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. SturmLiouville problems.
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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.
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Specific proficiencies
 CE7 To analyze, validate and interpret mathematical models of realworld situations, using the tools provided by differential and integral calculus of several variables, complex analysis, integral transforms and numerical methods to solve them.
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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.
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Methodology



A1 Expository / participative classes






A3 Studying and autonomous work of the student












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Evaluation
No minimum grade is required in either of the two evaluation systems. The written test, carried out in the ordinary evaluation period, can be recovered in the extraordinary exam. The ordinary call consists in four midcourse exams distributed homogenously along the course. Each exam will last an hour and have the same weight for the final mark. Pocketcalculator is permitted in the exams.
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Agenda
 Introduction to differential equations. Motivation and basic definitions. Elementary differential equations.
 First order differential equations. Separation of variables. Homogeneous. Exact equations. Integrating factor. First order linear. Changes of variables.
 Theoretical aspects. Initial value problem. Existence and uniqueness theorem. Boundary problems. Approximate solutions.
 Linear differential equations. General theory. Constant coefficients. Regular and singular points. Analytical solutions. Power series and Frobenius methods. Special functions. Introduction to SturmLiouville problems.
 Linear systems of equations. General theory. Constant coefficients. Homogeneous and nonhomogeneous systems.
 Nonlinear equations and systems. 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:
 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.
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Location
Universidad Pública de Navarra, Campus Arrosadía, Pamplona.
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