Numerical Methods

Code:

EEC0016

Acronym:

MNUM

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2013/2014 - 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	268	Syllabus (Transition) since 2010/2011	2	-	6	63	162
		Syllabus	2	-	6	63	162

Teaching language

Portuguese

Objectives

To offer a wide range of state-of-the-art techniques in the area of numerical methods.
To empower the student with the capacity of correctly applying numerical techniques to resolve engineering problems, which presupposes:
- an understanding of the fundamental concepts;
- knowing how apply the methods, using calculators and computational tools and
- knowing the number of iterations needed to achieve a established precision.

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, knowing which method(s) to apply and how to adapt the various tools, studied 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: Trapese and Simpson rules. Errors. Romberg technique. Gaussian quadrature.
Integration of differential equations: Euler and Taylor methods. Truncation errors and consistency. Predictor-corrector methods. Runge-Kutta method.

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 (T): Presentation of the various topics, with illustrative examples.  
Discussion sessions (TP): Problem resolution and discussions.

keywords

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

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	103,00
Total:	103,00

Eligibility for exams

Students that attend for the 1st time: In order to gain access to the final examination the student must:
1) Not exceed the maximum allowed number of absences to the discussion sessions and
2) Obtain at least an average of seven as a grade (in 20) on the two Mini Tests (MTs) given during the semester.  

A repeating student that gained access to the final exam in a previous edition:
1) Is isempt from attending the discussion sessions (TP);
2a) If the MTs were taken with success during the 2012/13 edition, the student may opt for keeping those grades (Does not take the MTs during the 2013/14 edition). This choice is made before the 1st MT and is irreversible. The student must notify the regent, per email, of the decision taken.
2b)  If the student did not take the MTs during the 2012/13 edition, he has to take them during the current edition.

Calculation formula of final grade

The final grade (N) will be based on the grades obtained in the two semester tests (MT1 and MT2) and in the final exam (EF), whose minimum of 9.5 has to be obtained:
N =   0.25 * (MT1 +  MT2) + 0.50 * EF
The different component grades are in a 0 to 20 scale.

Examinations or Special Assignments

See Special Evaluation.

Internship work/project

None

Special assessment (TE, DA, ...)

A student who enjoys a sepecial status and misses one or both of the tests given during the semester must take a substitution exam.

 

Classification improvement

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

Observations

As mentioned above, a repeating student that gained access to the final exam in a previous edition:
1) Is isempt from attending the discussion sessions (TP);
2a) If the MTs were taken with success during the 2012/13 edition, he may opt for keeping those grades (Student does not take again the MTs during the 2013/14 edition). This choice is made before the 1st MT and is irreversible. The student must notify the regent, per email, of the decision taken.
2b)  If the student did not take the MTs the 2012/13 edition, he has to take them during the current edition.

Student consulting hours:
Consult the respective teacher homepage. NOTE: Please send an email to make the appointment, particularly if it is for a time outside the published hours.