Degree | Type | Year | Semester |
---|---|---|---|
2501915 Environmental Sciences | OT | 4 | 0 |
The prerequisite is to have passed the subjects of Mathematics and Statistics of the degree.
1. Discrete time models in dimension 1.
The law of Malthus
Nonlinear models The discrete logistic model. Fixed points and stability. Graphic iteration.
Periodic behaviors and chaotic behaviors.
2. Linear models at discrete time in dimension greater than 1.
Systems of linear equations in differences. General solution
Populations with age structure. The Leslie model. Asymptotic behavior: the fundamental theorem of demography.
Markov chains.
3. Continuous time models in dimension 1: Differential equations.
Examples: Exponential growth. Migrations Radioactive decay Solutions
Differential equations of first order separable and linear.
The logistic differential equation. The Allee effect.
The hysteresis effect. A model of ecology. A model about the global energy balance.
4. Continuous time models in dimension greater than 1: Systems of differential equations.
Introduction: trajectories, equilibrium points, periodic orbits.
The linear systems. General solution Balances and stability: centers, spotlights, chairs and nodes.
The model of Lotka and Volterra.
Non-linear systems Linealització. Models of Ecology and kinetics chemistry.
In the process of learning the subject is fundamental the homework of the student who at all times will have the help of the teacher.
The contact hours are distributed in:
Lectures: The teacher introduces the corresponding basic concepts in the subject of the subject by showing several examples of its application. The student will have to supplement the teacher's explanations with the personal study.
Problem session: The understanding and application of the concepts and tools introduced in the theory class, with the realization of exercises. The student will have lists of problems, a part of which will be solved in the problem classes. The rest will have to be solved by the student as part of his autonomous work.
Lab session: The student will use packages of symbolic and numerical calculation programs. The practical classes will be held in the computer rooms. In these classes the application of mathematical tools will be applied to models that require the use of computer software.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Lab session | 9 | 0.36 | 2, 3, 6, 5, 4, 7, 1, 11, 8, 10, 9 |
Lectures | 32 | 1.28 | 3, 7, 10 |
Problem session | 9 | 0.36 | 2, 3, 6, 5, 4, 7, 1, 11, 8, 10 |
Type: Autonomous | |||
Solving problems and studying theoretical concepts | 95 | 3.8 | 2, 3, 6, 5, 4, 7, 11, 8, 10, 9 |
There will be two partial exams with a value of 40% of the mark each one of them and the qualification of the lab sessions will add 20% of the overall mark. In case that the average is not less than 5 or the mark of any of the partial exams is less than 3, a resit exam will be carried out that will not be able to change the lab mark but the one of the remaining 80%.
To ask for a resit the student must have been received a mark in activities that represent at least 2/3 of the global mark during the course.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Assessment Lab session | 20% | 1 | 0.04 | 2, 3, 6, 5, 4, 7, 1, 11, 8, 10, 9 |
Final test | 40% | 2 | 0.08 | 2, 3, 6, 5, 4, 7, 1, 11, 10 |
Mid-term test | 40% | 2 | 0.08 | 2, 3, 6, 5, 4, 7, 1, 11, 8, 10 |
Basic:
Complementary: