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. [Mentoring ]  LOPEZ GARCIA, JOSE LUIS (Resp) [Mentoring ] 
Methodology  Activity 
Attendance 
Selfstudy 
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 
Educational activity 
Proficiency 
A1 Expository / participative classes 
CB3, CB5, CG1, CE7 
A2 Hands on learning 
CB3, CB5, CG1, CE7 
A3 Studying and autonomous work of the student 
CB3, CB5, CG1 
A4 Tutorials 
CB3, CG1, CE7 
A5 Assessment tests 
CB3, CB5, CG1 
Learning outcome 
Assessment activity 
Weight (%)  It allows test resit 
Minimum required grade 

RA1RA5  Tasks and Report: Continuous Assessment  20%  Yes  0 
RA1RA5  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).
First order differential equations. Linear equations and power series solutions. Linear systems. Dynamical systems. Differential equations of physics. SturmLiouville problems.
1. Introduction to differential equations. Motivation and basic definitions. Elementary differential equations.
2. Firstorder differential equations. Separation of variables. Homogeneous. Exact equations. Integrating factor. Firstorder 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 SturmLiouville problems.
5. Linear systems of equations. General theory. Constant coefficients. Homogeneous and nonhomogeneous 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. McGrawHill, 1991.
[4] G. Strang. Differential Equations and Linear Algebra. WellesleyCambridge Press, 2015.
[5] F. Ayres. Schaum's Outline of Differential Equations. McGrawHill, 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. McGrawHill, 1995.