Mathematics
Code: 107948 ECTS Credits: 4| Degree | Type | Year |
|---|---|---|
| Environmental Biology | OB | 1 |
Contact
- Name:
- Silvia Cuadrado Gavilan
- Email:
- silvia.cuadrado@uab.cat
Teachers
- Laura Rodriguez Cima
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Rational and real numbers, numerical approximation, and exponential notation. Absolute value and inequalities.
Elementary functions: linear, polynomial, rational, exponential, logarithmic, and trigonometric.
Objectives and Contextualisation
For a university degree in Biologia Ambiental it is important to achieve a solid mathematical formation. In this sense, this subject has a double aim. On one hand, to give the student the necessary mathematical background in the fields of linear algebra and differential calculus, allowing him/her, and this is the second aim, to build up mathematical models for some biological problems.
Learning Outcomes
- CM02 (Competence) Integrate relevant mathematical data to make judgments applied to the field of environmental biology and that include multidisciplinary reflection.
- KM05 (Knowledge) Describe natural phenomena in the field of biology through mathematics.
- KM06 (Knowledge) Apply exponential, logarithmic and potential functions to solve biological problems.
- KM07 (Knowledge) Produce vectors and matrices, recognizing the simplification that this entails in solving problems of biological interest.
- SM03 (Skill) Apply the basic concepts of linear algebra, differential calculus, and integral calculus to solve and model biological problems and ecological data.
- SM04 (Skill) Apply classical mathematical models to the population growth of different living organisms.
Content
1. A brief review
1.1 The derivative. Geometric and kinematic interpretations. Chain rule. Growth and decay. Maxima, minima, and optimization. Graphs.
1.2 The integral. The fundamental theorem of calculus. Antiderivative calculation. Applications.
2. Differential equations
2.1 Differential equations with separable variables. Exponential growth. Mass balances. The logistic differential equation.
2.2 Linear equations. Mass balances.
2.3 Geometric interpretation of differential equations. The initial value problem.
2.4 The qualitative method: equilibria and stability.
3. Linear algebra
3.1 Systems of linear equations, matrices, and matrix computation.
3.2 Eigenvalues and eigenvectors. Diagonalization.
3.3 Discrete-time population dynamics: iteration. Age dependence.
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| oral expositions | 19 | 0.76 | CM02, KM05, KM06, KM07, SM03, SM04, CM02 |
| practical classes | 14 | 0.56 | CM02, KM05, KM06, KM07, SM03, SM04, CM02 |
| Type: Supervised | |||
| tutorial assistance | 6 | 0.24 | CM02, KM05, KM06, KM07, SM03, SM04, CM02 |
| Type: Autonomous | |||
| Studying | 47 | 1.88 | CM02, KM05, KM06, KM07, SM03, SM04, CM02 |
Oral expositions will be devoted to transmit the different topics and scientific knowledge of the subject to the student.
Problem sessions are fundamental for the student to achieve a deep understanding of these contents. These classes are organized around a list of problems that the students try to solve.
This is complemented with individual tutorial assistance to clarify some doubts, or to discuss the results of the diferent evaluation activities.
The student will have to solve some special exercices, which contribute with a 15% to the final marks.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| 1. Partial exam | 35% | 4 | 0.16 | CM02, KM05, KM06, KM07, SM03, SM04 |
| 2. Global exam | 50% | 6 | 0.24 | CM02, KM05, KM06, KM07, SM03, SM04 |
| 3. Submission of exercises | 15% | 4 | 0.16 | CM02, KM05, KM06, KM07, SM03, SM04 |
The final grade for the course will consist of several components:
-
Quizzes/assignment submissions, which may be completed during class time (15%). This activity cannot be retaken.
-
Two assessments for the course: a midterm exam (35%) and a final exam (50%). It is mandatory to score at least 3.5 out of 10 on the final exam in order to avoid the make-up exam.
Students who do not achieve a final grade of 5 or higher may take a make-up exam, which will account for 85% of the final grade.
Honors distinctions will be awarded based on the first full evaluation of the course. They will not be granted to another student who achieves a higher grade after the make-up exam.
Students will receive a "Not Assessable" grade if the evaluation activities they complete account for less than 25% of the final grade.
Students choosing the single assessment option will take a comprehensive final exam on the same day as the final exam for the rest of the class. This exam will include a section related to the assignments completed by other students. If the student fails this exam, they may take the make-up exam on the same day as the make-up exam for the rest of the class, under the conditions previously described.
Bibliography
There is no text book fitting exactly the content of the subject. The following text books cover different parts of the course.
- Matemàtiques i modelització per a les ciències ambientals, Jaume Aguadé, Dipòsit digital de documents de la UAB
- Matemáticas para ciencias de C. Neuhauser (Pearson, Prentice Hall)
- Matemáticas básicas para biocientíficos de E. Batschelet (Editorial Dossat)
- Mathematical ideas in Biology de J. Maynard Smith (Cambridge U.P.)
- Introducción al álgebra lineal, H. Anton (Editorial Limusa)
Software
No mathematical software is used
Groups and Languages
Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 2 | Catalan | first semester | morning-mixed |
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |