Floating point representation of numbers and round off errors. Conditioning of the problems and stability of the algorithms. Basic numerical methods for solving nonlinear equations and linear algebraic systems, polynomial interpolation, composite quadrature formulas and Richardson extrapolation. Basic notions of programming language FORTRAN.
1) M.G. Gasparo, R. Morandi: Elementi di calcolo numerico, metodi e algoritmi, McGraw Hill, 2008
2) G.Aguzzi, M.G.Gasparo, M.macconi: FORTRAN 77, uno strumento per il calcolo scientifico, Pitagora ed.,1987
Learning Objectives
Being able to write FORTRAN codes and use free codes. Having a whole vision of existing numerical methods for the problems discussed during the lessons and being able to choose the best one for solving a given problem. Being able to compare different methods based on theoretical properties and practical behaviors.
Prerequisites
Courses required: Mathemathics I
Teaching Methods
Total number of hours for Lectures (hours): 36
Total number of hours for Laboratory-field practice : 18
Type of Assessment
The exam consist in an oral test which consists in questions about the arguments seen during the course.
Course program
Introduction to algorithms and their main structures.
Floating point representation of numbers and round off errors. Conditioning of the problems and stability of the algorithms. Basic numerical methods for solving: nonlinear equations (bisection, Newton) ; linear algebraic systems (Gauss method with and without pivot), conditioning of a linear system, error analysis; polynomial interpolation (Lagrange polynomial), interpolation error, conditioning of interpolation problem, trigonometric interpolation and truncated Fourier Series,linear least-squares; Integration rules:
Trapezi and Simpson methods, composite quadrature formulas (Trapezoidal formula, Simpson formula, Richardson extrapolation). Basic notions of programming language FORTRAN.