 90
Practical class (hours/year in lecture theatre): 0
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

A. Quarteroni, F. Saleri , P. Gervasio. Calcolo scientifico: Esercizi e problemi risolti con MATLAB e Octave (V ed.). Springer, 2012.

Testing and exams

Written midterm exam at the end of the first semester (numerical analysis); written midterm exam at the end of the second semester (programming) for students who passed the first midterm exam. Written exams on the entire program for student who fail the midterms. Oral exam for students who do not reach a prescribed threshold. More details are available from the web page: http://www-dimat.unipv.it/gugliel/teaching.html