This book is intended to give the reader an opportunity to master solving PDE problems.
Our main goal was to have a concise text that would cover the classical tools
of PDE theory that are used in today’s science and engineering, such as characteristics,
the wave propagation, the Fourier method, distributions, Sobolev spaces,
fundamental solutions, and Green’s functions. While introductory Fourier method
– based PDE books do not give an adequate description of these areas, the more
advanced PDE books are quite theoretical and require a high level of mathematical
background from a reader. This book was written specifically to fill this gap, satisfying
the demand of the wide range of end users who need the knowledge of how
to solve the PDE problems and at the same time are not going to specialize in this
area of mathematics. Arguably, this is the shortest PDE course, which stretches far
beyond common, Fourier method – based PDE texts. For example, [Hab03], which
is a common thorough textbook on partial differential equations, teaches a similar
set of tools while being about five times longer