Mathematics for Biology
Code
10648
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Paulo José Fernandes Louro Ribeiro Doutor
Weekly hours
6
Total hours
88
Teaching language
Português
Objectives
To provide the basis for some working knowledge of mathematical techniques (in the Algebra and Analysis domains) relevant for Biology problem modelization
Prerequisites
The student must be familiar with mathematics taught at pre-university level in Portugal (science area).
Subject matter
1. Topics on matrices
- Systems of Linear Equations
- Operations with Matrices
- Vector spaces
- Norm, inner product, angle and orthogonality
- Determinants
- Eigenvalues and eigenvectors
2. Antiderivatives and integrals
- Antidifferentiation
- Integral calculus
3. Differential equations
- Separable equations
- First order linear equations
- Second order linear equations with constant coefficients
Bibliography
Lecture notes covering all the program contents, available for students
Howard Anton and Chris Rorres, Elementary Linear Algebra with Applications (9th Edition), John Wiley & Sons, 2005. ISBN: 978-0-471-66959-3
William F. Trench, Introduction to Real Analysis, Pearson Education, 2003 (Free Download from http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml).
Cabral, I., Perdigão, C., Saiago, C., Álgebra Linear, Escolar Editora, (4ª edição) 2014.
Teaching method
In this module there are theoretical and practical classes.
Theoretical lectures consist on the introduction of theoretical concepts, and the presentation of proofs of some results, using blackboard and slides.
Practical lectures consist of solving and discuss some of the proposed exercises.
Students dispose from texts covering all subjects, including lists of suggested exercises and application problems.
Substantial part of the study is done on learner autonomy, using the lecture texts and bibliographic brackets, and with the support of teachers outside the classroom, on pre-established schedules reserved for the students'''''''''''''''' attendence.
Evaluation method
Rules of evaluation
The student will be excluded of the evaluation if his presences in problem-solving lessons is inferior to 2/3.
The student may be evaluated by three tests with value 6, 7, and 7 and will be approved if the three tests sum up (rounded) at least 10. The grade will be the rounded sum of the tests.
The student may also be approved by a final exam if the exam''s grade is at least 10. The grade will be the one attained in the exam (rounded) and any grade in any test will be discarded.