Mathematical Modeling

Code:

M4042

Acronym:

M4042

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2025/2026 - 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:ENM	18	Official Study Plan since 2023/2024	1	-	6	48	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

We aim 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

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 will be used for evalutation purposes. 

Software

wxMaxima

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	110,00
Frequência das aulas	48,00
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:

C1 - component corresponding to the first part of the syllabus - 8 points (consisting of (a) resolution of an exercise of 2 points from the first group of exercises and (b) and assessment with score of 6 points)

C2 - component corresponding to the second part of the syllabus - 6 points (consisting of (a) resolution of an exercise of 2 points from the second group of exercises and (b) and assessment with score of 4 points)

C3 - component corresponding to the second part of the syllabus - 6 points (consisting of (a) resolution of an exercise of 2 points from the thrid group of exercises and (b) and assessment with score of 4 points)

In the second call the final grade is the grade obtained an exam with a total score of 20 points. 

Special assessment (TE, DA, ...)

Students with special status who are exempted from distributed evaluation, will not be eliminated. They will be able to attend the exam in the second call and special exams.

Classification improvement

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