Mathematics and Statistics

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 evaluation consists of a final exam or, alternatively, two intermediate tests. For the tests’ admission the presence of 75% of all classes is required.

Learning Outcomes

The Course Mathematics and Statistics 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 and probability 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

1. Differential Calculus: Real Functions. Differentiation. Indeterminate forms. Application to biological and chemical models.

2. Integral Calculus: Antiderivatives: integration by parts and by substitution. The definite integral: definition and properties. Applications of integral calculus.  Improper integrals. Application to biological and chemical models.

3. Differential Equations: Modeling using differential equations. Separable variables differential equations. Exponential growth. Logistic equation.  Linear differential equations. Application to biological and chemical models

4. Systems of linear equations: Gaussian elimination method. Matrix notation and matrix operations. Inverses and transpose.  Indeterminate and Impossible systems. Application to biological and chemical models

5. Probability: Random phenomena. Definition of Probability. Conditional probability. Independent events.  

Head Lecturer(s)

Maria da Graça Santos Temido Neves Mendes

Assessment Methods

Final assessment
Exam: 100.0%

Continuous assessment
Frequency: 100.0%

Bibliography

Adérito Araújo, “Biomatemática”, Departamento de Matemática da Faculdade de Ciências e Tecnologia da Universidade de Coimbra, 2010.

James Stewart,  "Cálculo", vol. I e II,  4ª ed., São Paulo, Thomson Learning, 2000.

M. Teresa F. Oliveira-Martins,  "Álgebra Linear e Geometria Analítica", Departamento de Matemática da Faculdade de Ciências e Tecnologia da Universidade de Coimbra, 2003.

Earl G. Swokowski,  "Cálculo com Geometria Analítica", vol. I e II, São Paulo, McGraw-Hill, 1983.

 Gilbert Strang, "Introduction to Linear Algebra", 3ª ed., Wellesley-Cambridge Press, 2005.