Mathematical Modeling

Code:

M4042

Acronym:

M4042

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:A_ASTR	9	Plano de Estudos oficial desde_2013/14	1	-	6	56	162
			2
M:ENM	16	Official Study Plan since 2013-2014	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

The aim of this curricular unit is to study some of the models, techniques and algorithms more frequently used in other áreas of knowledge. Each technique should be used for resolution of problems arising in other sciences and for establishing mathematical models for such problems. 

Learning outcomes and competences

One aims at:

a) Completing and structuring the students’ background;

b) Developing the ability of modeling and solving problems; 

c) Promoting the knowledge and the use of methods which are relevant in applications;

d) Favouring the students’ contact with the construction and use of algorithms.

Working method

Presencial

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

One semester of Linear Algebra and two semesters of Infinitesimal Calculus or Real Analysis are recommended. However, students can overcome the lack of background with extra work. 

Program

1. Optimization models with one and several variables, with and without restrictions; computational methods for optimization.

2. Discrete time dynamic models with one and several variables, linear and nonlinear analysis, fixed points and stability, diagrams.

3. Continuous time dynamic models with one and several variables, steady state and qualitative analysis, phase portraits, first integrals.

Each technique will be illustrated with examples of application to different fields of knowledge.

Mandatory literature

Meerschaert Mark M. 1955-; Mathematical modeling. ISBN: 978-0-12-487650-7 hbk
Shone Ronald; Economic dynamics. ISBN: 0-521-01703-3
Britton Nicholas F.; Essential mathematical biology. ISBN: 1-85233-536-X

Complementary Bibliography

Giordano Frank R.; A first course in mathematical modeling. ISBN: 0-53-403367-9

Teaching methods and learning activities

Lectures will be used to present the mathematical techniques and examples of their applications. They will also be used to solve problems with such techniques and, if possible, for computer simulation.

Some lectures can be used for evalutation purposes. 

Software

Maxima

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	52,00
Trabalho escrito	4,00
Total:	162,00

Eligibility for exams

Students should be present in all the lectures in which assessments take place (to be fixed in the beginning of the academic year).

Calculation formula of final grade

The final grade is the sum of all the points obtained in the assessments indicated below:
T1 - assessment corresponding to the first part of the syllabus
T2 - assessment corresponding to the second part of the syllabus
T3 - assessment corresponding to the third part of the syllabus.

In the second call the final grade is the grade obtained in an exam. 

Classification improvement

Exams for improvement of classification will take place in the second call only.