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2 I.Ecuaciones diferenciales de primer orden 1.Teoría básica y métodos de solución. 2.Breviario de aplicaciones físicas. II.Ecuaciones diferenciales de segundo orden 1.Ecuaciones homogéneas de coeficientes constantes. 2.Ecuación de Euler-Cauchy. 3.Ecuaciones heterogénea y métodos de solución. Coeficientes indeterminados y variación de parámetros. 4.Solución en series de potencias. 5.Ecuaciones diferenciales de Bessel, Legendre, Hermite y Laguerre 6.Solución usando transformada de Fourier. 7.Funciones especiales: gamma y error. III.Introducción a las ecuaciones en derivadas parciales 1.Ecuaciones lineales y separación de variables. 2.Problemas de condición de frontera, valores propios y funciones propias. 3.Ecuaciones especiales: de difusión, de onda y de Laplace. 4.Solución en series de Fourier.
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37 We emphasize that it is not particularly important if we are unable to determine the general coefficient a n in terms of a 0 and a 1. What is essential is that we can determine as many coefficients as we want. Thus we can find as many terms in the two series solutions as we want, even if we cannot determine the general term. While the task of calculating several coefficients in a power series solution is not difficult, it can be tedious. A symbolic manipulation package can be very helpful here; some are able to find a specified number of terms in a power series solution in response to a single command. Elementary Differential Equations and Boundary Value Problems. Ninth edition. William E. Boyce &Richard C. DiPrima
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52 We emphasize that it is not particularly important if we are unable to determine the general coefficient a n in terms of a 0 and a 1. What is essential is that we can determine as many coefficients as we want. Thus we can find as many terms in the two series solutions as we want, even if we cannot determine the general term. While the task of calculating several coefficients in a power series solution is not difficult, it can be tedious. A symbolic manipulation package can be very helpful here; some are able to find a specified number of terms in a power series solution in response to a single command. Elementary Differential Equations and Boundary Value Problems. Ninth edition. William E. Boyce &Richard C. DiPrima
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