Numerical Methods

Code:

M232

Acronym:

M232

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	2	Plano de Estudos a partir de 2008	2	-	7,5	-
L:B	1	Plano de estudos a partir de 2008	3	-	7,5	-
L:F	0	Plano de estudos a partir de 2008	3	-	7,5	-
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-

Teaching language

Portuguese

Objectives

Familiarize the students with robust numerical methods used in solving mathematical problems in science and engineering, including their conditions of applicability and their limitations, with a particular emphasis on applications and the development of algorithms in solving problems. It is intended that the students acquire the knowledge necessary to identify and use the most robust numerical methods in solving problems.

Learning outcomes and competences

The student must show skills in solving numerically mathematical problems in the areas described.

Working method

Presencial

Program

Error theory:

 

Types of errors. Absolute and relative error. Rounding error and truncation error. Propagation of the error. Computation of the sum of a convergent series. 

 

Nonlinear equation:

 

Root finding methods: bisection method, fixed point method , Newton method and variants. Systems of linear equations:

 

Direct methods. Gauss elimination. Pivoting. 

 

Polynomial interpolation:

 

Lagrange method. Error in interpolation. Aitken-Neville method. Divided differences. Newton method. Inverse interpolation. 

 

Approximation:

 

Least squares polynomial approximation of a set of points. Generalized least squares approximation. Least squares approximation of a function defined in an interval. 

 

Numerical differentiation and integration:Newton-Cotes formulas. Simple and composite rules of rectangles, trapezium and Simpson. Truncation errors. Numerical differentiation formulas.

 

Mandatory literature

Pina Heitor; Métodos numéricos. ISBN: 972-8298-04-8

Complementary Bibliography

Quarteroni Alfio; Numerical mathematics. ISBN: 0-387-98959-5
Zaglia Michela Rediva; Calcolo numerico. ISBN: 88-87331-49-9
Fernandes Edite Manuela da G. P.; Computação numérica. ISBN: 972-96944-1-9

Teaching methods and learning activities

Lectures, problems  and computational projects.

Software

Maxima
Scilab
Python
Matlab

keywords

Physical sciences > Mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Participação presencial	0,00
Teste	60,00
Trabalho laboratorial	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	0,00
Frequência das aulas	0,00
Total:	0,00

Eligibility for exams

A minimum of  3.5 points in the practical classification.

Calculation formula of final grade

Theoretical classification (CT): Sum of the classifications of 4 tests ( 3 points each) or a final examination (12 points)
Practical classification (CP): sum of classifications obtained in 4 practical tests (2 points each)
Final classification (CF): CT+CP

Special assessment (TE, DA, ...)

One final examination (theoretical and practical).