A. D. Polyanin and A. V. Manzhirov Handbook of Mathematics for Engineers and Scientists Publisher: Chapman & Hall/CRC Press Publication Date: 27 November 2006 Number of Pages: 1544 Summary Features Preface Contents Index

Preface

This book can be viewed as a reasonably comprehensive compendium of mathematical definitions, formulas, and theorems intended for researchers, university teachers, engineers, and students of various backgrounds in mathematics. The absence of proofs and a concise presentation has permitted combining a substantial amount of reference material in a single volume.

When selecting the material, the authors have given a pronounced preference to practical aspects, namely, to formulas, methods, equations, and solutions that are most frequently used in scientific and engineering applications. Hence some abstract concepts and their corollaries are not contained in this book.

• This book contains chapters on arithmetics, elementary geometry, analytic geometry, algebra, differential and integral calculus, differential geometry, elementary and special functions, functions of one complex variable, calculus of variations, probability theory, mathematical statistics, etc. Special attention is paid to formulas (exact, asymptotical, and approximate), functions, methods, equations, solutions, and transformations that are of frequent use in various areas of physics, mechanics, and engineering sciences.
• The main distinction of this reference book from other general (nonspecialized) mathematical reference books is a significantly wider and more detailed description of methods for solving equations and obtaining their exact solutions for various classes of mathematical equations (ordinary differential equations, linear and nonlinear partial differential equations, integral equations, difference equations, etc.) that underlie mathematical modeling of numerous phenomena and processes in science and technology. In addition to well-known methods, some new methods that have been developing intensively in recent years are described.
• For the convenience of a wider audience with different mathematical backgrounds, the authors tried to avoid special terminology whenever possible. Therefore, some of the methods and theorems are outlined in a schematic and somewhat simplified manner, which is sufficient for them to be used successfully in most cases. Many sections were written so that they could be read independently. The material within subsections is arranged in increasing order of complexity. This allows the reader to get to the heart of the matter quickly.

The material in the first part of the reference book can be roughly categorized into the following three groups according to meaning:

1. The main text containing a concise, coherent survey of the most important definitions, formulas, equations, methods, and theorems.
2. Numerous specific examples clarifying the essence of the topics and methods for solving problems and equations.
3. Discussion of additional issues of interest, given in the form of remarks in small print.

For the reader's convenience, several long mathematical tables -- finite sums, series, indefinite and definite integrals, direct and inverse integral transforms (Laplace, Mellin, and Fourier transforms), and exact solutions of ordinary differential, partial differential, integral, functional, and other mathematical equations -- which contain a large amount of information, are presented in the second part of the book.

This handbook consists of chapters, sections, subsections, and paragraphs (the titles of the latter are not included in the table of contents). Figures and tables are numbered separately in each section, while formulas (equations) and examples are numbered separately in each subsection. When citing a formula, we use notation like (3.1.2.5), which means formula 5 in Subsection 3.1.2. At the end of each chapter, we present a list of main and additional literature sources containing more detailed information about topics of interest to the reader.

Special font highlighting in the text, cross-references, an extensive table of contents, and a detailed index help the reader to find the desired information.

We would like to express our deep gratitude to Alexei Zhurov for fruitful discussions and valuable remarks. We also appreciate the help of Vladimir Nazaikinskii and Grigorii Yosifian for translating several chapters of this book and are thankful to Kirill Kazakov and Mikhail Mikhin for their assistance in preparing the camera-ready copy of the book.

The authors hope that this book will be helpful for a wide range of scientists, university teachers, engineers, and students engaged in the fields of mathematics, physics, mechanics, control, chemistry, biology, engineering sciences, and social and economical sciences. Some sections and examples can be used in lectures and practical studies in basic and special mathematical courses.

Andrei D. Polyanin
Alexander V. Manzhirov