Mathematical Methods in Biology and Medicine

Code:

M386

Acronym:

M386

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=1453
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	0	Plano de estudos a partir de 2008	3	-	7,5	63	202,5
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	63	202,5
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	63	202,5
L:M	25	Plano de estudos a partir de 2009	3	-	7,5	63	202,5
L:Q	0	Plano de estudos Oficial	3	-	7,5	63	202,5

Teaching language

Portuguese

Objectives

Application of already known mathematical techniques to models in Biology and Medicine, study of new mathematical techniques that may be used in the analysis of these models.

Learning outcomes and competences

Applications of mathematical techniques in the analysis of models in Biology and Medicine.

 

Working method

Presencial

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

Calculus in several variables; basic notions of ordinary differential equations, specially  the linear case.

Phase portraits and stability of equilibria in linear ordnary differential equations.

Linear partial differential equations, separation of variables.

Program

Mathematical methods for treatment of models, among the following:

- continuous time dynamical systems, ordinary differential equations;

- systems of  differential equations with two time-scales;

- partial differential equations, in particular reaction-diffusion equations;

- models with symmetry, coupled cell systems.

Study of examples of mathematical models in Biology and Medicine using these methods, like, for instance:

- population ecology, interaction of species;

- propagation of infectious diseases;

- propagation of nerve impulse;

- pattern formation.

 

Mandatory literature

Britton Nicholas F.; Essential mathematical biology. ISBN: 1-85233-536-X
Murray J. D. James Dickson; Mathematical biology. ISBN: 978-0-387-95223-9 (vol. 1) 0-387-95223-3
Brauer Fred; Mathematical models in population biology and epidemiology. ISBN: 0-387-98902-1

Complementary Bibliography

Arrowsmith D. K.; Ordinary differential equations
Hirsch Morris W.; Differential equations, dynamical systems, and linear algebra. ISBN: 0-12-349550
Braun Martin; Differential equations and their applications. ISBN: 0-387-97894-1
Golubitsky Martin; The symmetry perspective. ISBN: 3-7643-6609-5
Ermentrout G. Bard; Mathematical foundations of neuroscience. ISBN: 978-0-387-87707-5

Teaching methods and learning activities

Presentation of topics in lectures.

Exercises presented in the course's homepage, solved in example classes.

 

keywords

Physical sciences > Mathematics > Mathematical analysis > Differential equations
Physical sciences > Mathematics > Chaos theory
Natural sciences > Biological sciences > Biology > Population biology
Natural sciences > Biological sciences > Biology > Developmental biology
Health sciences > Medical sciences > Medicine > Infections
Natural sciences > Environmental science > Ecology > Ecosystems

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Calculation formula of final grade

For approval in the tests the student should obtain a total of 9,5 points in the two tests and a mimimum mark of 3 out of 10 in each test.

 A minimum of 9.5 in the exam is required for approval.

The final mark is either the sum of the marks obtained in the two tests or the result of the final exam.

 

An additional test, either written or oral, may be asked of students aiming at marks over 15 out of 20.