Numerical Analysis

Code:

EM207

Acronym:

AN

Instance: 2003/2004 - 1S

Active?	Yes
Web Page:	http://gatiup.iric.up.pt
Responsible unit:	Mathematics Section
Course/CS Responsible:	Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEM	254	Plano de Estudos EM Oficial a partir de 2000	2	3	4,5	-
		Plano para Bachareis EM a partir 2000	1	3	4,5	-

Teaching language

Portuguese

Objectives

To learn the most efficient and common methods for the solution of each basic Numerical Analysis problem. The students are expected to learn the theorems and conditions of convergence of each method, to be able to program them, and to test them effectively on a computer and discuss the results obtained.

Program

Series expansions computation of transcendental functions using series developments.
Number systems and errors ; number systems on computers; representation of integers and floating point arithmetic; round-off error; absolute error and relative error, significant digits, Taylor's formula and error estimation; error analysis.
Linear systems of equations: solution of triangular systems; Gaussian elimination, pivoting strategies; application to the computation of determinants and to the inversion of matrices. Iterative methods: Jacobi and Gauss-Seidel; convergence theorems.
Non linear equations: general conditions for the solution, stopping criteria for iterative methods; some iterative methods: successive bissection, fixed point iteration, Newton's method, secant method; polynomial equations.
Polynomial interpolation: divided differences; methods of Newton and Lagrange; error of the interpolating polynomial.
Approximation. Least squares approximation. Orthogonal polynomials.
Numerical integration: Newton-Cotes formulae (ex: Trapezoidal and Simpson rules) Gaussian quadrature; composite rules; numerical quadrature errors.
Ordinary Differential equations: Euler’s method for ODE of order 1; Taylor methods. Order of a method for ODE of order1. Runge-Kutta methods of order 2 and 4.
Small computer projects using WINDOWS or UNIX and MATLAB.

Main Bibliography

“Numerical methods using Matlab”, John Mathews; Kurtis Fink, Prentice Hall, 1999
or
"Elementary Numerical Analysis", S. Conte, C. de Boor, Ed. McGraw-Hill, 1980
or
"Métodos Numéricos", Maria Raquel Valença, Ed. Livraria do Minho, 1993
or
"Métodos Numéricos", Heitor Pina, Ed. McGraw-Hill, 1995

Complementary Bibliography

“ANonline” online tutorial by Filomena Dias d’Almeida available from
http://ead.reit.up.pt:8900/webct/public

Software

MATLAB

Evaluation Type

Distributed evaluation with final exam

Eligibility for exams

Minimum requirements to be admitted to the exam:
registration, not to exceed the maximum number of
absences permitted, pass the practical test with a minimum grading of 7 .

Calculation formula of final grade

exam x 0.75 + practical test x 0.25

Special assessment (TE, DA, ...)

A written exam (for students who have more than 15 in this exam the final mark will take in account the classification of an oral examination too) and a practical computer test.

Classification improvement

A written exam (for students who have more than 15 in this exam the final mark will take in account the classification of an oral examination too)