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.
Table of Contents
Arithmetic and Elementary Algebra
Limits and Derivatives
Functions of Complex Variables
Ordinary Differential Equations
Partial Differential Equations
Special Functions and Their Properties
Physical Foundations of Mechanics
Molecular Physics and Thermodynamics
Oscillations and Waves
Quantum Mechanics. Atomic Physics
Quantum Theory of Crystals
Elements of Nuclear Physics
ELEMENTS OF APPLIED AND ENGINEERING SCIENCES
Dimensions and Similarity
Mechanics of Point Particles and Rigid Bodies
Elements of Strength of Materials
Mass and Heat Transfer
Empirical and Engineering Formulas and Criteria for Their Applicability
Orthogonal Curvilinear Systems of Coordinates
Ordinary Differential Equations
Some Useful Electronic Mathematical Resources
References appear at the end of each chapter.
Andrei D. Polyanin is a professor in the Institute for Problems in Mechanics at the Russian Academy of Sciences and a professor of mathematics at Bauman Moscow State Technical University. He is a member of the Russian National Committee on Theoretical and Applied Mechanics as well as the Mathematics and Mechanics Expert Council of the Higher Certification Committee of the Russian Federation. A prolific author of more than 30 books and over 140 research papers, Dr. Polyanin has been a recipient of the Chaplygin Prize from the Russian Academy of Sciences and an award from the Ministry of Education of the Russian Federation.
Alexei I. Chernoutsan is a professor, dean of the Faculty of Natural Sciences Education, and head of the Department of Physics at Gubkin Russian State University of Oil and Gas. Dr. Chernoutsan is a prominent scientist in the fields of statistical physics, fluctuation kinetics, phase transitions, and percolation theory. He is deputy editor-in-chief of Kvant, a popular Russian educational magazine for schoolchildren and students.
Concise presentation (without proofs), mindfulness of differing mathematical backgrounds (avoidance of special terminology when possible), and emphasis on practical aspects (formulas, problems, methods, and laws that occur frequently in engineering applications) contribute to the usefulness of this single-volume reference. Many sections are self contained; subsections are arranged in increasing order of complexity; and a bibliography is included for each chapter. …
—SciTech Book News, February 2011