Libro de ecuaciones diferenciales de zill

Ecuaciones diferenciales ordinarias 1.00
´ Alvaro Tejero Cantero(*) Pablo Ruiz M´zquiz(**) u

13 de mayo de 2002

alqua.com, la red en estudio

* **

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Ayuda a mantener el proyecto alqua (http://alqua.com)

´ Indice general

1. Ecuaciones diferenciales de orden 1 1.1. Introducci´n. Generalidades. Ejemplos. . . . . . . . . . o 1.1.1. De?nici´n ytipos de eds . . . . . . . . . . . . . o 1.1.2. Existencia y unicidad. Condiciones impuestas. . 1.1.3. Notaci´n diferencial . . . . . . . . . . . . . . . o 1.2. Ecuaciones ordinarias de primer orden . . . . . . . . . 1.2.1. Diferenciales exactas . . . . . . . . . . . . . . . 1.2.2. Factores integrantes . . . . . . . . . . . . . . . 1.2.3. Ecuaciones separables . . . . . . . . . . . . . . 1.2.4.Ejemplos varios . . . . . . . . . . . . . . . . . . 1.2.5. Homog´neas . . . . . . . . . . . . . . . . . . . . e 1.2.6. edos lineales . . . . . . . . . . . . . . . . . . . . 1.2.7. Ecuaci´n de Bernoulli . . . . . . . . . . . . . o 1.2.8. Ecuaci´n de Ricatti . . . . . . . . . . . . . . o 1.2.9. Reducci´n de orden . . . . . . . . . . . . . . . o 2. Sistemas de edos lineales 2.1. Planteamiento . . . . . .. . . . . . . . . . . . . . . . 2.2. Relaci´n entre un sistema y una ecuaci´n . . . . . . o o 2.2.1. De ecuaci´n a sistema . . . . . . . . . . . . . o 2.2.2. De sistema a ecuaci´n . . . . . . . . . . . . . o 2.3. Existencia y unicidad . . . . . . . . . . . . . . . . . . 2.4. Sistemas homog´neos . . . . . . . . . . . . . . . . . . e 2.4.1. Exponencial de una matriz . . . . . . . . . . 2.4.2. Casossencillos de exponenciales. Ejemplos . . 2.4.3. Cambio de base . . . . . . . . . . . . . . . . . 2.4.4. Soluci´n exponencial del sistema homog´neo o e 2.4.5. M´todo Jordan directo . . . . . . . . . . . . e 2.4.6. M´todo del polinomio interpolador . . . . . . e 2.4.7. El tercer m´todo, o RFJ . . . . . . . . . . . e 2.5. Sistemas lineales inhomog´neos . . . . . . . . . . . . e 2.5.1. Planteamientodel problema . . . . . . . . . . 2.5.2. M´todo de variaci´n de las constantes . . . . e o 2.6. Ecuaciones de orden n . . . . . . . . . . . . . . . . . 2.6.1. Planteamiento y notaci´n . . . . . . . . . . . o . . . . . . . . . . . . . . . . . .

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11 11 11 12 17 18 19 21 23 27 30 33 36 37 38 41 41 41 41 43 43 43 46 47 49 50 51 64 68 71 71 72 74 74

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´ Indice general 2.6.2. 2.6.3. 2.6.4.2.6.5. 2.6.6. Ecuaciones homog´neas . . . . . . . . . . . . . . . . e Coe?cientes variables: m´todo de reducci´n de orden e o Coe?cientes variables: ecuaciones de Euler . . . . . Coe?cientes constantes, ecuaci´n homog´nea . . . . o e Coe?cientes constantes, ecuaci´n inhomog´nea . . . o e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ….

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