Provides exact solutions Describes numerical methods or numerical solutions, analytical methods, stability/instability issues Focus on partial differential equations

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.

The main purpose of the book is to present the recent advances in the methods of separation of variables (primarily, various modifications of the methods of functional separation of variables) for nonlinear PDEs. There are no direct competitors as this book presents the most recent results on the topic. Mathematicians and physical scientists will find this book indispensable as it relates recent results to applications and models.

Hydrodynamics, Mass and Heat Transfer in Chemical Engineering contains a concise and systematic exposition of fundamental problems of hydrodynamics, heat and mass transfer, and physicochemical hydrodynamics, which constitute the theoretical basis of chemical engineering in science. Areas covered include: fluid flows; processes of chemical engineering; mass and heat transfer in plane channels, tubes and fluid films; problems of mass and heat transfer; the motion and mass exchange of power-law and viscoplastic fluids through tubes, channels, and films; and the basic concepts and properties of very specific technological media, namely foam systems. Topics are arranged in increasing order of difficulty, with each section beginning with a brief physical and mathematical statement of the problem considered, followed by final results, usually given for the desired variables in the form of final relationships and tables.

This book contains about 3,000 first order partial differential equations with solutions. A lot of new exact solutions to linear and nonlinear equations are included.
The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. At the beginning of each section, basic solution methods for the corresponding types of differential equations are outlined and specific examples are considered. It presents equations and their applications; these include differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more.
This handbook is an invaluable reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences.

This book contains a concise and systematic exposition of fundamental problems of hydrodynamics, heat and mass transfer, and physicochemical hydrodynamics, which constitute the theoretical basis of chemical engineering in science. Areas covered include: fluid flows; processes of chemical engineering; mass and heat transfer in plane channels, tubes and fluid films; problems of mass and heat transfer; the motion and mass exchange of power-law and viscoplastic fluids through tubes, channels, and films and the basic concepts and properties of very specific technological media, namely foam systems.
Topics are arranged in increasing order of difficulty, with each section beginning with a brief physical and mathematical statement of the problem considered, followed by final results, usually given for the desired variables in the form of final relationships and tables.

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.

Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handbook now contains the exact solutions to more than 6200 ordinary differential equations. The authors have made significant enhancements to this edition, including:

" An introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ordinary differential equations
" The addition of solutions to more than 1200 nonlinear equations
" An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily
" Expansion of the supplement on special functions

This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.

Includes nearly 4,000 linear partial differential equations (PDEs) with solutions Presents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fields Outlines basic methods for solving various problems in science and engineering Contains much more linear equations, problems, and solutions than any other book currently available Provides a database of test problems for numerical and approximate analytical methods for solving linear PDEs and systems of coupled PDEs New to the Second Edition More than 700 pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutions Systems of coupled PDEs with solutions Some analytical methods, including decomposition methods and their applications Symbolic and numerical methods for solving linear PDEs with Maple, Mathematica, and MATLAB (R) Many new problems, illustrative examples, tables, and figures To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.

The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent 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 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, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including thoseof exact solutions of various types of equations.

This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.