ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Mathematical Analysis
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable
Introduce students to certain global aspects of the qualitative theory of Ordinary Differential Equations such as those relating to periodic orbits, including, in the case of two dimensional dynamic systems, the Poincaré-Bendixon theory and the index theory.
Familiarize students with the classical theory of equations of Partial Differential Equations. Know techniques for solving first and second order equations. Classify second order equations. Know the results of existence and uniqueness of parabolic, hyperbolic and elliptic problems.
1.- Poincaré-Bendixson theory. Index theory. Applications (20h.)
2.- First integrals. Methods for obtaining first integrals. (4h)
3.- Linear and quasi-linear partial differential equations of the first order. Resolution using characteristic curves and first integrals. (8h)
4.- Nonlinear first-order partial differential equations: The Monge cone. (12h)
5.- Partial differential equations of second order. Classification and canonical forms of linear equations. Elliptic, hyperbolic and parabolic problems. (12h)
Basic Bibliography:
CABADA, A. Problemas Resueltos de Ecuaciones en Derivadas Parciales. http://webspersoais.usc.es/export9/sites/persoais/persoais/alberto.caba…
JOHN, F. Partial Differential Equations. Springer – Verlag, 1991.
PERAL, I. Primer Curso de Ecuaciones en Derivadas Parciales. Addison – Wesley, 1995.
PERKO L., Differential Equations and Dinamical Systems, Springer, 1996. (1202 287, 34 400)
SOTOMAYOR, J., Liçoes de Equaçoes Diferenciais Ordinarias, IMPA, 1979. (1202 83, 34 165)
STAVROULAKIS, I. P.; TERSIAN, S. A. Partial Differential Equations. An Introduction with Mathematica and MAPLE. World Scientific, 2003.
Complementary Bibliography:
ARNOLD, V. Ecuaciones Diferenciales Ordinarias, Rubiños, 1995 (1202 78, 34 466)
COURANT, R.; HILBERT, D. Methods of Mathematical Physics, Vol. I e II. Wiley – Interscience, 1962. (00 9)
DOU, A Ecuaciones en Derivadas Parciales. Dossat, 1970. (35 139)
EVANS, L. C. Partial Differential Equations. AMS, 1998. (1202 347, 35 402)
GOCKENBACH, M. S., Partial differential equations. Analytical and numerical Methods, Siam, 2011. (35 512)
HYUN-KU, R. First-order partial differential equations. Dover Publications 2001 (35 442)
KEVORKIAN, J. Partial differential equations: analytical solution techniques. Chapman & Hall, 1990 (35 421)
MCOWEN, R. Partial differential equations: methods and applications. Upper Saddle River, 2003 (35 459)
PETROVSKY, I.G., Lectures on Partial Differential Equations. Interscience, 1964. (35 45)
STRAUSS, W. A. Partial Differential Equations, an Introduction. John Wiley, 1992. (35 318)
WEINBERGER, H. F. Ecuaciones Diferenciales en Derivadas Parciales. Reverté, 1992. (1202 13, 35 142)
Online accessible bibliography:
• Teschl, Gerald. Ordinary Differential Equationsand Dynamical Systems. URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.444.2949&rep=r…
The following links are accessible at Springer Link (See: https://www.youtube.com/watch?v=t8hPlEwNFLg&feature=emb_logo)
• David G. Schaeffer, John W. Cain. Ordinary Differential Equations: Basics and Beyond. URL: https://link.springer.com/book/10.1007/978-1-4939-6389-8
• Walter G. Kelley, Allan C. Peterson. The Theory of Differential Equations. URL: https://link.springer.com/book/10.1007/978-1-4419-5783-2
• Shankar Sastry. Nonlinear Systems. URL: https://link.springer.com/book/10.1007/978-1-4757-3108-8
• Hartmut Logemann, Eugene P. Ryan. Ordinary Differential Equations. https://link.springer.com/book/10.1007/978-1-4471-6398-5
• Colin Christopher, Chengzhi Li. Limit Cycles of Differential Equations. URL: https://link.springer.com/book/10.1007/978-3-7643-8410-4
• Qingkai Kong. A Short Course in Ordinary Differential Equations. URL: https://link.springer.com/book/10.1007/978-3-319-11239-8
• David Betounes. Differential Equations: Theory and Applications. URL: https://link.springer.com/book/10.1007/978-1-4419-1163-6
• Jan Willem Polderman, Jan C. Willems. Introduction to Mathematical Systems Theory. URL: https://link.springer.com/book/10.1007/978-1-4757-2953-5
In this subject, the competences included in the USC Mathematics Degree Title Report will be worked on (see the link https://www.usc.es/export9/sites/webinstitucional/gl/servizos/sxopra/me…)
In particular we will focus on the basic skills CB2, CB3, CB4 and CB5; in transversal competences CT1, CT2, CT3 and CT5; as well as in all the general and specific competences.
As regards the specific knowledge of the subject, an effort will be made to ensure that students understand and rigorously express the concepts and techniques that are developed in the program, as well as apply the theoretical and practical knowledge acquired in the subject. The capacity for analysis and abstraction in the definition, formulation and search for solutions to problems will be worked on, both in academic contexts and in possible applications. We will focus on the ability to translate, in terms of differential equations, some problems that occur in nature (physics, biology, engineering, etc.) and interpret the obtained results.
The general methodological indications established in the USC Mathematics Degree Report will be followed.
The teaching is programmed in expository, interactive seminar and laboratory classes and tutorials in the classroom. In the expository classes the essential contents of the discipline will be exposed, in the interactive ones the problems collected in the corresponding bulletins will be proposed and solved. The tutorials will be dedicated to the resolution of doubts and to the discussion and debate with the students of the different concepts developed throughout the subject.
The development of the different competences will be done in the daily presentation of the different topics of the subject by the teacher and will be worked on in more detail in the interactive classes.
The general evaluation criteria established in the USC Mathematics Degree Report will be followed.
The evaluation will consist of two parts: a continuous evaluation and a final exam.
The continuous evaluation will consist of two written tests that will be carried out during class hours. Its exact date will be announced well in advance. One of them will be related to Ordinary Differential Equations and the other to Partial Differential Equations.
In the final written exam, the knowledge achieved by the students will be measured in relation to the concepts and results of the subject, both from the theoretical and practical point of view, also assessing the clarity and logical rigor shown in the exposition of the themselves.
For the calculation of the final grade of the first opportunity (CF), the continuous assessment grade (AC) and the final exam grade (EF) will be taken into account, and the formula CF = AC*3/5 +(1- AC*3/50)*EF will be applied.
It will be understood as not presented to the one who, having not passed the subject with the note of the continuous evaluation, does not appear for the final exam.
On the second opportunity, the same evaluation system will be used, with the same qualification of the continuous evaluation, but with the final grade corresponding to the second opportunity, which will be a final written exam of the same type as the first one.
WORK IN CLASSROOM
Lectures (28h)
Seminar classes (14h)
Laboratories (14h)
Tutorials in very small groups (2h)
Total hours of work in classroom: 58
STUDENT PERSONAL WORK
Individual or group autonomous study (56h)
Writing exercises, conclusions and other works (20h)
Programming/experimentation and other computer work (10h)
Recommended readings, activities in the library or similar (6h)
Total hours of personal student work: 92
TOTAL: 150 hours
Students must have a good knowledge of the topics covered in the Mathematical Analysis subjects and especially of what is studied in the subjects "Introduction to Ordinary Differential Equations", "Ordinary Differential Equations" and "Fourier Series and Introduction to Partial Differential Equations”.
Starting from this situation, they must work regularly (daily) and rigorously. It is essential to actively participate in the learning process of the subject. Attend and participate regularly in both theoretical and practical classes, attend classes in a participatory way, especially in small group classes, and ask pertinent questions that allow them to clarify any doubts that may arise in relation to the subject.
Alberto Cabada Fernandez
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813206
- alberto.cabada [at] usc.gal
- Category
- Professor: University Professor
| Monday | |||
|---|---|---|---|
| 18:00-19:00 | Grupo /CLE_01 | Galician | Classroom 07 |
| Tuesday | |||
| 18:00-19:00 | Grupo /CLE_01 | Galician | Classroom 07 |
| Thursday | |||
| 17:00-18:00 | Grupo /CLIS_01 | Galician | Classroom 03 |
| 18:00-19:00 | Grupo /CLIL_01 | Galician | Classroom 03 |
| 19:00-20:00 | CLIL_02 | Galician | Classroom 03 |
| 06.04.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 07.09.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |