Public University of Navarre



Castellano | Academic year: 2025/2026 | Previous academic years:  2024/2025  |  2023/2024  |  2022/2023  |  2021/2022 
Double Bachelor's Degree in Data Science and Management, Business Administration at the Universidad Pública de Navarra
Course code: 507203 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 ]

Partes de este texto:

 

Module/Subject matter

  • Subject Matter Level 1: Mathematics
  • Subject Matter Level 2: Advanced Mathematics

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Contents

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

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General proficiencies

Not applicable

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Specific proficiencies

Not applicable

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Learning outcomes

RA01. Apply analytical and abstract thinking skills, intuition, and logical reasoning to identify and analyze complex problems, as well as to seek and formulate solutions in a multidisciplinary environment. TYPE: Knowledge or content
 
RA19. Analyze, validate, and interpret mathematical models of real-world situations using tools from multivariable differential and integral calculus, complex variables, integral transforms, and numerical methods to solve them. TYPE: Competencies

 

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Methodology

Methodology - Activity 

Attendance 

Self-study 

A1- Expository / participative classes 

42 

 

A2- Hands on learning  

14 

 

A5- Studying and autonomous work of the student  

 

88 

A6- Tutorials  

 

2 

A7- Assessment tests 

4 

 

Total 

60 

90 

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Evaluation

 

Assessment
activity		 Weight (%) It allows
test resit 		Minimum
required grade
SE4. Tasks and Report: Continuous Assessment 20% Yes 0
SE1. 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). 

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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.

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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.

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Languages

English.

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Location

Universidad Pública de Navarra, Campus Arrosadía, Pamplona.

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