Guías Docentes Electrónicas
1. General information
ECTS credits:
2351 -
Academic year:
602 -
First quarter
Main language:
Second language:
Use of additional languages:
English Friendly:
Web site:
Lecturer: JUAN GABRIEL BELMONTE BEITIA - Group(s): 20 
Phone number
Office hours
Se informará a comienzo del curso

Lecturer: ALICIA MARTINEZ GONZALEZ - Group(s): 20 
Phone number
Office hours
Al comienzo de curso se hará público en Moodle.

Lecturer: VICTOR MANUEL PEREZ GARCIA - Group(s): 20 
Phone number
Office hours
To be determined

2. Pre-Requisites

Basic knowledge of Linear Algebra, Mathematical Analysis, Ordinary Differential Equations and Dynamic Systems

3. Justification in the curriculum, relation to other subjects and to the profession

The analysis of the interaction between species that cohabit in the same environment, and the related issue of the propagation of behaviors or infections, is not only a topic of great interest in Biology, but has largely motivated the development of the theory of differential equations in the 20th century. In this course, we will review the basic mathematical models in this field, and we will pay special attention to the study of some representative examples.

4. Degree competences achieved in this course
Course competences
Code Description
CE07 Ability to understand and apply advanced knowledge of mathematics and numerical or computational methods to problems of biology, physics and astrophysics, as well as to build and develop mathematical models in science, biology and engineering
CE08 Ability to model, interpret and predict from experimental observations and numerical data
CG01 Know how to work in a multidisciplinary team and manage work time
CG02 Ability to generate and independently develop innovative and competitive proposals in research and professional activity in the scientific field of Physics and Mathematics
CG03 Present publicly the research results or technical reports, to communicate the conclusions to a specialized court, interested persons or organizations, and discuss with their members any aspect related to them
CG04 Know how to communicate with the academic and scientific community as a whole, with the company and with society in general about Physics and/or Mathematics and its academic, productive or social implications
CG05 Gain the ability to develop a scientific research work independently and in its entirety. Be able to search and assimilate scientific literature, formulate hypotheses, raise and develop problems and draw conclusions from the obtained results
CG06 Gain the capacity for dialogue and cooperation with scientific and business communities from other fields of research, including social and natural sciences
5. Objectives or Learning Outcomes
Course learning outcomes
Gain the skill to apply and study classical mathematical methods. Critical analysis of mathematical results and their interpretation in terms of the starting model, with a view to its possible improvement
Know and compare the basic models in Population Dynamics, both continuous and discrete
Additional outcomes
Not established.
6. Units / Contents
  • Unit 1: Introduction to the mathematical problems on ecology
  • Unit 2: Continuous Models. Interaction of species. Predator / prey models.
  • Unit 3: Infections Propagation studies.
  • Unit 4: Discrete models. Periodicity and chaos. Matrix models and biological cycles.
  • Unit 5: Other models and applications
7. Activities, Units/Modules and Methodology
Training Activity Methodology Related Competences ECTS Hours As Com R Description
Class Attendance (practical) [ON-SITE] Lectures CE07 1.6 40 Y N Y
Class Attendance (practical) [ON-SITE] Project/Problem Based Learning (PBL) CE08 1.4 35 Y N Y
Practicum and practical activities report writing or preparation [OFF-SITE] Individual presentation of projects and reports CG01 0.66 16.5 Y N Y
Problem solving and/or case studies [ON-SITE] Case Studies CG02 0.5 12.5 Y N Y
Writing of reports or projects [OFF-SITE] Reading and Analysis of Reviews and Articles CG03 0.8 20 Y N Y
Progress test [ON-SITE] Assessment tests CG04 0.12 3 Y N Y
Study and Exam Preparation [OFF-SITE] CG06 0.92 23 Y N Y
Total: 6 150
Total credits of in-class work: 3.62 Total class time hours: 90.5
Total credits of out of class work: 2.38 Total hours of out of class work: 59.5
As: Assessable training activity
Com: Training activity of compulsory overcoming
R: Rescheduling training activity
8. Evaluation criteria and Grading System
  Grading System  
Evaluation System Face-to-Face Self-Study Student Description
Assessment of active participation 10.00% 0.00%
Final test 60.00% 0.00%
Assessment of problem solving and/or case studies 30.00% 0.00%
Total: 100.00% 0.00%  

Evaluation criteria for the final exam:
Evaluation criteria not defined
Specifications for the resit/retake exam:
Evaluation criteria not defined
Specifications for the second resit / retake exam:
Evaluation criteria not defined
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours

Unit 1 (de 5): Introduction to the mathematical problems on ecology
Group 20:
Initial date: 23-09-2019 End date: 23-09-2019

Unit 3 (de 5): Infections Propagation studies.
Group 20:
Initial date: 04/11/2019 End date: 16/12/2019

Unit 4 (de 5): Discrete models. Periodicity and chaos. Matrix models and biological cycles.
Group 20:
Initial date: 13/01/2020 End date: 20/01/2020

10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
F. Brauer, C. Castillo-Chavez Mathematical Models in Population Biology and Epidemiology  
J Muller, C. Kuttler Methods and Models in Mathematical Biology  
J. Hale, H. Koyac Dynamics and Bifurcations  
J. Murray Mathematical Biology Vol 1  
J. Murray Mathematical Biology Vol 2  
S. Wiggins Introduction to Applied Nonlinear Dynamics Systems and Chaos  

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