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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) math-
ematical 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, 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 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 sep-
arately 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

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