Lecturer: Luisa Donatella Marini  

Course name: Numerical Analysis and Programming
Course code: 502525
Degree course: Ingegneria Civile e Ambientale
Disciplinary field of science: ING-INF/05 MAT/08
L'insegnamento costituisce attività di base per: Ingegneria Civile e Ambientale
University credits: CFU 12
Course website: http://www.imati.cnr.it/marini

Specific course objectives

The course is meant to make the students aquainted with the basic tools of Numerical Analysis and Programming. In particular, the most commonly used numerical algorithms to deal with practical problems will be illustrated, together with their practical implementation.

Course programme

The course is made of two modules: NUMERICAL ANALISIS and PROGRAMMING. These two modules complement each other, and will be carried out mostly together. Classes and practical programming sessions will go one after the other, in order to deeply develop, from theory to practice, all the subjects presented.

NUMERICAL ANALYSIS Module
The following is a list of the subjects which will be developed:

• Nonlinear equations: bisection and Newton's methods. Convergence and order of convergence. Stopping criteria.
• Functions and data approximation: Lagrange interpolation, simple and composite. Least square method for data fitting: linear regression and other examples.
• Numerical derivation and integration: Approximation of derivatives. Quadrature formulae: mid-point, trapezoidal, and Simpson rules, simple and composite.
• Direct methods for solving linear systems: Conditioning problem; Gaussian elimination and LU factorization; Implementational aspects of LU factorization and costs; Simmetric and positive definite matrices: Cholesky factorization.
• Iterative methods for solving linear systems: Jacobi, Gauss-Seidel, and relaxation methods; Convergence results and implementational aspects; Stopping criteria.
• Numerical solution of ordinary differential equations: One-step methods: explicit and implicit Euler, Crank-Nicolson, Heun;Stability and A-stability, consistence, convergence and orders of convergence; Computational aspects.

COMPUTER PROGRAMMING Module

• Representation of information: binary and hexadecimal notation.
• Types of data: integer and real number, string, array, matrix, file.
• Algorithm: fundamental, programming and debugging.
• MatLab programming language: development kit, types of data, control structures, toolbox, file system, scientific visualization.
• Fortran programming language: development kit, types of data, control structures, file system.

Course entry requirements

Integral and differential calculus for real functions; complex numbers; vectors and matrices. Windows Operating System.

Course structure and teaching

Lectures (hours/year in lecture theatre): 70
Practical class (hours/year in lecture theatre): 34
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

A. Quarteroni, F. Saleri. Introduzione al Calcolo Scientifico - II Edizione. Springer-Verlag Italia..

Adrian Biran, Moshe Breiner. MATLAB for engineers . Addison-Wesley.

Testing and exams

Final written exam. Oral exam (not compulsory) after a sufficient grade in the written part. For details on the oral part see http://www.imati.cnr.it/marini

Writing and debugging of software MatLab and Fortran.