Page 8 - Schaum's Outline of Differential Equations

PREFACE

Differential equations are among the linchpins of modern mathematics which, along with matrices, are
essential for analyzing and solving complex problems in engineering, the natural sciences, econom-
ics, and even business. The emergence of low-cost, high-speed computers has spawned new tech-
niques for solving differential equations, which allows problem solvers to model and solve complex
problems based on systems of differential equations.
As with the two previous editions, this book outlines both the classical theory of differential equa-
tions and a myriad of solution techniques, including matrices, series methods, Laplace transforms and
several numerical methods. We have added a chapter on modeling and touch upon some qualitative
methods that can be used when analytical solutions are difficult to obtain. A chapter on classical dif-
ferential equations (e.g., the equations of Hermite, Legendre, etc.) has been added to give the reader
exposure to this rich, historical area of mathematics.
This edition also features a chapter on difference equations and parallels this with differential
equations. Furthermore, we give the reader an introduction to partial differential equations and the
solution techniques of basic integration and separation of variables. Finally, we include an appendix
dealing with technology touching upon the TI-89 hand-held calculator and the MATHEMATICA
software packages.
With regard to both solved and supplementary problems, we have added such topics as integral
equations of convolution type, Fibonacci numbers, harmonic functions, the heat equation and the wave
equation. We have also alluded to both orthogonality and weight functions with respect to classical
differential equations and their polynomial solutions. We have retained the emphasis on both initial
value problems and differential equations without subsidiary conditions. It is our aim to touch upon
virtually every type of problem the student might encounter in a one-semester course on differential
equations.
Each chapter of the book is divided into three parts. The first outlines salient points of the theory
and concisely summarizes solution procedures, drawing attention to potential difficulties and sub-
tleties that too easily can be overlooked. The second part consists of worked-out problems to clarify and,
on occasion, to augment the material presented in the first part. Finally, there is a section of problems
with answers that readers can use to test their understanding of the material.
The authors would like to thank the following individuals for their support and invaluable assis-
tance regarding this book. We could not have moved as expeditiously as we did without their support
and encouragement. We are particularly indebted to Dean John Snyder and Dr. Alfredo Tan of
Fairleigh Dickinson University. The continued support of the Most Reverend John J Myers, J.C.D.,
D.D., Archbishop of Newark, N.J., is also acknowledged. From Seton Hall University we are grateful
to the Reverend Monsignor James M. Cafone and to the members of the Priest Community; we also
thank Dr. Fredrick Travis, Dr. James Van Oosting, Dr. Molly Smith, and Dr. Bert Wachsmuth and the
members of the Department of Mathematics and Computer Science. We also thank Colonel Gary
W. Krahn of the United States Military Academy.
Ms. Barbara Gilson and Ms. Adrinda Kelly of McGraw-Hill were always ready to provide any
needed guidance and Dr. Carol Cooper, our contact in the United Kingdom, was equally helpful.
Thank you, one and all.

VII
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