Class Mathematics for Biology

A wide variety of fundamental mathematical methods are exposed, intending to cover a wide range of problems occuring in Life Sciences.

In addition, an algebrization of some topics intends to induce a general reasoning which applies to several seemingly different problems occuring in many situations in this field of expertise.

1. Introduction to Natural, Integer, Rational and Real numbers. Main properties.
2. Real sequences: Monotone and limited sequences. Convergent sequences. The number e.
3. Functions:  Domain. Codomain and graphic.  Sum, product and composition of functions. Inverse function and its graphic representation.
4. The exponencial function and its inverse.

1. Limits, Continuity and Differenciability.
2.  
3. Local Extremes and inflection points
4. Álgebraic curves. Conical curves. Surfaces in space.
5. Real Functions with vectorial variables. Domain, Tangent plane and local extreme points.

1. Classification of improper integrals.

Integration in space. Calculation of volumes.

If time allows, some tópics will be presented, concerning the corresponding cycle of studies (Biology), whose modelation and ultimately its resolution, depend on tools that share affinities with the pending syllabus and may hopefully motivate students for durther investigations.

• Sárrico, C.; Análise Matemática ¿ Leitura e exercícios, Col. Trajetos Ciência 4, Gradiva, Lisboa, 1999.
• Apostol, T.; Cálculo I, Editora Reverte.