The course will discuss, from both the analytic and computational points of view, the principal basic numerical methods for the solution of nonlinear equations, linear systems, polynomial data fitting and numerical quadrature. The course has a Laboratory component where the methods studied will be implemented using the MATLAB programming platform (using either the official Matlab from Mathworks or else the open source version GNU OCTAVE). At the end of the course the student will be expected to demonstrate that s/he has attained a level of competence in the computational and computer aspects of the course subject, as well as the ability to recognize which algorithms are appropriate for basic problems of numerical analysis.
The course will discuss the following topics:
Methods for finding zeros of functions (bisection, secant, Newton and its variants)
Floating point numbers and error theory
Methods for solving linear systems (conditioning, Gaussian elimination, LU factorization, Cholesky factorization, matrix norms)
Polynomial interpolation and piecewise linear interpolation
Quadrature rules, simple and composite (Rectangle Rule, Trapezoidal Rule, Simpson’s Rule, Romberg extrapolation)
It is expected that there will be a tutor to help with the correction of assigned exercises and with the Laboratory sessions.
|E. Süli, D. F. Mayers||An Introduction to Numerical Analysis (Edizione 1)||Cambridge University Press||2003|
|S. De Marchi||Appunti di Calcolo Numerico (Edizione 1)||Societa Edirice Esculapio||2011||978-88-7488-473-5|
|A. Quarteroni, F. Saleri||Calcolo Scientifico, Esercizi e problemi risolti con MATLAB e OCTAVE||Springer||2008|
|J. Stoer, R. Bulrisch||Introduction to Numerical Analysis (Edizione 1)||Springer||1993|
The purpose of the exam is to see if the student is able to recall and reproduce the theory of basic Numerical Analysis and knows how to use Computer resources for possible further investigation. Moreover, the student must show that s/he knows how to program in the specific software introduced during the course. The exam will consist of two parts. The first part will be held in a Laboratory where the student will be given two hours to individually implement the numerical methods necessary for the solution of the assigned questions. The questions will be based on the entire course material. A pass will be given for a mark of 18/30 or higher. To be admitted to the second part of the exam, the oral, it is required to have first passed the written part. Marks for the written part will remain valid until, and not after, the beginning of the following semester. The oral exam will be based on the topics discussed during the classroom lectures. The final course mark will be the average of the marks for the two parts of the exam.