Mathematical Methods in the Sciences

Code:

M3012

Acronym:

M3012

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	1	Official Study Plan	3	-	6	48	162
L:CC	3	study plan from 2021/22	2	-	6	48	162
			3
L:F	3	Official Study Plan	3	-	6	48	162
L:G	0	study plan from 2017/18	2	-	6	48	162
			3
L:M	53	Official Study Plan	3	-	6	48	162
L:MA	0	Official Study Plan	3	-	6	48	162
L:Q	0	study plan from 2016/17	3	-	6	48	162

Teaching language

Portuguese

Objectives

Study of mathematical models in Physics and Biology.

Learning outcomes and competences

The students should master the mathematical theory underlying the models and also its use in the resolution of problems.

Working method

Presencial

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

Two semesters of Linear Algebra, two semesters of Real Analysis and one semester of Differential Equations are advised. Gaps in these subjects may require additional effort.

Program

Study of the following:

1. Module in Conservative Mechanics - study of the mathematical theory underlying the Lagrangian formalism of conservative mechanical systems and resolution of classical problems using this formalism. 
2. Module in Epidemiology - study of the mathematical theory underlying the study of models for spread of infectious diseases and its application to real life problems.

Mandatory literature

V. I. Arnold; Mathematical methods of classical mechanics. ISBN: 0-387-96890-3
Fred Brauer; Mathematical models in population biology and epidemiology. ISBN: 0-387-98902-1
Maia Martcheva; An Introduction to Mathematical Epidemiology, Springer, 2015. ISBN: 978-1-4899-7612-3

Comments from the literature

The slides used in the lectures will be available for download.

Teaching methods and learning activities

Classes with exposition of the theory and illustration by examples. The last part of each class will be used for resolution, by the students, of concrete problems.

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	111,00
Frequência das aulas	48,00
Trabalho escrito	3,00
Total:	162,00

Eligibility for exams

Studentes should be present in the two assessments, which will take place in class time.

Calculation formula of final grade

In the first call the final score will be the sum of the scores obtained in two assessments:
Assessment 1 - Conservative Mechanics - 12 points, minimum score of 4 points; 
Assessment 2 - Epidemiology - 8 points, minimum score of 3 points.

In the second call the final score will be the score obtained in the exam, with a total score of 20 points and divided in two parts, corresponding to the assessments:
Part 1 - Conservative Mechanics - 12 points, minimum score of 4 points;
Part 2 - Epidemiology - 8 points, minimum score of 3 points.

Special assessment (TE, DA, ...)

Any special assessment will consist of an exame in the same conditions of the first and second call.

Classification improvement

Improvement of grade must be done in the second call.