Learning objectives
Knowledge and critical use of numerical algorithms for the numerica solution of engineering applications.
Prerequisites
Knowledge and use of the basic elements of mathematical analysis and linear algebra.
Course unit content
1. INTERPOLATION and APPROXIMATION - Polynomial Interpolation. Divided differences and the Newton form of the interpolating polynomial. Interpolation at equally spaced points. Error of polynomial interpolation. Polynomial interpolation with derivative data. Interpolation by linear and cubic splines. Interpolation in several variables.
2. SOLUTION of LINEAR SYSTEM of EQUATIONS - Gauss elimination Pivoting and scaling in Gauss elimination. LU-decomposition. Condition numbers and error estimates. Iterative improvement. Iterative methods (Jacobi's method).
3. SOLUTION of NONLINEAR EQUATIONS - Introduction. Bracketing methods. Newton's method. Rate of convergence.
4. NUMERICAL INTEGRATION - Introduction. Interpolatory numerical integration. Newton-Cotes formulas. Errors of quadrature formulas. Composite rules for numerical integration. Multiple integrals.
5. MATLAB.
Full programme
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Bibliography
1. G. Monegato: Fondamenti di Calcolo Numerico. CLUT
2. G. Naldi, L. Pareschi, G. Russo: Introduzione al Calcolo SCIENTIFICO. MacGraw-Hill.
3. A. Mazzia: Laboratorio di Calcolo Numerico, Applicazioni con MATLAB e OCTAVE, Pearson.
4. L. Scuderi: Laboratorio di Calcolo Numerico, CLUT.
5. Lee W. Johnson, R. Dean Riess: Numerical Analysis, Addison- Wesley Publishing Company.
Teaching methods
Frontal lessons.
Assessment methods and criteria
The exam consists of a short written test with some numerical exercises and programming of simple numerical algorithms in MATLAB and a subsequent oral test. It is possible to be exempted from the written test by delivering the exercises that will be proposed by the teacher during the period of the lessons. The exemption from the written test is valid for the entire academic year.
Other information
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