Degree | Type | Year | Semester |
---|---|---|---|
2503740 Computational Mathematics and Data Analytics | OB | 2 | 1 |
It is very convenient for the student to have achieved a good knowledge of the contents in Calculus in one variable, Linear algebra and Numerical analysis of the first course.
Ordinary differential equations
1. Differential equations as a modeling tool. The initial value problem. Existence and uniqueness and dependence on initial conditions and parameters.
2. The scalar differential equations. Autonomous differential equations. Asymptotic behavior. Examples and applications: the balance of matter and population dynamics.
4. Systems of nonlinear differential equations. Lyapunov stability. Linearization. Phase plane. Applications to mechanics, ecology and chemical kinetics.
5. Numerical resolution methods. The Runge-Kutta methods.
Two hours of theory class per week correspond to this subject. In addition, 11 hours of seminar will be held where students will solve exercises raised by the teacher, both with conventional tools and using a symbolic manipulator. There will also be 12 hours of practical classes that will be devoted mainly to the approximate calculation of solutions of differential equations. It is essential that students have at their disposal the software that teachers recommend during the course. The Virtual Campus of the subject will provide all the material and all the information related to this subject that is necessary for the student.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Theory classes | 30 | 1.2 | 16, 5, 4, 1, 2, 7, 9, 10, 14, 13, 12, 8, 17 |
Type: Supervised | |||
Practical classes | 12 | 0.48 | 16, 4, 15, 3, 7, 9, 6, 10, 12, 11, 8, 17 |
Seminars | 11 | 0.44 | 5, 4, 1, 15, 3, 7, 9, 6, 10, 14, 13, 12, 11, 17 |
Type: Autonomous | |||
Personal study | 64 | 2.56 | 16, 5, 4, 1, 15, 2, 3, 7, 9, 6, 10, 14, 12, 11, 8, 17 |
Program design and report writing | 27 | 1.08 | 16, 5, 4, 1, 15, 3, 7, 9, 6, 10, 14, 13, 12, 11, 8, 17 |
The assessment of the course will be carried out mainly from four activities:
Evaluable seminars. Partial exam (EP): exam of part of the subject, with theoretical questions and problems. Final exam (EF): exam of the whole subject, with theoretical questions and problems. Computer Practices (PR): code explained delivery.
In addition, students will be able to submit to a ressiting exam (ER) with the same characteristics as the previous exams. Practices will not be recoverable.
It is a requirement to pass the subject that PR> = 3.5.
The final grade of the subject will be
max(0.3*EP+0.3*EF,0.6*EF,0.6*ER)+0.25*PR + 0.2*SEM (if this mark does not exceed 10, otherwise, 10).
The "matrícula de honor" will be awarded to the first complete evaluation of the subject. Later achievements will not be considered for this purpose.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Final exam | 30% | 3 | 0.12 | 16, 5, 1, 15, 2, 3, 7, 14, 13, 12, 11 |
Partial exam | 30% | 3 | 0.12 | 16, 5, 1, 2, 3, 7, 14, 13, 12, 11 |
Practices | 25% | 0 | 0 | 16, 5, 4, 1, 15, 3, 9, 6, 10, 13, 11, 8, 17 |
Seminars evaluation | 20% | 0 | 0 | 16, 5, 4, 1, 15, 2, 3, 7, 9, 6, 14, 13, 12, 11, 8, 17 |
Borrelli, R., Coleman C.S. Ecuaciones diferenciales. Una perspectiva de modelación. Oxford University Press (2002)
Lynch, Stephen Dynamical Systems with applications using Python. Birkhauser, 2018
Lynch, Stephen Dynamical Systems with applications using Mathematica. Birkhauser, 2007 [Recurs electrònic]
Martínez, R. Models amb Equacions Diferencials, Materials de la UAB no. 149. Bellaterra, 2004
Noonburg, V. W. Differential Equations: From Calculus to Dynamical Systems. AMS, 2019 [Recurs electrònic]
Perelló, C. Càlcul Infinitesimal amb Mètodes Numèrics i Aplicacions, Enciclopèdia Catalana, 1994
Zill, Dennis G. Ecuaciones diferenciales con aplicacions de modelado. Cengage Learning, 2015
Zill, Dennis G. A First Course in Differential Equations with Modeling Applications, International Metric Edition, 2017 [Recurs electrònic]
There are no software requirements. The student will be able to use what he knows, in particular algebraic manipulation tools such as Maxima, Sage, Maple, etc., as well as numerical computation languages such as C. The use of one of the symbolic manipulators of open source could be mandatory.