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University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

NUMERICAL METHODS FOR APPLICATIONS
cod. 23699

Academic year 2007/08
1° year of course - First semester
Professor
Academic discipline
Analisi numerica (MAT/08)
Field
Discipline scientifiche e ingegneristiche
Type of training activity
Related/supplementary
32 hours
of face-to-face activities
4 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

<br /> <br /> <br />One of aims of this course is to present background material of several numerical methods in branches of mathematics with which numerical analysis has made its principal contacts.

Prerequisites

<br /> <br />First principles of Analysis and Geometry.

Course unit content

<br /> <br />Stability and Conditioning. Interpolation and Approximation. Polynomial interpolation. Hermite interpolation. Runge phenomenon for standard polynomial interpolation. Splines. Least-square approximations. Trigonometric interpolation.<br />Solution of linear system of equations. Gauss elimination. Operations counts. Pivoting and Scaling in Gauss elimination. LU decompositions. Cholesky decomposition. QR decomposition. Least-squares solution of over-determined linear systems. <br />Numerical integration. Newton-Cotes Formulas. Composite formulas. Error estimate. Adaptive quadrature.<br />Solution non-linear equations. Bisection. Newton method in one variable. Secant method. Construction. Practical considerations.<br />Ordinary Differential Equations. Initial-value problems. One-step methods. Convergence and error analysis for one-step methods. Practical implementation of one-step methods. Boundary-value problems for ordinary differential equations: shooting methods, finite-difference methods, collocation methods.

Full programme

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Bibliography

<br /> <br />A.Quarteroni, R.Sacco, F.Saleri, Matematica Numerica, Springer-Verlag. <br />G.Naldi, L.Pareschi, G. Russo, Introduzione al Calcolo Scientifico (metodi e applicazioni con Matlab),  McGraw-Hill.<br />G.Monegato, Fondamenti di Calcolo Numerico, CLUT, Torino.<br />William J. Palm III, Introduction to MATLAB 7 for engineerings,  McGraw-Hill.

Teaching methods

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Assessment methods and criteria

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Other information

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