Guías Docentes Electrónicas
1. General information
ECTS credits:
Academic year:
First quarter
Main language:
Second language:
Use of additional languages:
English Friendly:
Web site:
2. Pre-Requisites

BA or Graduated in Physics, Mathematics and other experimental sciences. Technicians are also appreciated, mainly those who have a cross-disciplined profile to develop different activities and a significant knowledge of differential equations.

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

A clear trend to the creation of high level interdisciplinary studies has been observed within all of our neighbouring countries. Given the interdisciplinary character of modern science, very versatile graduates are obtained, those who also are better adapted to changing technologies and markets, and technology transfer processes are improved. In many scientific fields, a series of mathematical concepts (such as fractals, chaos, bifurcations, attractors, solitons, complex systems, interfaces, cellular automata, pattern formation, catastrophes, critical phenomena, self-similarity, self-criticality, scale invariance have a relevant role, renormalization group, among others) are today associated to some of the most promising scientific research lines. At present, the relationship between Physics and Mathematics and other sciences is providing important perspectives and new ways of the future. The understanding of reality through its modelling is a fascinating and motivating challenge in nearby fields of interesting evolution such as Ecology, Mathematical Engineering, Astronomy, Economics, Medicine, Biology or Telecommunications. One of the purposes of this subject is to enhance and provide the necessary foundations that allow to connect with these lines of work, introducing and analysing the theoretical concepts that facilitate learning in solving problems in these areas.

Differential equations and dynamic systems appear in the description of real systems infinity. This subject covers, at a medium level, the theory of dynamic systems and their applications to mechanics. The Student target is to handle the tools of differential equations analysis and dynamic systems to approach real problems in Science and Engineering, Astrophysics, Physics and Mathematics in a practical way, those that have been modelled by this type of mathematical objects.

4. Degree competences achieved in this course
Course competences
Code Description
CB06 Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context.
CB07 Apply the achieved knowledge and ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to the area of study
CB08 Be able to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of knowledge and judgments
CB09 Know how to communicate the conclusions and their supported knowledge and ultimate reasons to specialized and non-specialized audiences in a clear and unambiguous way
CB10 Have the learning skills which allow to continue studying in a self-directed or autonomous way
CE02 Develop the ability to decide the appropriate techniques to solve a specific problem with special emphasis on those problems associated with the Modeling in Science and Engineering, Astrophysics, 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
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
CT03 Develop critical reasoning and the ability to criticize and self-criticize
5. Objectives or Learning Outcomes
Course learning outcomes
A coherent development of the theory of Hamiltonian systems
A collection of useful mathematical tools (for physicists)
An integrated view between the mathematical theory of dynamic systems and classic mechanics
The point of view of mechanics in the interpretation of known results (for mathematicians)
Additional outcomes
Use the abilities that have been provided by the usual computer programs of symbolic and numerical calculation, as a resourcefor the analysis and study of some ofthe posed problems.
6. Units / Contents
  • Unit 1: Qualitative Theory of Differential Equations.
  • Unit 2: Discrete and Continuous Dynamic Systems.
  • Unit 3: Hamiltonian Systems.
  • Unit 4: Applications to Mechanics.
  • Unit 5: Practices.
7. Activities, Units/Modules and Methodology
Training Activity Methodology Related Competences ECTS Hours As Com R Description *
Class Attendance (theory) [ON-SITE] Lectures CB06 CB10 CE02 CG05 CT03 1.04 26 N N N Theoretical development of the subjects contents.
Class Attendance (practical) [ON-SITE] Problem solving and exercises CB06 CB07 CB08 CB10 CE02 CT03 0.4 10 N N N Problems solving.
Workshops or seminars [ON-SITE] Workshops and Seminars CB06 CB08 CG03 CT03 0.24 6 Y Y N Assistance to possible conferences or seminars on topics that are related to the subject. Contact with other research groups that use similar techniques or develop related research. Attendance to the exhibition and defence of the final work of the subject made by each of the students of the subject. Analysis of sources and documents. Professors and lecturers must be contacted by those students who are not able to perform this activity partially or totally for fair reasons.
Writing of reports or projects [OFF-SITE] Self-study CB06 CB07 CB08 CB10 CE02 CG05 CT03 2.8 70 Y Y Y Problems solving by the student on the topics of each of the subjects of the subject. Bibliographic review of background, methodology and resources and preparation of a possible final research work (hypothesis, background, objectives, experimental design, methodology, etc.). Analysis of Sources and documents.
Project or Topic Presentations [ON-SITE] Individual presentation of projects and reports CB09 CG03 0.04 1 Y Y Y Defence of the subject final work.
Study and Exam Preparation [OFF-SITE] Self-study CB06 CB07 CB08 CB10 CE02 CG05 CT03 1.4 35 N N N Autonomous personal study of the student and defence training for the subject final work.
Individual tutoring sessions [ON-SITE] Other Methodologies CB06 CE02 CG05 CT03 0.08 2 N N N Direct interaction between the faculty members and the student. The student can be assisted by the faculty members to resolve any academic question of the subject. The opening hours will be published at the beginning of the semester. Although the time of attention in ECTS has been valued, each student will use the time that is necessary according to their needs.
Total: 6 150
Total credits of in-class work: 1.8 Total class time hours: 45
Total credits of out of class work: 4.2 Total hours of out of class work: 105

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 5.00% 0.00% Attendance at conferences or seminars that are related to the course or contacts with other research groups will be valued through an activity report.
Assessment of problem solving and/or case studies 30.00% 0.00% Problems solving and memories of practices elaboration by the student on the topics of each one of the subjects by means of symbolic calculation programs such as Matlab, Mathematica, etc.
Theoretical papers assessment 55.00% 0.00% Bibliographic review of background, methodology and resources and elaboration of a possible research work (hypothesis, background, objectives, experimental design, methodology, etc.). Analysis of sources and documents.
Oral presentations assessment 10.00% 0.00% For the defence of the subject final work.
Total: 100.00% 0.00%  

Evaluation criteria for the final exam:
In the ordinary call, the grade will depend on the marks obtained in each one of the training activities evaluated. The delivery dates of problems (practices) and the final essay title of the subject will be communicated in advance in the virtual platform. The final grade will be the weighted average according to the assessments (percentages) established in the evaluation criteria. To pass the subject it is necessary to obtain a minimum grade of 5 in each of these criteria corresponding to the compulsory overcoming training activities.
Specifications for the resit/retake exam:
The same criteria will be followed as in the Ordinary Call.
Specifications for the second resit / retake exam:
The same criteria will be followed as in the Ordinary Call.
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours

Unit 1 (de 5): Qualitative Theory of Differential Equations.
Teaching period: Weeks 1-4
Comment: The dates that have been planned for each week are estimated.

Unit 2 (de 5): Discrete and Continuous Dynamic Systems.
Teaching period: Weeks 5-10
Comment: The dates that have been planned for each week are estimated.

Unit 3 (de 5): Hamiltonian Systems.
Teaching period: Weeks 11 - 13
Comment: The dates that have been planned for each week are estimated.

Unit 4 (de 5): Applications to Mechanics.
Teaching period: Weeks 1 - 13
Comment: This subject will be developed throughout the Semester. The dates that have been planned for each week are estimated.

Unit 5 (de 5): Practices.
Teaching period: Weeks 1 - 13
Comment: This subject will be developed throughout the Semester. The dates that have been planned for each week are estimated.

General comments about the planning: The subjects will be taught consecutively taught by means of being adapted to the current calendar that corresponds to the first term of the 2019-20 academic year. The topics delivery order may be altered for any justified cause. The "Applications to Mechanics" and "Practices" subjects (Topics 4 and 5) will be alternated throughout the Semester. The dates that have been planned for each week are estimated. The last week of the semester will be focused on the subject final work presentation.
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
Bellido Guerrero, J. Carlos Ecuaciones diferenciales ordinarias Madrid Paraninfo, 978-84-283-3015-2 2014 Ficha de la biblioteca
Block, L. S.(Louis Stuart)1947- Dynamics in one dimension Springer-Verlag 0-387-55309-6 1992 Ficha de la biblioteca
Devaney, Robert L.1948- An Introduction to chaotic dynamical systems Addison-Wesley Company 0-8053-1601-9 1987 Ficha de la biblioteca
George F. Simmons y Steben G. Krantz Ecuaciones diferenciales. Teoría, técnica y práctica México MacGraw-Hill 978-0-07-286315-4 2007 Ficha de la biblioteca
Guckenheimer, John Nonlinear oscillations, dynamical systems and bifurcations of vector fields Springer-Verlag 0387-90819-6 1997 Ficha de la biblioteca
K,R. Meyer, G.R. Hall and D. Offin Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Springer-Verlag 978-0-387-09723-7 2009  
Lampart, M. Dynamical Systems for Geoinformatics 2013  
Siegel, C., Moser, J. Lectures on Celestial Mechanics Springer 1971  
Strogatz, Steven H.Steven Henry Nonlinear dynamics and chaos: with applications to Physics, Biology, Chemestry, and Engineering Westview 978-0-7382-0453-6 2000 Ficha de la biblioteca
Víctor Jiménez López Ecuaciones diferenciales Murcia Servicio de Publicaciones de la Universidad de Murcia 2000  
Wiggins, Stephen Introduction to applied non linear dynamical systems and chaos Springer-Verlag 0-387-00177-8 2003 Ficha de la biblioteca

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