Numerical Analysis

Code:

EC0007

Acronym:

ANUM

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2006/2007 - 2S

Active?	Yes
Web Page:	https://moodle.fe.up.pt/login/index.php
Responsible unit:	Mathematics Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEC	4	Plano de estudos de transição para 2006/07	1	6	6	60	160
MIEC	322	Syllabus since 2006/2007	1	-	6	60	160
		Plano de estudos de transição para 2006/07	1	-	6	60	160

Teaching language

Portuguese

Objectives

To introduce some fundamental concepts of numerical analysis. To introduce notions of stability of methods and condition number of problems. Use of different numerical techniques to solve some problems. Study their efficiency, applicability and stability. Solve some case studies. Knowing how to choose and decide which method of numerical analysis to apply and which is the most efficient. Discuss the numerical results.

Program

1. Goal for numerical analysis.
2. Theory of errors: basic concepts, errors definitions. Error propagation. Floating-point arithmetic.
3. Solution of non-linear equations: iterative methods, bisection method, false position method, secant method, and simple iterative method. General conditions for the resolution and stopping criteria for iterative methods.
4. Systems of linear equations:
4.1. Direct methods: Gauss elimination, pivoting techniques;
4.2. Iterative methods: Jacobi, Gauss-Seidel, convergence theorems;
5. Polynomial approximation:
5.1. Polynomial interpolation: divided differences, Newton and Lagrange methods, interpolation error, and direct and inverted interpolation.
5.2. Introduction to the least squares method.
6. Numerical differentiation.
7. Numerical integration:
7.1. Newton-Cotes formulas (e.g.: trapezes and Simpson);
7.2. Composed formulas;
7.3. Gauss formulas;
7.4. Errors in numerical integration.

Mandatory literature

Ana Maria Faustino; Apontamentos de Análise Numérica
Valença, Maria Raquel; Métodos numéricos

Complementary Bibliography

Kharab, Abdelwahab; An introduction to numerical methods. ISBN: 1-58488-281-6
Fausett, Laurene V.; Applied numerical analysis using Matlab. ISBN: 0-13-319849-9
Pina, Heitor; Métodos numéricos. ISBN: 972-8298-04-8
Burden, Richard L.; Numerical analysis. ISBN: 0-534-38216-9
Bradie, Brian; A friendly introduction to numerical analysis. ISBN: 0-13-191171-6

Teaching methods and learning activities

Concepts and techniques are presented according to Analysis and Algebra knowledge and, whenever possible, the theoretical exposition is supported by practical examples and graphic representations. Theoretical aspects are presented with enough detail to exhibit the applicability of formulas. Additionally, methods are analyzed and compared in what concerns their efficiency, accuracy and applicability. The students are encouraged to program their calculation machines and explore them in all their capacity. In practical classes, several case studies are solved on the computer using Matlab.

Software

MATLAB,Maple

keywords

Physical sciences > Mathematics > Applied mathematics > Numerical analysis

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial
	Total:	-	0,00

Eligibility for exams

Limit of allowed absences is fixed by the Article 4ª-nº 1 (25% of nº of foreseen practical and theoretical-practical lessons).

Calculation formula of final grade

E: result of the final written exam
P: result of works performed during the semester, three of them individual and one a group work

Final grade: max {E, 0.8 E+0.2 P}

Examinations or Special Assignments

Evaluations higher than 17 are submitted to an oral exam.

Special assessment (TE, DA, ...)

Final written exam.

Classification improvement

Final written exam.

Observations

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Working time estimated out of classes: 4 hours