Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| 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. [Mentoring ] | LOPEZ GARCIA, JOSE LUIS (Resp) [Mentoring ] | ||||
Module/Subject matter
- Subject Matter Level 1: Mathematics
- Subject Matter Level 2: Advanced Mathematics
Contents
First order differential equations. Linear equations and power series solutions. Linear systems. Dynamical systems. Differential equations of physics. Sturm-Liouville problems.
General proficiencies
- CB3¿ Ability to collect and interpret relevant data (usually within their area of study) in order to make judgments that include reflection on relevant issues of a social, scientific or ethical nature.
- CB5- Learning skills necessary to undertake further studies with a high degree of autonomy.
- CG1- Apply the acquired analytical and abstraction skills, intuition, and logical thinking to identify and analyze complex problems, and to seek and formulate solutions in a multidisciplinary environment.
Specific proficiencies
- CE7- To analyze, validate and interpret mathematical models of real-world situations, using the tools provided by differential and integral calculus of several variables, complex analysis, integral transforms and numerical methods to solve them.
Learning outcomes
- RA17- Mastering the concept of differential equation and system of differential equations, existence and uniqueness of solution.
- RA18- Knowing the basic techniques for solving first order differential equations.
- RA19- Understanding the structure of the space of solutions of differential equations and linear systems. Mastering the basic techniques of solving differential equations and linear systems with constant coefficients.
- RA20- Handling the technique of solving linear differential equations using power series and its usefulness in the equations of mathematical physics.
- RA21- Learning concepts of dynamical system and acquiring the associated fundamental concepts.
Methodology
|
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 |
Evaluation
| 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).
Agenda
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.
Bibliography
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.