Public University of Navarre

Castellano | Academic year: 2024/2025 | Previous academic years:  2023/2024  |  2022/2023  |  2021/2022  |  2020/2021 
Bachelor's Degree in Science at the Universidad Pública de Navarra
Course code: 504209 Subject title: ORDINARY DIFFERENTIAL EQUATIONS
Credits: 6 Type of subject: Mandatory Year: 2 Period: 1º S
Department: Estadística, Informática y Matemáticas
PALACIAN SUBIELA, JESUS FCO. (Resp)   [Mentoring ]

Partes de este texto:


Module/Subject matter


Matemáticas/Ecuaciones Diferenciales y Álgebra



First-order differential equations. Linear equations and power series solutions. Linear systems. Dynamical systems. Differential equations of physics. Sturm-Liouville problems.


General proficiencies

CB4 - That students can transmit information, ideas, problems and solutions to both a specialized and non-specialized audience.


Specific proficiencies

CG1 - Apply acquired analytical and abstraction skills, intuition, and logical thinking to identify and analyze complex problems and seek and formulate solutions in a multidisciplinary environment.

CG5 - Prepare, plan and develop the contents of the topics and subjects of the scientific field corresponding to pre-university education.

CE19 - Propose and analyze mathematical models of real situations, applying the techniques of ordinary differential equations, partial differential equations, algebra and geometry to solve them.


Learning outcomes

RA 1. Master the concept of differential equation and system of differential equations, existence and uniqueness of solution.

RA 2. Know the basic techniques for solving first order differential equations.

RA 3. Understand the structure of the space of solutions of differential equations and linear systems. Master the basic techniques of solving differential equations and linear systems with constant coefficients.

RA 4. Handle the technique of solving linear differential equations using power series and its usefulness in the equations of mathematical physics.

RA 5. Get some knowledge concept of dynamical system and acquire the associated fundamental concepts.



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




Weight (%) It allows
test resit
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.






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.