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.
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.
Course competences | |
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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 |
Course learning outcomes | |
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Description | |
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 | |
Description | |
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. |
Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | 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
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% |
Not related to the syllabus/contents | |
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Hours | hours |
Unit 1 (de 5): Qualitative Theory of Differential Equations. | |
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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. | |
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Teaching period: Weeks 5-10 | |
Comment: The dates that have been planned for each week are estimated. |
Unit 3 (de 5): Hamiltonian Systems. | |
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Teaching period: Weeks 11 - 13 | |
Comment: The dates that have been planned for each week are estimated. |
Unit 4 (de 5): Applications to Mechanics. | |
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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. | |
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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. |