This handbook, authored by a Professor Emeritus of Mathematics and Statistics at Old Dominion University, Norfolk, Virgina, has the feel of a collection of well used and perfected class notes covering those topics in undergraduate graduate mathematics that undergird much of physics and engineering.
The book consists of nine chapters: (1) Preliminaries; (2) Selected Fundamental Concepts; (3) Geometry; (4) Calculus; (5) Vector Calculus; (6) Ordinary Differential Equations; (7) Special Functions; (8) Probability and Statistics; and (9) Selected Applied Mathematical Topics. Appendices include tables of units of measurement and integrals. The book has a ten-page index.
The Preliminaries chapter provides a nice overview of the history of mathematics, some basic arithmetic, including alternative algorithms for adding, subtracting and dividing numbers. The chapter on Selected Fundamental Concepts includes fundamental topics in algebra and trigonometry. The Geometry chapter reviews fundamental concepts and tools from Euclidean Geometry and Analytic Geometry. Calculus provides a solid review of the fundamental concepts, theorems and techniques typically mastered by an undergraduate majoring or minoring in mathematics. The Vector Calculus chapter delves into the mathematics essential for undergraduate and graduate work in physics and engineering. The Ordinary Differential Equations chapter is just that. (There is no discussion of partial differentiation beyond a simple definition in the Calculus chapter.) The Special Functions chapter covers a broad range of functions and transforms found in physics, probability and statistics, and engineering. The Probability and Statistics chapter is largely limited to probability basics, not statistics. The concluding Selected Applied Mathematical Topics chapter contains brief discussions of classical topics in Newtonian dynamics, vibrations, resonance, electrical circuits, and even chemical kinetics.
Covering this broad range of topics in less than six hundred pages, the exposition is necessarily often rather terse, though always meticulous. As such, the handbook is indeed a reference text, not a textbook.
The handbook has approximately two dozen tables and three hundred numbered figures or smaller embedded illustrations. The tables, figures and illustrations are black and white with shading achieved through dots and lines. I found the layout of the handbook refreshingly old-fashioned without the distraction of numerous sidebars.
This is a nice book to have on your desk. I enjoyed reviewing topics I’d learned as a physics and mathematics major and professional, but have rarely used in my chosen career of operations research analysis. I enjoyed finding things I did not know, such as a simple subtraction algorithm based on adding rather than borrowing.
You can find more comprehensive mathematical handbooks at triple the size and triple the price of Heinbockel’s. But this paperback book’s physical size (6"x9"x1.25") is convenient to take on a walk or slip in a briefcase. The price, less than $25.00, is appealing for an ancillary handbook.
H. Ric Blacksten is a Principal Analyst with Innovative Decisions, Inc. He has worked as a physicist, mathematician and, for the latter part of his career, an operations research analyst specializing in mathematical modeling and simulation. His email address is firstname.lastname@example.org