Mathematical Models

Code:

M182

Acronym:

M182

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2012/2013 - 2S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=176103
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:AST	6	Plano de Estudos a partir de 2008	1	-	7,5	-
L:B	1	Plano de estudos a partir de 2008	3	-	7,5	-
L:CC	0	Plano de estudos de 2008 até 2013/14	3	-	7,5	-
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:M	84	Plano de estudos a partir de 2009	1	-	7,5	-
			2
			3
L:Q	0	Plano de estudos Oficial	3	-	7,5	-
PGMP	0	PE da PG em Matemática para Professores	1	-	7,5	-

Teaching language

Portuguese

Objectives

Application of mathematical concepts to the resolution of concrete problems: identification of the problem, proposal of a mathematical model, simulation with real data, conclusions.

Learning outcomes and competences

The student should be able to translate the proposed problems in mathematical language, classify them, propose an adequate model and test such model. 

Whenever possible, the student should solve the problem analytically as well as obtaining a graphic representation of it. He should also be capable of using the Maxima software for graphic representation and simulation of solutions to the problem. 

Working method

Presencial

Program

Discrete mathematical modeling with classical examples of application: 

a) modeling in one dimension: dynamical system and its variation, exact modeling, resolution of linear and affine model, quadratic model, fixed points; models in economics and pharmacokinetics; 

b) modeling in dimension two and three: resolution of the dynamical system in the linear case; fixed points; models in ecology and epidemiology; 

c) modeling with proportionality. 

Adapting a model to data: graphical method and least square method. 

Continuous mathematical modeling: 

a) first order ordinary differential equation (o.d.e.): resolution of the linear o.d.e. and of separable o.d.e.s; continuous model in pharmaco-kinetics, Newton's cooling law and population models; 

b) phase portrait of an autonomous o.d.e.: equilibria, growth intervals, concavity; graph of the solutions by analysis of the phase portrait.

Mandatory literature

000102121. ISBN: 978-0-495-55877-4

Teaching methods and learning activities

Theoretical classes: exposition of the theory and indication of problems to be treated in practical classes. 
Practical classes: resolution of concrete problems with use of computer and adequate software for the resolution of problems in class time.

Software

Maxima

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	85,00
first theoretical assessment	Teste		35,00
Second theoretical assessment	Teste		35,00
Practical assessment	Teste		30,00
	Total:	-	100,00

Calculation formula of final grade

1. The final grade will be the sum of the points obtained in three partial components: 
T1 - theoretical assessment (will take place on the 24th of April): 7 points, minimum 2.5 points. 
T2 - theoretical assessment (will take place on the 5th of June): 7 points, minimum 2.5 points. 
P - practical assessment using computer (will take place on the day of the exam of first call): 6 points, minimum 2 points. 

2. In the second call all three components T1, T2 and P will take place on the day of the exam. The conditions are the same as the conditions referred to in the previous item. 

3. Exception: if the sum of the points obtained in the three components is greater than 17, then a (eventually oral) complementary assessment will take place in a date to fix with the student. The final grade can be 17, 18, 19 or 20.

Special assessment (TE, DA, ...)

Students that, due to special conditions, are exempted from distributed assessment will have an exam under the conditions described for the second call.

Classification improvement

The improvement of final grade will consist of an exam containing three components T1, T2 and P as follows: 
T1 - theoretical component: 7 points, minimum 2.5 points. 
T2 - theoretical component: 7 points, minimum 2.5 points. 
P - practical component using computer: 6 points, minimum 2 points.

If the sum of the points obtained in the three components is greater than 17, then a (eventually oral) complementary assessment will take place in a date to fix with the student. The final grade can be 17, 18, 19 or 20.