Numerical Methods

Code:

EMG0012

Acronym:

MN

Keywords
Classification	Keyword
OFICIAL	Physical Sciences (Mathematics)

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Civil and Georesources Engineering
Course/CS Responsible:	Bachelor in Mining and Geo-Environmental Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EA	62	Syllabus	2	-	6	52	162
L.EMG	29	Plano de estudos oficial a partir de 2008/09	2	-	6	52	162

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:

• dentify 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.

Learning outcomes and competences

The student will be able to:

• Identify numerically solvable  engineering problems;

 

• Put forward numerical solutions for a given engineering problem, comparing and choosing appropriate methods;

 

• Identify issues in that solution;

 

• Criticise results;

 

• Implement a reasonably efficient computational solution.

Working method

Presencial

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

Calculus, Algebra, Introductory Programming.

 

Ability for the  use of interactive calculation environments - worksheets, calculators, CAS.
Familiarity with computer programming languages.

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.http://en.wikipedia.org/wiki/Glenn_Gould

Mandatory literature

Carlos Madureira, Cristina Vila, José Soeiro Carvalho; Métodos Numéricos, um curso para o Mestrado Integrado em Engenharia Informática e Computadores da FEUP, 2009 (available in e-learning server)
Steven C. Chapra, Raymond P. Canale; Numerical methods for engineers. ISBN: 0-07-112180-3

Complementary Bibliography

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

Teaching methods and learning activities

Classes are computer based, using packages such as 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.
Students may be subject to small assessment quizzes during classes.

Software

Maxima
folha de cálculo
Matlab

keywords

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

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	50,00
Teste	40,00
Participação presencial	10,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	52,00
Total:	162,00

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 every class).

Calculation formula of final grade

Students will be assessed on two class quizzes (Ti).
They must also attend a final exam. 
The quiz final score  (MTi) will be the quiz average.

To access the first call exam, the quiz average (MTi)  must be greater or equal to 5,0.

The presential component depends on attendance, class participation, problem answering, ... 
The final score after the first call exam will be calculated as follows: 

NE1 = 0,4* MTi +0,5*NE +0,1 P

Where: 
NE1 – Final grade after the first call; 
MTi- individual assessment tests average;
NE – Exam score;
P - presential score

Students with score NE1
The grade after the 2nd call is the highest value obtained by weighing the exam and the distributed evaluation grades  (NMT) or just the 2nd call exam. 

NER = max( 0,4* MTi + 0,1 P +0.5*NR ; NR) 

Where: 
NER – Final grade after 2nd call; 
NR – 2nd call exam 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 with final exam", but choice must be comunicated to teachers not after the fourth theoretical class. Otherwise, they can only attend the second call exam.

Classification improvement

Special global examination, simultaneous with 2nd call.