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Subject: NUMERICAL COMPUTING AND MATHEMATICAL SOFTWARE (A.A. 2019/2020)

degree course in AUTOMOTIVE ENGINEERING

Course year 2
CFU 9
Teaching units Unit calcolo numerico e software matematico
Mathematics, Information Technology and Statistics (lesson)
  • TAF: Basic compulsory subjects SSD: MAT/08 CFU: 9
Teachers: Emanuele GALLIGANI
Mandatory prerequisites Analisi Matematica IAnalisi Matematica IIGeometria e Algebra Lineare
Exam type written
Evaluation final vote
Teaching language Italiano
Contents download pdf download

Teachers

Emanuele GALLIGANI

Overview

Analysis and implementation of basic numerical methods.

Admission requirements

Introductory concepts of Calculus in one and in several variables and Linear Algebra.

Course contents

Floating point arithmetics and introduction to Matlab. Matrix computation. Matrix norm and conditioning of linear systems. Solution of simple linear systems. Gaussian elimination method and LU factorization. Choleski factorization. Backward error analysis. Householder matrix, QR factorization and applications.
Polynomial interpolation: Lagrange, Hermite and Newton formulae. Least squares approximation. Spline functions.
Numerical differentiation and integration (Newton-Cotes formulae, Gaussian quadrature, composite and adaptive formulae).
Fixed point iteration. Bisection and regula falsi methods. Newton method for equations and systems of nonlinear equations.
Eigenvalues and eigenvectors. Power method and inverse iteration. Iterative QR method. Jacobi and Gauss-Seidel methods for linear and non linear systems.

Teaching methods

Lectures.

Assessment methods

Written exam on questions about the course content and elective oral exam. See the course web site: http://dolly.ingmo.unimore.it/2019

Learning outcomes

Knowledge and understanding of basic methods of Scientific Computing. Skill to write a Matlab program implementing basic numerical methods.

Readings

Il corso prevede le dispense fornite dal docente e reperibili al sito http://dolly.ingmo.unimore.it/2019
I testi indicati sotto (in ordine alfabetico) e altri testi di riferimento per il corso, possono essere reperiti presso la Biblioteca Scientifica Interdipartimentale dell'Università di Modena e Reggio Emilia (www.bsi.unimore.it) nella sezione A12.

•Atkinson K.E.: An Introduction to Numerical Analysis, John Wiley & Sons, New York, 1989.
•Burden R.L., Faires D.: Numerical Analysis, 7th Edition, Brooks/Cole, Pacific Grove, 2001.
•Burden R.L., Faires D.: Numerical Methods, 3rd Edition, Brooks/Cole, Pacific Grove, 2003.
•Deuflhard P., Hohmann A.: Numerical Analysis in Modern Scientific Computing: An Introduction, 2nd Edition, Springer, New York, 2003.
•Hämmerlin G., Hoffmann K-H.: Numerical Mathematics, Springer, New York, 1991.
•Isaacson E., Keller H.B.: Analysis of Numerical Methods, J.Wiley & Sons, New York, 1966 (ripubblicato da Dover Pub. Inc., New York, 1994).
•Johnson L.W., Riess R.D.: Numerical Analysis, Second Edition, Addison Wesley, Reading, 1982.
•Kincaid D., Cheney W.: Numerical Analysis: Mathematics of Scientific Computing, 3rd edition, Brooks/Cole, Pacific Grove, 2001.
•Moler C.B.: Numerical Computing with MATLAB, SIAM, Philadelphia, 2004.
•Stewart G.W.: Afternotes on Numerical Analysis, SIAM, Philadelphia, 1996.
•Stoer J., Bulirsch R.: Introduction to Numerical Analysis, Springer-Verlag, New York, 1980.
•Süli E., Mayers D.F.: An Introduction to Numerical Analysis, Cambridge Univ. Press, Cambridge, 2003.