Handbook of Mathematics for Engineers and Scientists
Publisher: Chapman & Hall/CRC Press
Publication Date: 27 November 2006
Number of Pages: 1544
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
differential and integral calculus,
elementary and special functions,
functions of one complex variable,
calculus of variations,
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
(ordinary differential equations,
linear and nonlinear partial differential 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:
- The main text containing a concise, coherent survey of the most
important definitions, formulas, equations, methods, and theorems.
- Numerous specific examples clarifying the essence of the topics
and methods for solving problems and equations.
- 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
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 (188.8.131.52), 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
Andrei D. Polyanin
Alexander V. Manzhirov