Course code: 505205 | Subject title: ORDINARY DIFFERENTIAL EQUATIONS | ||||
Credits: 6 | Type of subject: Mandatory | Year: 2 | Period: 1º S | ||
Department: Estadística, Informática y Matemáticas | |||||
Lecturers: | |||||
PALACIAN SUBIELA, JESUS FCO. (Resp) [Mentoring ] |
First order differential equations. Linear equations and power series solutions. Linear systems. Dynamical systems. Differential equations of physics. Sturm-Liouville problems.
Methodology - Activity |
Attendance |
Self-study |
A1- Expository / participative classes |
42 |
|
A2- Hands on learning |
14 |
|
A3- Studying and autonomous work of the student |
|
88 |
A4- Tutorials |
|
2 |
A5- Assessment tests |
4 |
|
Total |
60 |
90 |
Learning outcome |
Assessment activity |
Weight (%) | It allows test resit |
Minimum required grade |
---|---|---|---|---|
RA1-RA5 | Tasks and Report: Continuous Assessment | 20% | Yes | 0 |
RA1-RA5 | Individual written test (long answer tests) | 80% | Yes | 5 |
If the student did not get the minimum grade to weigh in any of the activities, the grade of the subject would be 4.9 out of 10 at most (fail).
1. Introduction to differential equations. Motivation and basic definitions. Elementary differential equations.
2. First-order differential equations. Separation of variables. Homogeneous. Exact equations. Integrating factor. First-order linear. Changes of variables.
3. Theoretical aspects. Initial value problem. Existence and uniqueness theorem. Boundary problems. Approximate solutions.
4. Linear differential equations. General theory. Constant coefficients. Regular and singular points. Analytical solutions. Power series and Frobenius methods. Special functions. Introduction to Sturm-Liouville problems.
5. Linear systems of equations. General theory. Constant coefficients. Homogeneous and non-homogeneous systems.
6. Nonlinear equations. Introduction to dynamical systems. Applications in real life.
Access the bibliography that your professor has requested from the Library.
Basic bibliography
[1] D.G. Zill. A First Course in Differential Equations with Modeling Applications Problems, Tenth Ed., Brooks/Cole, Cengage Learning, 2013.
Additional bibliography
[1] F. Diacu. An Introduction to Differential Equations: Order and Chaos. W.H. Freeman, 2000.
[2] M.W. Hirsch, S. Smale y R.L. Devaney. Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press, 2012.
[3] F. Marcellán, L. Casasús y A. Zarzo. Ecuaciones diferenciales. Problemas lineales y aplicaciones. McGraw-Hill, 1991.
[4] G. Strang. Differential Equations and Linear Algebra. Wellesley-Cambridge Press, 2015.
[5] F. Ayres. Schaum's Outline of Differential Equations. McGraw-Hill, 1992.
[6] Ó. Ciaurri. Instantáneas diferenciales. Métodos elementales de resolución de ecuaciones diferenciales ordinarias, estudio del problema de Cauchy y teoría de ecuaciones y sistemas lineales. Universidad de La Rioja, 2011.
[7] S. Novo, R. Obaya y J. Rojo. Ecuaciones y sistemas diferenciales. McGraw-Hill, 1995.