Numerical Analysis

Code:

M2018

Acronym:

M2018

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MI:ERS	18	Plano Oficial desde ano letivo 2014	2	-	6	56	162

Teaching language

Portuguese

Objectives

The main aim of this subject is given a mathematical problem,  to study sufficient conditions for the existence and unicity of its solution, to establish a constructive method to solve it, to study and control the errors  involved, to give an algoritmh for the solution and to implement it in a computer and to study and interpret the numerical results.

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).