Titlebook: Introduction to Partial Differential Equations; David Borthwick Textbook 2016 Springer Nature Switzerland AG 2016 linear equations.partial

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https://doi.org/10.1007/978-3-319-48936-0linear equations; partial differential equations; Laplace equation; mathematical analysis; wave equation

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978-3-319-84051-2Springer Nature Switzerland AG 2016

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Introduction,Continuous phenomena, such as wave propagation or fluid flow, are generally modeled with . (PDE), which express relationships between rates of change with respect to multiple independent variables.

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Separation of Variables,Some PDE can be split into pieces that involve distinct variables. For PDE that admit separation, it is natural to look for product solutions whose factors depend on the separate variables.

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The Heat Equation,In this chapter we will discuss the derivation of the heat equation and develop some basic properties, our first example of a PDE of parabolic type.