Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| Course code: 504209 | 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 ] | |||||
Module/Subject matter
ORDINARY DIFFERENTIAL EQUATIONS
Matemáticas/Ecuaciones Diferenciales y Álgebra
Contents
First-order differential equations. Linear equations and power series solutions. Linear systems. Dynamical systems. Differential equations of physics. Sturm-Liouville problems.
Learning outcomes
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RA01 - Apply acquired analytical and abstract skills, intuition, and logical thinking to identify and analyse complex problems and seek and formulate solutions in a multidisciplinary environment. TYPE: Knowledge or content
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RA05 - Develop, plan, and develop the content of syllabi and subjects in the scientific field corresponding to pre-university education. TYPE: Knowledge or content
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RA30 - Propose and analyze mathematical models of real-life situations, using the tools of ordinary differential equations, partial differential equations, algebra, and geometry to solve them. TYPE: Competencies
Methodology
| Methodology - Activity | Attendance | Self-study |
| A-1 Expository / participative classes | 42 | |
| A-2 Hands on learning | 14 | |
| A-3 Cooperative learning activities | ||
| A-4 Carrying out tasks / group projects | ||
| A-5 Studying and autonomous work of the student | 88 | |
| A-6 Tutorials | 2 | |
| A-7 Assessment Tests | 4 | |
| Total | 60 | 90 |
Evaluation
| Assessment system |
Weight (%) | It allows test resit |
Minimum required grade |
|---|---|---|---|
| SE1. Individual written test (long-answer tests) | 80% | Yes | 5 |
| SE4. Tasks and Reports: Continuous Assessment | 20% | Yes | 0 |
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] Notes given by the teacher, 2025.
[2] 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] E. Kreyszig. Advances Engineering Mathematics. John Wiley & Sons, 2011.
Location
Public University of Navarre. Aulario building (the room will be posted on the website). The specific places where each of the activities takes place will be announced at the beginning of the course.