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Solving Linear Partial Differential Equations: Spectra (Hardcover)
Loot Price: R3,725
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Solving Linear Partial Differential Equations: Spectra (Hardcover)
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'This booklet provides a very lucid and versatile introduction to
the methods of linear partial differential equations. It covers a
wealth of very important material in a concise, nevertheless very
instructive manner, and as such it may serve as an excellent guide
to further, more advanced and detailed reading in this area of both
classical and contemporary mathematics.'zbMATHPartial differential
equations arise in many branches of science and they vary in many
ways. No one method can be used to solve all of them, and only a
small percentage have been solved. This book examines the general
linear partial differential equation of arbitrary order m. Even
this involves more methods than are known. We ask a simple
question: when can an equation be solved and how many solutions
does it have?The answer is surprising even for equations with
constant coefficients. We begin with these equations, first finding
conditions which allow one to solve and obtain a finite number of
solutions. It is then shown how to obtain those solutions by
analyzing the structure of the equation very carefully. A
substantial part of the book is devoted to this. Then we tackle the
more difficult problem of considering equations with variable
coefficients. A large number of such equations are solved by
comparing them to equations with constant coefficients.In numerous
applications in the sciences, students and researchers are required
to solve such equations in order to get the answers that they need.
In many cases, the basic scientific theory requires the resulting
partial differential equation to have a solution, and one is
required to know how many solutions exist. This book deals with
such situations.
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