The Mathematica Handbook 0120415364

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Abbreviations of Mathematica Objects in Alphabetical Order += AddTo 4 7

&& And78 @@ ApplY7 10

I

_ _ _ ; /; --

Altematives 77 Blan~31

BiankNullSequence731 BiankSequence733 CompoundExpression763 Condition764 Decrement782 Derivative791 / Divide7 104 /= DivideBY7 104 ~108

== Equat 135 « Ge~ 181 1

Factorial 7 152

:=

1 1 Factorial27 152 & Function7 174

>

Greater, 184

>= GreaterEqual,185 ++ Incremen~ 206 ?? Infonnation, 209

< Less 256 PutAppend, 374 •• Repeated, 391 • •• RepeatedNull, 391 /. ReplaceAlI, 392 / /. ReplaceRepeated, 394 -> Rule,402 : > RuleDelayed, 402 === SameQ,405 > Skeleton, 430 = Set, 415 SetDelayed; 417 1 1 show file, 383 :# Slo~433 ## SlotSequence, 433 StringJoin, 443 - Subtract, 447 -= SubtractFrom, 448 / : ••• = TagSet, 456 TagSetDelayed, 457 TagUnse~ 457 * Times. 465 *= TimesBy,466 1 Unequal,481 1 UnsameQ, 483 Unset, 484 A= UpSet, 485 UpSetDelayed, 485 ?

/ : ••• := / : ••• =•

262

/@ Map, 279 / /@ MapAU, 281

:: MessageName, 295 Minus,298 ** NonCommutativeMuitiply, 316 Not, 319 : Optional, 330 II Or,332 " 0u~334 [ [ • • • ]] Part, 341

= == =. = A

:

Selected Mathematical Functions and Objects (continued inside back cover) Abs,1 AiryAi,4 AiryAiPrime, 5 AiryBi,5 AiryBiPrime, 6 ArcCos, 11 ArcCosb,12

ArcCo~ 13 ArcCoth,14 ArcCsc,14 ArcCscb,14 ArcSec,15 ArcSecb,15 ArcSin, 16

ArcSinh,16 ArcTan. 17 ArcTanh,17 ArithmeticGeometricMean, 19 BemoulliB, 24 Bessell,25

The Mathematica Handbook

Martha L. Abell Department of Mathematics and Computer Science Georgia Southern University Statesboro, Georgia

James P. Braselton Department ofMathematics and Computer Science Georgia Southern University Statesboro, Georgia

11'~ OF£SS\O~

AP PROFESSIONAL A Division of Harcourt Brace & Company Boston San Diego New York London Sydney Tokyo Toronto

This book is printed on acid-free paper.

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Copyright © 1992 by Academic Press, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher.

Mathematica is a registered trademark of Wolfram Research, Inc.

Cover design by Peter Altenberg AP PROFESSIONAL 955 Massachusetts Avenue, Cambridge, MA 02139 An Imprint of ACADEMIC PRESS, INC. A Division of HARCOURT BRACE & COMPANY United Kingdom Edition published by

ACADEMIC PRESS LIMITED 24-28 Oval Road, London NWI7DX

Library of Congress CataIoging-in-Publication Data

Abell, Martha L., date. The Mathematica handbook I Martha L. Abell, James P. Braselton. p. cm. ISBN 0-12-041536-4 I. Mathematica (Computer program) 2. Mathematics-Data processing. I. Braselton, James P., date. II. Title. 92-13599 QA76.95.A22 1992 510' .285'5369--

Example:

(6)

Sinlntegrol

na

fnfff:D[Sinlntegral[x ] #x]

computes the derivative

ßutftj= Sin[x]

Of

Jo —

'X Ö11UU

Plot[Sinlntegral[x], {x , 0 , 6 P i } , P l o t R a n g e - > U . l ] J

graphs Sinlntegral[x] for 0 < x < 6τι.

10 12.5 15 17.5

OiJtf3j= -Graphicsj» · i ■ · \tttttuttttttttnttiuuumtA

]J \o\

lioo% ▼ ΙΦΙ TOQ

Preface

Vll

Features of a typical entry in the first section include: (1) The name of the command or object; (2) Other pages within The Mathematica Handbook on which the command appears, if any; (3) Pages of Mathematica: A System for Doing Mathematics by Computer, Second Edition, on which the command appears, if any; (4) Related commands; (5) A description of the command; and (6) A typical example. The second section, consisting of Chapter 27: Calculus Packages (see page 584), Chapter 28: Statistics Packages (see page 610), and Chapter 29: Numerical Math Packages (see page 714), contains a listing of the commands contained in the frequently used packages found in the Calculus, Statistics, and Numerical Math folders (or directories). Brief descriptions of all standard packages shipped with Version 2.0 of Mathematica are included in the Technical Report: Guide to Standard Mathematica Packages, by Philip Boyland, and published by Wolfram Research, Inc. A typical entry in the second section of The Mathematica Handbook looks similar to the following: (1) (2) ANOVAIbble Package: L i n e a r K e g r e s s i o n . ■ ANDVAIUble is a possible entry in OutputList which leads to the table of the analysis of variance to be included in the list of output of the functions R e g r e s s and DesignedSegress. This table is computed for a smaller model by assuming independent samples, normal populations, and equal population standard deviations. It includes the degrees of freedom, the sum of the squares, and the mean squares due to the model and the residuals. It also includes the F-statistic vhich compares the two models and the p-value. If the p-value is large, then the null hypothesis is rejected. Example: In the folkrwing example, the ANOYAIbble option setting is illustrated. With the indicated settings, only AHOYAT&ble is given as output of

Regress.

IDI

(3)

(4)

\m

HNOURTable

inf73j:= R e g r e s s [ h e a r t , { l # x } , x ,Outp-utCcmtrol-> MoPrint, OutputList->{AJOTArable} ] Outf?&J* {AHOTATable -> Model

DoF 1

SoS 709.728

HeanSS 709.728

Error

8

112.372

14.0465

Total

822.1

HEZ3ioo% ▼

FRatio 50.5269

PValue } 0.000101168

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