Numerical Methods

Code:

EEC0016

Acronym:

MNUM

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2012/2013 - 1S

Active?	Yes
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEEC	304	Syllabus (Transition) since 2010/2011	2	-	6	63	162
		Syllabus	2	-	6	63	162

Teaching language

Portuguese

Objectives

To afford the student the possibility of learning the fundamental numerical methods, used in solving problems with which engineers are frequently confronted.

 

Covered are the subjects of errors, linear and nonlinear equations, polynomial interpolation and numerical integration.

 

The MatLab programming tool is used during the semester, to develop scripts that implement the different iterative methods learned, applying them to the resolution of typical exercises.

 

Learning outcomes and competences

After attending this course the student will have acquired a solid technical base of numerical methods. Developed will be the capacity of, given a specific situation, to know which method(s) to apply and how to adapt the various tools, developed during the semester, to the problem at hand, including knowing the number of iterations needed to achieve a established precision.

 

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Algebra and Calculus 1 and 2

 

Program

Error theory: absolute and relativo error of approximation. Real numbers representation. Error propagation in function evaluation. Error caused by series truncation.

 

Nonlinear equations: Methods of successive bisections, false position, iterative simple, Newton and secant. Error and convergence.

 

 

Nonlinear equations systems: the methods of the fixed point and Newton. Error and convergence.

 

 

Linear equations systems: Gauss elimination and pivot techniques. Iterative methods: Jacobi and Gauss-Seidel. Approximate solution error and residue: relation between the two.

 

 

Function fitting: the minimum squared method and its extensions.

 

 

Polynomial Interpolation: the interpolating polynomial. Divided and finite differences. Interpolation error. Double and inverse interpolation.

 

 

Numerical integration: trapezoidal and Simpson rules. Errors. Romberg integration. Gaussian quadrature.

 

 

Integration of differential equation: methods of Euler and Taylor. Truncation errors and consistency.

 

Methods of Runge-Kutta, Milna and Adams.

 

 

Mandatory literature

A. Matos; Apontamentos de Análise Numérica, 2005
Burden, Richard L.; Numerical analysis. ISBN: 0-53491-585-X
Conte, S. D.; Elementary numerical analysis. ISBN: 0-07-012447-7
E. Fernandes; Computação Numérica, Universidade do Minho

Complementary Bibliography

Pina, Heitor; Métodos numéricos. ISBN: 972-8298-04-8
W. Cheney, R. Kincaid; Numerical Mathematics and Computing, Brooks Cole

Teaching methods and learning activities

Lectures: Presentation and discussion of subject matter; analysis of illustrative examples.

 

 

Discussion sessions: programming in Matlab the covered Numerical Analysis methods; Resolution of exercises.

 

Software

Matlab

keywords

Physical sciences > Mathematics > Applied mathematics > Numerical analysis
Physical sciences > Mathematics > Applied mathematics > Numerical analysis

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	56,00	0,00
Midterms	Teste	3,00	35,00
Final exam	Exame	3,00	55,00
Sessions participation	Participação presencial	56,00	10,00
	Total:	-	100,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Study	Estudo autónomo	78
Preparation for exams	Estudo autónomo	25
	Total:	103,00

Eligibility for exams

In order to gain access to the final examination the student must

 

-- not exceed the maximum allowed number of absences to the discussion sessions;

 

-- obtain an average of seven as a grade (in 20) on the two tests given during the semester.

 

The repeating student that gained access to the final exam in a previous edition may select, according to the established rules, not to attend the discussions. This choice is made at the semester beginning and is irreversible.

 

 

 

Calculation formula of final grade

For the first-time student the final grade (N) will be computed based on the grades obtained in the two semester tests (MT1 and MT2), the discussion sessions (TP) and the grade obtained in the final exam (EF), as given by:

 

 

N = 10% * TP + 17.5% * MT1 + 17.5% * MT2 + 55% * EF

 

 

The different component grades are on a 0 to 20 scale.

 

 

Permission to take the final examination is accorded to the student that meets the TP attendance requirements and that has obtained an average grade of at least 7 in the two semester tests.

 

 

The TP grade is calculated by adding the satisfactory participation in the TPs (40%) and the grade obtained in the MatLab part of each semester test (60%).

---

 

 

 

The repeating student that choses not to attend the discussion sessions

 

has two options:

 

 

 

1) Takes the semester tests. The final grade (N) is given by

 

N = 0.10 * FA + 0.175 * MT1 + 0.175 * MT2 + 0.55 * EF

 

Note: The student does not do the MatLab part of the semester tests.

 

 

 

2) The student does not take the semester tests and the grade is given by

 

N = 0.25 * FA + 0.75 * EF

 

Examinations or Special Assignments

See Special Evaluation

 

Internship work/project

None

Special assessment (TE, DA, ...)

The evaluation of the student with working status (TE) or of other students with special status (that may chose not to attend the discussion sessions) will be different in the following point:

 

-- the TP evaluation will be replaced by a program exercise (P), realized on a date to be arranged

 

Classification improvement

The improvement of a final grade equal or superior to 18 is only possible after an oral examination.

 

Observations

The repeating student that choses to maintain the FA from the previous year will not allowed to register in the discussion sessions.