Degree | Type | Year | Semester |
---|---|---|---|
2503740 Computational Mathematics and Data Analytics | OB | 3 | 1 |
It is convenient that the student has already passed the subjects Ordinary differential equacions and Calculus in more than one variable
Partial differential equations are a fundamental tool in deterministic modeling of problems in physics, engineering, biology, medicine or finance, among others. The objective of the course is a first introduction to these equations both from an analytical and numerical point of view. We will start with the first order equations by first studying the most basic aspects of the characteristics method for quasi-linear equations. Some of the applications of these models, such as the traffic equation, will be used to visualize the difficulties of modeling and the appearance of weak solutions. Later, the "typical" second order linear equations of mathematical physics will be studied: wave, heat and Laplace. As with ordinary differential equations, in very few cases there are closed formulas available for solving partial differential equations, which is why numerical methods are required to approximate the solutions. In this course, the finite difference method will be introduced as a numerical approximation of the solutions of some of the equations studied.
This course consists of two hours of theory class per week. In addition, 10 hours of seminar will be held where students will solve exercises proposed by the teacher. There will be 12 hours of practical classes that will be devoted mainly to the approximate calculation of solutions of partial differential equations. All the material and all the necessary information for the development of the subject will be provided in the Virtual Campus.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Theory lessons | 30 | 1.2 | 1, 2, 3 |
Type: Supervised | |||
Practical classes | 12 | 0.48 | 6, 7 |
Seminars | 12 | 0.48 | 4, 3, 5 |
Type: Autonomous | |||
Problem solving and practices | 40 | 1.6 | 4, 1, 2, 3, 5, 6, 7 |
Study | 50 | 2 | 4, 1, 2, 3, 5, 7 |
The following evaluation activities will be carried out:
Partial exam (EP). Exam with theoretical questions and problems similar to those worked on during the course.
Final Exam (EF). Exam of the whole subject with theoretical questions and problems similar to those worked on during the course.
Practice mark (PR). It will be evaluated from the project (program) and the corresponding report.
In addition, students will be able to take a recovery exam (ER) with the same characteristics as the exam (EF). The practice mark will not be recoverable.
It is a requirement to pass the subject that max (0.35 * EP + 0.65 * EF, EF, ER)> = 3.5 and that PR> = 3.5.
The final grade for the course will be
0.65 * max (0.35 * EP + 0.65 * EF, EF, ER) + 0.35 PR
The honors will be awarded in the first evaluation in which the subject can be passed.
A student who has participated in assessment activities corresponding to less than 50% of the grade according to the established weight will be considered non-evaluable.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Final exam | 40% | 3 | 0.12 | 4, 1, 2, 3, 5, 7 |
Partial Exam | 25% | 3 | 0.12 | 4, 1, 2, 3, 5, 7 |
Practice Delivery | 35% | 0 | 0 | 4, 1, 2, 3, 5, 6, 7 |
- Y. Pinchover and J. Rubinstein. An introduction to partial differential equations. 2005.
- I. Peral, Primer Curso de EDPs, Addison-Wesley/UAM, 1995.
- L. C. Evans, Partial Differential Equations, Graduate Studies in
Mathematics 19, AMS, 1998.
- S. Salsa, Partial Differential Equations in action: from modelling to theory, Springer, 2008.
- F. John, Partial Differential Equations, Springer-Verlag, 1980.
- W. A. Strauss, Partial Differential Equations: An Introduction,
John Wiley \& Sons, 1992.
- J. C. Strikwerda, Finite Difference Schemes and Partial
Differential Equations, SIAM 2004.
- R. Haberman. Mathematical Models: Mechanical Vibrations, Population
Dynamics, and Traffic Flow. 1998.