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Essential Mathematical Methods for the Physical Sciences by K. F. Riley, M. P. Hobson

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11

Solution methods for PDEs

In the previous chapter we demonstrated the methods by which general solutions of some PDEs may be obtained in terms of arbitrary functions. In particular, solutions containing the independent variables in definite combinations were sought, thus reducing the effective number of them.

In the present chapter we begin by taking the opposite approach, namely that of trying to keep the independent variables as separate as possible; the aim is to reduce the partial differential equation to a set of ordinary differential equations, each of which contains only one of the independent variables. We then consider integral transform methods by which one of the independent variables may be eliminated, at least from differential ...

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