Partial Differential Equations II

  • Brian Davies
Part of the Texts in Applied Mathematics book series (TAM, volume 41)


The use of the Fourier transform to obtain a form of solution to a partial differential equation (together with associated boundary conditions) is a very general technique.1 For simple problems, the integral representation obtained as the solution will be amenable to exact analysis; more often the method converts the original problem to the technical matter of evaluating a difficult integral. Numerical methods may be necessary in general, although asymptotic and other useful information may often be obtained directly by appropriate methods. We illustrate some of the more simple problems in this chapter, leaving applications involving mixed boundary values. Green’s functions, and transforms in several variables, to later chapters.


Partial Differential Equation Surface Elevation Water Wave Velocity Potential Periodic Disturbance 
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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Brian Davies
    • 1
  1. 1.Mathematics Department, School of Mathematical SciencesAustralian National UniversityCanberraAustralia

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