Numerical Analysis

Code:

EM0016

Acronym:

AN

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2006/2007 - 1S

Active?	Yes
Web Page:	http://vista.up.pt
Responsible unit:	Mathematics Section
Course/CS Responsible:	Master in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEM	2	Plano de estudos de transição para 2006/07	2	6	6	56	160
MIEM	263	Syllabus since 2006/2007	2	-	6	56	160
		Plano de estudos de transição para 2006/07	2	-	6	56	160

Teaching language

Portuguese

Objectives

To know the most efficient and common methods for the solution of each basic Numerical Anaysis 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

Numerical Analysis:
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.
Polynomial interpolation: divided differences; methods of Newton and Lagrange; error of the interpolating polynomial.
Numerical integration: Newton-Cotes formulae (ex: Trapezoidal and Simpson rules); composite rules; numerical quadrature errors.
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: convergence theorems and algorithms; polynomial equations.
Linear systems of equations: solution of triangular systems; Gaussian elimination, pivoting strategies; LU factorization; application to the computation of determinants and to the inversion of matrices. Iterative methods: Jacobi and Gauss-Seidel; convergence theorems and algorithms.
Approximation. Least squares approximation. Orthogonal polynomials. Curve fitting.
(If there is time enough: 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.

Mandatory literature

Cleve Moler; Numerical Computing with Matlab , SIAM , 2004
John Mathews; Kurtis Fink ; Numerical Methods using Matlab , Prentice Hall , 1999
Heitor Pina; ; Métodos numéricos, McGraw Hill , 1995
Maria Raquel Valença; Métodos Numéricos , Livraria do Minho, 1993
S. Conte, C. de Boor; Elementary Numerical Analysis , McGraw-Hill , 1980
Filomena Dias d' Almeida; Análise Numérica curso e-learning, ver em http://vista.up.pt/webct

Complementary Bibliography

Rosário, Pedro ; Núnez, José ; Pienda, Júlio; Comprometer-se com o estudar na universidade : cartas do Gervásio ao seu umbigo, Livraria Almedina, 2006

Teaching methods and learning activities

Lectures with "Powerpoint". Small illustrating computer projects supervised by teachers in the computer room, with Matlab.

Software

Matlab 7.0

Evaluation Type

Evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	56,00
Small computer projects in Matlab proposed almost every week	Trabalho escrito	30,00
Solution of more exercises about the chapters treated in the tutorials.	Teste	26,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
	Estudo autónomo	30
	Estudo autónomo	20
	Total:	50,00

Eligibility for exams

Minimum requirements to be admitted to the exam:
registration and not to exceed the maximum number of absences permitted.

Calculation formula of final grade

Classification of the final exam.
(For students who have more than 16 in this exam the final mark will take in account the classification of an oral examination too).

Examinations or Special Assignments

The students will do small computer projects and self evaluation tests available on the e-learning plattform WebCT--Vista, from IRICUP, that do not count directly to the final classification . The final exam will include questions about knowledge acquired in these projects and quizzes.

Special assessment (TE, DA, ...)

exam

Classification improvement

exam

Observations

Alguém com acesso a esse campo devia mudar o título da secção 'frequency attainment' que é ridículo.