Numerical Methods

Code:

EIC0021

Acronym:

MNUM

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2011/2012 - 1S

Active?	Yes
E-learning page:	http://moodle.fe.up.pt/
Responsible unit:	Mining Engineering Department
Course/CS Responsible:	Master in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEIC	130	Syllabus since 2009/2010	2	-	5	56	135

Teaching language

Suitable for English-speaking students

Objectives

The course aims at providing the student with solid numerical methods foundations. It is topic oriented, covering numerical error analysis, algebraic and differential equation and systems solving, definite integration, non-linear optimization and curve fitting.
The student will be able to:
- identify numerical problems, choosing and implementing the right solution method, after doing numerical experimentation;
- understand numerical methods in the context of engineering, working on examples from engineering practice;
- criticise results, from the methodological, implementation and problem context points of view.

Program

- Number representation;
- Numerical error analysis;
- Roots of equations;
- Systems of non linear equations;
- Systems of linear equations;
- Numerical integration;
- Ordinary Differential equations;
- Single and multi-variable unconstrained optimization;
- Curve fitting.

Mandatory literature

Madureira, C.; Soeiro de Carvalho, J.; Vila,C; “Análise Numérica um curso para a Licenciatura em Engenharia Informática e de Computadores da FEUP”,, 2003
Steven C. Chapra, Raymond P. Canale; Numerical methods for engineers. ISBN: 978-007-126759-5

Complementary Bibliography

Conte, S. D.; Elementary numerical analysis. ISBN: 0-07-012447-7
Dahlquist, Germund; Numerical Methods. ISBN: 0-13-627315-7
Cheney, Ward; Numerical mathematics and computing. ISBN: 978-0-495-11475-8

Teaching methods and learning activities

Classes are computer based, using packages like Maxima, MatLab and Excel. Students will also implement computer solutions in their choice programming language. Working focus will be on precision, efficiency and robustness of computer solutions.
Students will be challenged by small non trivial problems.

Software

Linguagem de Programação
The Mathworks - Matlab - Release 11.1
Folha de Cálculo
Maxima

keywords

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

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	56,00
Problems	Teste	20,00
T1 - first test	Exame	1,50		2011-10-19
T2 - second test	Exame	1,50		2011-12-07
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Daily study	Estudo autónomo	30
Exam and test preparation	Estudo autónomo	26
	Total:	56,00

Eligibility for exams

To obtain attendance students may not exceed the maximum number of missed classes, complying with school attendance rules. (attendance registration will be done in all the classes).

Calculation formula of final grade

Students will be evaluated by two assessment tests (T1, T2), and a "participation" (P) component, involving several homework problems, attendance and general class intervention.
They must also attend a final exam.

The frequency grade is

NF = (0.1 * P + 0.45 * T1 + 0.45 * T2)
being:
T1, T2 – Midle tests;
P - Participation in class.

The final score after the first call will be calculated as follows:

NE1 = 0.45* NF +0.55 * NE

Being:
NE1 – Final grade after the first call;
NF - Distributed evaluation (frequency) grade;
NE – Exam grade.

Students who do not pass the 1st call exam can undertake a 2nd call exam.

The grade after the 2nd call is the highest value obtained by weighting together the exam and the distributed evaluation grades or just the 2nd call exam.

NER = max (0.45 * NF +0.55 * NR ; NR)
where:
NER – Final grade after 2nd call;
NR – 2nd call exam grade;
NF - Distributed evaluation grade

Grades over 18/20 will be subject to an oral discussion.

Special assessment (TE, DA, ...)

Students with special status may choose between the normal evaluation mode or "evaluation only with final exam", but choice must be told to teachers at the course start.

Classification improvement

Special global examination, simultaneous with 2nd call.