This book, the first printing of which was published as Volume 31
of the Encyclopaedia of Mathematical Sciences, contains a survey of
the modern theory of general linear partial differential equations
and a detailed review of equations with constant coefficients.
Readers will be interested in an introduction to microlocal
analysis and its applications including singular integral
operators, pseudodifferential operators, Fourier integral operators
and wavefronts, a survey of the most important results about the
mixed problem for hyperbolic equations, a review of asymptotic
methods including short wave asymptotics, the Maslov canonical
operator and spectral asymptotics, a detailed description of the
applications of distribution theory to partial differential
equations with constant coefficients including numerous interesting
special topics.
General
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