## Public University of Navarre

Castellano | Academic year: 2020/2021
 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 ]

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### 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

• 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 real-world 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

 Methodology - Activity Attendance Self-study 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

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### Evaluation

 Learning outcome Assessment activity Weight (%) Can be retaken RA17 ¿ RA21 Written tests 80% Yes RA17 ¿ RA21 Assignments and reports 20% No

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 mid-course exams distributed homogenously along the course. Each exam will last an hour and have the same weight for the final mark. Pocket-calculator 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 Sturm-Liouville problems.
• Linear systems of equations. General theory. Constant coefficients. Homogeneous and non-homogeneous 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.
• [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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English.

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### Location

Universidad Pública de Navarra, Campus Arrosadía, Pamplona.

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