An Atlas of Functions: with Equator, the Atlas Function Calculator - Hardcover

Oldham, Keith B.; Myland, Jan; Spanier, Jerome

Hardcover

ISBN 10: 0387488065 ISBN 13: 9780387488066

Publisher: Springer, 2008

Synopsis

koldham@trentu.ca,jmyland@trentu.caorjspanier@uci.edu.AnErrataofknownerrorsandrevisionswillbefound on the publisher's website; please access www.springer.com/978-0-387-48806-6 and follow the links. This will be updated as and if new errors are detected or clarifications are found to be needed. Use of the Atlas of Functions or Equator, the Atlas function calculator is at your own risk. The authors and the publisher disclaim liability for any direct or consequential damage resulting from use of the Atlas or Equator. It is a pleasure to express our gratitude to Michelle Johnston, Sten Engblom, and Trevor Mace-Brickman for theirhelpinthecreationoftheAtlasandEquator. Thefrankcommentsofseveralreviewerswhoinspectedanearly versionofthemanuscripthavealsobeenofgreatvalue. WegivesincerethankstoSpringer,andparticularlytoAnn KostantandOonaSchmid,fortheircommitmenttothelengthytaskofcarryingtheconceptofAnAtlasofFunctions through to reality with thoroughness, enthusiasm, skill, and even some humor. Their forbearance in dealing with the authors is particularly appreciated. WehopeyouwillenjoyusingAnAtlasofFunctionsandEquator,andthattheywillprovehelpfulinyourwork or studies. January 2008 Keith B. Oldham Jan C. Myland Jerome Spanier Every chapter has sections devoted to: notation, behavior, definitions, special cases, intrarelationships, expansions, particular values, numerical values, limits and approximations, operations of the calculus, complex argument, generalizations, and cognate functions. In addition, each chapter has the special features itemized below its title. PREFACE v GENERAL CONSIDERATIONS 1 What functions are. Organization of the Atlas. Notational conventions. Rules of the calculus. THE CONSTANT FUNCTION c 13 Mathematical constants. Complex numbers. Pulse functions. Series of powers of natural numbers. THE FACTORIAL FUNCTION n!21 Double and triple factorial functions. Combinatorics. Stirling numbers of the second kind. THE ZETA NUMBERS AND RELATED FUNCTIONS 29 Special values. Apery's constant. The Debye functions of classical physics.

About this title

About the Author

Keith B. Oldham is a professor of Chemistry at Trent University in Ontario, Canada. He has co-authored several books, contributed to numerous others, and has published over 200 articles. He co-authored, with Jerome Spanier, the first edition of An Atlas of Functions.

Jan C. Myland is a Research Associate in Electrochemistry at Trent University.

Jerome Spanier is a prominent mathematics professor emeritus, currently a researcher at University of California, Irvine. He has received many prestigious honors and awards and has authored or co-authored numerous publications.

From the Back Cover

This second edition of An Atlas of Functions, with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families of interest to scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, and many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while stressing utility throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in two- or three- dimensions depict their shape and qualitative features and flesh out the reader’s familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family.
Features that make the Atlas an invaluable reference tool, yet simple to use, include:
full coverage of those functions―elementary and "special”―that meet everyday needs
a standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus
extensive cross-referencing and comprehensive indexing, with useful appendices
the inclusion of innovative software--Equator, the Atlas Function Calculator
the inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.

Edition details

• Publisher: Springer
• Publication date: 2008
• ISBN 10: 0387488065
• ISBN 13: 9780387488066
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 759