Overall objectives:

O1 - To acquire the basic notions of real functions of one variable.
O2 - To master the basic methods for solving differential equations and difference equations.
O3 - To obtain knowledge of applied examples on the study of continuous and discrete populational models.

Syllabus:

1 - Real functions of one variable.
1.1 - General notions about functions.
1.2 - Some real functions of one variable.
1.3 - Limits and continuity.
1.4 - Differentiation.
1.5 - Anti-Derivatives and Integration
2 - Ordinary Differential Equations
2.1 - Differential equations of the first order
2.2 - Linear differential equations of the second order
2.3 - Linear differential equations of the higher order with constant coefficients
2.4 - Sistems of linear differential equations
2.5 - Stability of stationary points. Asymptotic behaviour of a solution.
3 - Difference Equations
3.1 - Linear difference equations of first and second order
3.2 - Stability and asymptotic behaviour of a solution.
4 - Some application to population models: Malthus law and Verhults law.

Literature/Sources:

Apostol, T. , 1983 , Cálculo , Ed. Reverté Lda
Campos Ferreira, J. , 2002 , Introdução à Análise Matemática , Fundação Calouste Gulbekian, Lisboa
Murray, J.D , Mathematical Biology , Springer
Burghes, D. M., Wood , 1984 , Mathematical models in the social, management and life sciences , Ellis Horwood
ELAYDI, Saber N. , 1995 , An introduction to difference equations , New York, Berlin, Heidelberg : Springer
Luís, Rafael D. G. , 2006 , Equações de diferenças e aplicações , Tese Mestrado, Universidade da Madeira

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
The classes are divided in lectures and tutorial classes. The lectures are used to introduce  the student to the notions and the methods. In the tutorial classes, students are encouraged to solve problems using what they had learned in the lectures, individually or in a group. The evaluation consists of two test. The final mark is obtained by taking the average of the marks obtained in each test.