In all countries around us there is a clear tendency towards the creation of interdisciplinary studies. Given the interdisciplinarity of modern science, versatile graduated students come out, who also adapt better to changing technologies and markets, so that technological transfer processes are improved. In many fields of Physics or Mathematics a series of mathematical concepts (fractals, chaos, bifurcations, attractors, solitons, complex systems, interfaces, cellular automata, pattern formation, catastrophes, critical phenomena, self-similarity, self-criticality, scale invariance, renormalization group, ...) have recently been extended today 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 exploration pathways for the future. The comprehension of reality through its modeling is a fascinating and motivating challenge in nearby fields such as Engineering, Biology, Medicine, Economics, Ecology or Telecommunications. One of the purposes of this course is to strengthen and provide the necessary tools that allow connecting with these lines of work, creating the teaching structures that facilitate learning by means of a problem-solving approach in these areas.
At present, it seems commonly accepted that the great challenge of physics and mathematics in the 21st century, as well as the international repertoires and calls, is the interaction with biology and medicine, which FisyMat intends to promote with a specialty or module. In some countries a term that includes part of the previous ideas begins to be generic: mathematical or physical engineering (also bioengineering). Our point of view, regardless of the denomination, is that this program from physics and mathematics is a commitment to a return to the essence of the origins of science: the knowledge of reality and the resolution of problems that is the basic idea of an integral science, without borders.
The program of this course aims to familiarize students with the modeling of complex physical systems in which a large number of particles or dynamic agents can interact through partial differential equations. Special attention will be given to problems originated in Kinetic Theory and Fluid Mechanics. Likewise, a theoretical basis of the variational formulation and analytical resolution techniques will be provided. Since PDEs appear in almost any field of Mathematics and Physics and lately it is gaining importance in other fields such as Biology, Medicine or Economics, it is a fundamental subject.
This course will also present a great interrelation with other subjects such as Dynamic Systems, Numerical Methods, Optimization and Biomathematics, to name just a few examples.
Course competences | |
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Code | Description |
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 |
CB10 | Have the learning skills which allow to continue studying in a self-directed or autonomous way |
CE01 | Solve physical and mathematical problems, planning their solutions based on the available tools and time and resource constraints |
CE05 | Know how to obtain and interpret physical and/or mathematical data that can be applied in other branches of knowledge |
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 |
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 |
CT05 | Autonomous learning and responsibility (analysis, synthesis, initiative and teamwork) |
Course learning outcomes | |
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Description | |
Carry out a critical analysis of a scientific article that addresses topics related to the course | |
Deepen aspects of modeling through the study of different interaction nuclei that represent shock, coagulation, fragmentation or dispersion phenomena | |
Learn non-linear analysis techniques to study the qualitative behavior of problem solutions from Kinetic Theory. This will allow to identify the qualitative and analytical differences between dispersion and diffusion models. | |
The previous point implies that the student will be able to handle easily specialized literature in EDPs | |
Additional outcomes | |
Not established. |
Training Activity | Methodology | Related Competences | ECTS | Hours | As | Com | R | Description * |
Class Attendance (theory) [ON-SITE] | Lectures | 1.2 | 30 | N | N | N | ||
Class Attendance (practical) [ON-SITE] | Problem solving and exercises | 0.6 | 15 | N | N | N | ||
Final test [ON-SITE] | Assessment tests | 0.2 | 5 | Y | Y | Y | ||
Writing of reports or projects [OFF-SITE] | Project/Problem Based Learning (PBL) | 2 | 50 | Y | Y | N | ||
Study and Exam Preparation [OFF-SITE] | Self-study | 2 | 50 | N | N | N | ||
Total: | 6 | 150 | ||||||
Total credits of in-class work: 2 | Total class time hours: 50 | |||||||
Total credits of out of class work: 4 | Total hours of out of class work: 100 |
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 |
Theoretical papers assessment | 100.00% | 0.00% | Problem handouts |
Total: | 100.00% | 0.00% |
Not related to the syllabus/contents | |
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Hours | hours |
Unit 1 (de 5): Introduction to PDEs in Science and Engineering | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 2 |
Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 1 |
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 5 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 5 |
Unit 2 (de 5): Models of Transport Equations in Kinetic Theory and Fluid Mechanics | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 2 |
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 10 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 10 |
Unit 3 (de 5): Variational Formulation | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 10 |
Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 5 |
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 15 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 15 |
Unit 4 (de 5): Analytic Methods for Solving PDEs in Transport Models | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 8 |
Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 4 |
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 12 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 12 |
Unit 5 (de 5): Nonlinear Transport PDEs | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 6 |
Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 3 |
Final test [PRESENCIAL][Assessment tests] | 5 |
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 8 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 8 |
Global activity | |
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Activities | hours |