Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa

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

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Languages

English.

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Evaluation

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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.
• 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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Location

Universidad Pública de Navarra, Campus Arrosadía, Pamplona.

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