This book covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underline the mathematical modelling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the pre-eminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible. Organized in ascending order of complexity, the material is divided into two parts.
The first part is a concise, coherent survey of the most important definitions, formulas, equations, methods and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, probability theory and much more. Numerous specific examples clarify the methods for solving problems and equations. The second parts provide many in-depth mathematical tables, including those of the exact solutions of various types of equations.
The absence of proofs and the concise presentation has permitted the combination of a substantial amount of reference material in a single volume. The main distinction of this reference book from other general 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, partial differential equations, integral equations, difference equations, etc). In addition to well-known methods, some new methods that have been developing intensively in recent years are described. 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. Some sections and examples can be used in lectures and practical studies in basic and more mathematically intense courses.