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Schaum's Outline of Differential Equations
by RICHARD BRONSON, Ph.D. & GABRIEL B. COSTA, Ph.D.
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, economics,
and even business. The emergence of low-cost, high-speed computers has spawned new techniques
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 equations
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 differential
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 subtleties
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.
PDF | 402 pages | 17.3 MB

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