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portada Solving Linear Partial Differential Equations: Spectra
Type
Physical Book
Author
Publisher
Language
English
Pages
408
Format
Hardcover
Dimensions
22.9 x 15.2 x 2.4 cm
Weight
0.71 kg.
ISBN13
9789811216305
Categories

Solving Linear Partial Differential Equations: Spectra

Martin Schechter (Author) · World Scientific Publishing Company · Hardcover

Solving Linear Partial Differential Equations: Spectra - Schechter, Martin

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Synopsis "Solving Linear Partial Differential Equations: Spectra"

'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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