Numerical Methods

Code:

EA0017

Acronym:

MN

Keywords
Classification	Keyword
OFICIAL	Interp/Personal professional attitudes and capac.
OFICIAL	Basic Sciences

Instance: 2008/2009 - 1S

Active?	Yes
Web Page:	http://moodle.fe.up.pt/course/view.php?id=776
Responsible unit:	Mining Engineering Department
Course/CS Responsible:	Master in Environmental Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEA	65	Syllabus since 2006/07	2	-	6	56	162

Teaching language

Portuguese

Objectives

Students are introduced to the main algorithms of numerical analysis, which are explored in different environments, namely by hand calculation, spreadsheets, calculators, programming languages and computer algebra systems.
The facts that "numbers are inaccurate" and that "error propagates" are also emphasized.

Program

- Precision and error checking;
- Root-finding (brackt methos - bissection and regula falsi, Newton's method, fixed-point iteration);
- Newton's method for systems of nonlinear equations;
- Linear systems (Gauss elimination and Choletsky decomposition methods) . Partial pivoting. Condioning. Error sensitivity analysis;
- Numerical integration (trapezoidal rule and Simpson's rule);
- Differential equations (1st and 2nd orders)- Euler method and Runge-Kutta methods;
- Nonlinear optimization: one and multi dimensional searches (golden section search, Powell's method, the method of steepest descent, gradient method, quadratic programming and Levenberg-Marquardt method);
- Curve fitting (least squares method).

Mandatory literature

Madureira, C.; Soeiro de Carvalho, J.; Vila, C. ; Análise Numérica

Complementary Bibliography

Conte, S. D.; Elementary numerical analysis. ISBN: 0-07-012447-7
Leader, J.J.; Numerical analysis and scientific computation, Pearson - Addison Wesley, 2004. ISBN: 0-321-22335-7
Fernandes, E.M.; Computação Numérica, Universidade do Minho, 1998. ISBN: 972-96944-1-9
Chapra, Steven C.; Numerical Methods for Engineers. ISBN: 0-07-079984-9
Cheney, Ward; Numerical mathematics and computing. ISBN: 0-534-38993-7

Software

Maple
Maxima
Matlab 6 R12.1

keywords

Physical sciences > Mathematics > Applied mathematics > Numerical analysis

Evaluation Type

Distributed evaluation without final exam

Calculation formula of final grade

N1=D*((P+T)/2)*20
where N1 is the final grade , P is the homework grade, T is the test grade and D is a performance coeficient between 0,9 and 1,1.