Mathematics

Recommended Prerequisites

Knowledge and mastery of the subjects taught in Mathematics in secondary education.

Teaching Methods

Detailed lectures introducing and explaining concepts, principles and theories. In the theoretical-practical classes, students will solve problems with the guidance of the teacher. The students should solve exercises at home which can discuss later with the professor. The evaluation consists of a final exam or, alternatively, two intermediate tests

Learning Outcomes

The Course of Biomathematics has formative and pragmatic goals. The formative goals consist of introducing a perspective of mathematics that values the intuition underlying the various concepts, showing the need of mathematical analysis in the development of creativity, critical spirit and ability to adapt to new problems. The pragmatic goals focus on developing effective skills in problem solving. It is further intended that, where appropriate, the issues addressed are within the scope of Pharmaceutical Science, Chemistry or Biology

Work Placement(s)

No

Syllabus

Chapter I Differential calculus

1.0 Elementary functions.

1.1 Functions of several real variables.

1.2 Partial derivatives and the gradient vector.

1.3 The chain rule.

1.4 Linear approximation.

1.5 Maximum and Minimum values of 2 variables functions.

1.6 Application to biological and chemical models.

Chapter II Integral calculus

2.1 Antiderivatives. Integration by parts and by substiyution.

2.2 The definitive integral: definition and properties.

2.3 Applications of integral calculus.

2.4 Improper integrals.

Chapter III Differential equations

3.1 Separable variables differential equations.

3.2 Linear differential equations.

3.3 Logistic equation.

3.4 Modeling using differential equations.

3.5 Application to biological and chemical models.

Chapter IV Systems of linear equations

4.1 Matrix notation and matrix operations.

4.2 Least squares method and linear regrssion line.

Head Lecturer(s)

Gonçalo Gutierres da Conceição

Assessment Methods

Assessment
Frequency: 100.0%

Assessment
Exam: 100.0%

Bibliography

Cálculo - Volumes I e II, James Stewart, 5ªedição, Thomson.

Introdução à Álgebra Linear, Ana Paula Santana e João Filipe Queiró, gradiva.

Notas de apoio à disciplina de Matemática do MICF, Gonçalo Gutierres, http://www.mat.uc.pt/~ggutc/MICF/MatFarm.pdf