Degree | Type | Year | Semester |
---|---|---|---|
2500250 Biology | FB | 1 | 1 |
This program of study has a double objective. The first is to give the student a basic mathematical training, focused on linear algebra and on one real variable calculus: derivation, integration and simple differential equations, which allows to understand the language of Science. The second is to introduce mathematical modeling of Biology, by means of simple examples that can be analyzed with the mathematical tools available to students.
With this idea in mind most of the contents will be presented motivated by scientific problems, usually from the field of Biology. In particular Population Dynamics and Ecology that are the most matematizable areas of Biology at an elementary level. Linear algebra will be addressed as the natural tool for the study of the linear growth and age-structured populations, while differential equations will be introduced as the fundamental tool for the study of the magnitudes that change with time continuously, biological populations, as well as concentrations of chemical substances, for example.
In short, the objective is that students see mathematics as a essential tool to describe most of the physical phenomena.
1. Functions and derivatives
1.1 Linear functions. Polynomial functions. Rational functions. Exponential functions. Inverse function. Logarithmic functions. Graphics
1.2 The derivative: tangent and velocity.
1.3 Growth. Optimization. Graphics revisited.
2. Integral calculus
2.1 The integral. The fundamental theorem of calculus. Primitives. Applications
3. Linear algebra
3.1 Systems of linear equations. Matrices.
3.2 Eigenvalues and eigenvectors. Diagonalisation.
3.3 Discrete population dynamics: iteration. Dependence on age
6. Differential equations
6.1 Differential equations of separate variables. Exponential growth. Balance of matter. The logistic differential equation.
6.3 Geometric interpretation of differential equations. The problem of initial value.
6.4 The qualitative method: balances and stability.
*Unless the requirements enforced by the health authorities demand a prioritization or reduction of these contents.
The student acquires the scientific knowledge of the subject by attending theory lectures and learns to use them in problem lectures. We must reinforce this knowledge through the personal study of the theoretical part to be able to apply it to the exercises.
The realization of exercises is one of the most important tasks of the study, they illustrate and motivate all the theoretical development. On the other hand, the objective of the subject is that students learn to use mathematics as a working tool and therefore learn to face different types of problems modeling it or turning them into a mathematical question that they can solve.
Theoretical lectures will be reinforced with as many applied examples as possible and in addition the student will be asked to give periodic exercises that will be focused on facing the student with these modeling tasks.
*The proposed teaching methodology may experience some modifications depending on the restrictions to face-to-face activities enforced by health authorities.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Exercises | 15 | 0.6 | 5, 7, 8, 6, 2, 18, 17 |
Theory | 35 | 1.4 | 5, 7, 8, 6, 2, 18, 17 |
Type: Supervised | |||
Tutoring | 5 | 0.2 | 5, 6, 17 |
Type: Autonomous | |||
Exercises | 35 | 1.4 | 5, 6, 2, 18 |
Study | 35 | 1.4 | 6 |
Tests | 15 | 0.6 | 6, 3 |
The final grade will be obtained from different parts.
To participate in the recovery, the students must have previously been evaluated in a set of activities whose weight equals to a minimum of two thirds of the total grade of the subject or module. Therefore, students will obtain the "Non evaluable" qualification when the assessment activities carried out have a weighting of less than 67% in the final grade.
Delivery of exercises is mandatory. The students will obtain the "Non evaluable" qualification when the number of deliveries is less than 80% of the scheduled deliveries.
The repeating students will have to do the same assessment activities as new entry students.
The Honor Grade can only be awarded to students who have obtained a final grade equal to or greater than 9. They can be awarded a maximum of 5% of the students enrolled.
(* This exam is not mandatory and can be used both to upgrade, and to recover the grade obtained in the partial tests).
*Student’s assessment may experience some modifications depending on the restrictions to face-to-face activities enforced by health authorities.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Exercises delivery | 30% | 2 | 0.08 | 16, 15, 4, 1, 5, 7, 8, 6, 9, 14, 13, 12, 10, 11, 2, 3, 17 |
First partial exam | 30% | 2 | 0.08 | 16, 15, 4, 1, 5, 7, 8, 6, 9, 14, 13, 12, 10, 11, 3, 18, 17 |
Recovery exam | 70% | 3 | 0.12 | 16, 15, 4, 1, 5, 7, 8, 6, 9, 14, 13, 12, 10, 11, 2, 17 |
Second partial exam | 40% | 3 | 0.12 | 16, 15, 4, 1, 5, 7, 8, 6, 9, 14, 13, 12, 10, 11, 2, 17 |
There are no texts in the literature that adapts exactly to the content of the course. For this reason, three general-purpose texts are proposed that cover most topics and in which mathematical concepts are introduced intuitively and illustrated with many practical examples. These three texts are complemented by books that allow you to explore the most important topics of the course.
General bibliography
Complementary bibliography