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Mathematica ® Navigator This page intentionally left blank Mathematica ® Navigator Mathematics, Statistics, and Graphics THIRD EDITION Heikki Ruskeepää Department of Mathematics University of Turku, Finland AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier The book is produced from PDF files prepared by the author with Mathematica® Academic Press is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobald’s Road, London WC1X 8RR, UK Copyright © 2009, Elsevier 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 Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier.com You may also complete your request online via the Elsevier homepage (http://elsevier.com), by selecting “Support & Contact” then “Copyright and Permission” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Ruskeepää, Heikki Mathematic navigator : mathematics, statistics, and graphics / Heikki Ruskeepää – 3rd ed p cm Includes bibliographical references and index ISBN 978-0-12-374164-6 (pbk : alk paper) Mathematics–Data processing Mathematica (Computer file) I Title QA76.95.R87 2009 510.285'5–dc22 2008044637 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-374164-6 For information on all Academic Press publications visit our Web site at www.elsevierdirect.com Printed in the United States of America 09 10 11 To Marjatta This page intentionally left blank Contents Preface xi Starting 1.1 What Is Mathematica 1.2 First Calculations 1.3 Important Conventions 12 1.4 Getting Help 15 1.5 Editing 22 Sightseeing 25 2.1 Graphics 26 2.2 Expressions 31 2.3 Mathematics 40 Notebooks 51 3.1 Working with Notebooks 52 3.2 Editing Notebooks 59 3.3 Inputs and Outputs 70 3.4 Writing Mathematical Documents 78 Files 93 4.1 Loading Packages 94 4.2 Exporting and Importing 100 4.3 Saving for Other Purposes 109 4.4 Managing Time and Memory 112 Graphics for Functions 115 5.1 Basic Plots for 2D Functions 116 5.2 Other Plots for 2D Functions 132 5.3 Plots for 3D Functions 139 5.4 Plots for 4D Functions 147 Graphics Primitives 151 6.1 Introduction to Graphics Primitives 152 6.2 Primitives and Directives 155 viii Mathematica Navigator Graphics Options 179 7.1 Introduction to Options 180 7.2 Options for Form, Ranges, and Fonts 189 7.3 Options for Axes, Frames, and Primitives 195 7.4 Options for the Curve 203 7.5 Options for Surface Plots 210 7.6 Options for Contour and Density Plots 226 Graphics for Data 231 8.1 Basic Plots 232 8.2 Scatter Plots 249 8.3 Bar Charts 253 8.4 Other Plots 260 8.5 Graph Plots 267 8.6 Plots for 3D Data 275 Data 283 9.1 Chemical and Physical Data 284 9.2 Geographical and Financial Data 293 9.3 Mathematical and Other Data 300 10 Manipulations 315 10.1 Basic Manipulation 316 10.2 Advanced Manipulation 338 11 Dynamics 357 11.1 Views and Animations 357 11.2 Advanced Dynamics 369 12 Numbers 395 12.1 Introduction to Numbers 396 12.2 Real Numbers 403 12.3 Options of Numerical Routines 409 13 Expressions 413 13.1 Basic Techniques 414 13.2 Manipulating Expressions 419 13.3 Manipulating Special Expressions 427 13.4 Mathematical Functions 435 14 Lists 443 14.1 Basic List Manipulation 444 14.2 Advanced List Manipulation 459 Contents 15 Tables 4670 15.1 Basic Tabulating 467 15.2 Advanced Tabulating 470 16 Patterns 4910 16.1 Patterns 491 16.2 String Patterns 505 17 Functions 5110 17.1 User-Defined Functions 512 17.2 More about Functions 523 17.3 Contexts and Packages 531 18 Programs 5410 18.1 Simple Programming 542 18.2 Procedural Programming 553 18.3 Functional Programming 568 18.4 Rule-Based Programming 584 18.5 Recursive Programming 596 19 Differential Calculus 6150 19.1 Derivatives 615 19.2 Taylor Series 624 19.3 Limits 630 20 Integral Calculus 6330 20.1 Integration 634 20.2 Numerical Quadrature 644 20.3 Sums and Products 666 20.4 Transforms 670 21 Matrices 6770 21.1 Vectors 677 21.2 Matrices 686 22 Equations 709 22.1 Linear Equations 710 22.2 Polynomial and Radical Equations 716 22.3 Transcendental Equations 730 23 Optimization 7410 23.1 Global Optimization 743 23.2 Linear Optimization 753 23.3 Local Optimization 759 23.4 Classical Optimization 768 23.5 Special Topics 777 ix Index NormalCI•, 1020 NormalDistribution, 978 Normalize, 685 NormalProbabilityPlot•, 983 NormalPValue•, 1024 NormalsFunction, 214, 222 NormFunction, 822, 866, 917 Norms of matrices, Norm, 702 of vectors, Norm, 684 Not H!L, 433 NotebookAutoSave, 52, 69 Notebooks, 52 cell styles in, 54 cells in, 23 checking spelling of, 53 editing, 22, 59 footers of, 53 headers of, 53 hyphenating, 53 manipulating graphics in, 120 opening, 24, 52 options for, 61 page breaks in, 54 printing, 54 printing settings of, 53 saving, 52 screen environments of, 55 structure of, 61 style sheets of, 55 to packages, 535 Notebook’s Default Context Hmenu commandL, 533 NProduct, 670 NProductFactors, 670 NResidue•, 627 NSeries•, 627 NSolve, 44, 717-718 NSum, 667 options for, 668 NSumTerms, 668 Nullclines, 855 NullSpace, 703 Number of bytes, ByteCount, 114 of characters, StringLength, 434 of elements, Length, 425, 444 of occurrences, Count, 493 of primes, 552 Number theory, 16, 395 NumberForm, 399, 980 numberFromFactors, 572 Numbering of formulas, 79, 90 of page references, 89 1093 of sections, 91 NumberQ, 431 Numbers, 396 accuracy of, Accuracy, 403 arbitrary|precision, 113, 405 complex, 396, 400 decimal, N, 31 domains of, 420 fixed|precision, 405 Gaussian integer, 396 integer, 396 machine|precision, 405 Mersenne prime, precision of, Precision, 403 prime, 4, 396 random, RandomReal, etc., 962 ranges of, Range, 36, 446 rational, 396, 400 real, 396, 398, 403 Roman, 54 tests for, 431 truncation of, Chop, 399 NumberString, 509 Numerator, 428 Numerical methods for derivatives, ND•, 621 for differential equations, NDSolve, 49, 849 for global optimization, NMinimize, 45, 747 for integer optimization, NMinimize, 747 for integrals, NIntegrate, 644 for limits, NLimit•, 632 for local optimization, FindMinimum, 46, 759 for nonlinear least squares, FindFit, 818 for nonlinear regression, NonlinearRegress•, 1035 for partial differential equations, NDSolve, 909 for polynomial equations, NSolve, 44, 717 for products, NProduct, 670 for sums, NSum, 667 for transcendental equations, FindRoot, 44, 732 high precision in, 544 monitoring, 411 precision of, 409 programs for, 542 NumericalCalculus` package, 621, 627, 632, 804 NumericalDifferentialEquationAnalysis` package, 664-665 NumericQ, 431 OddQ, 397, 431 Off, 524 Offset, 159, 166 On, 524 1094 OneStepRowReduction, 712 Opacity, 150, 154, 169, 178 Open Hmenu commandL, 52 OpenAppend, 104 Opener, 385 OpenerView, 361 OpenRead, 104 OpenWrite, 104 Optimization by calculus of variations, 789 by classical methods, kktOptimize, 768 by cylindrical algebraic decomposition, Minimize, 743 by dynamic programming, 780 by global numerical methods, NMinimize, 747 by integer programming, NMinimize, 747 by linear programming, LinearProgramming, 757 by linear programming, Minimize, 753 by local numerical methods, FindMinimum, 759 Option Inspector, 60-61 Option Inspector Hmenu commandL, 52, 62 Optional, 501 OptionQ, 431, 737 Options comparison of, 182 conflicting, 125 defining, 538 filtering, FilterRules, 539 for Animate, 368 for ArrayPlot, 691 for BarChart•, 254 for BarChart3D•, 278 for Dynamic, 373 for FindFit, 822 for FindMaximum, 762 for FindMinimum, 762 for FindRoot, 734 for FullSimplify, 423 for Graphics, 184 for Graphics3D, 210 for GraphicsColumn, 124 for GraphicsGrid, 124 for GraphicsRow, 124 for GraphPlot, 268 for Grid, 470, 475 for Integrate, 640 for ListAnimate, 369 for ListContourPlot, 277 for ListDensityPlot, 277 for ListLinePlot, 234 for ListPlot, 234 for ListPlot3D, 277 Mathematica Navigator for ListPointPlot3D, 278 for Manipulate, 352 for MatrixForm, 687 for MatrixPlot, 691 for MiniMaxApproximation•, 828 for NDSolve, 865, 917 for NIntegrate, 645 for NMinimize, 749 for NonlinearRegress•, 1036 for NSum, 668 for ParametricPlot, 184 for ParametricPlot3D, 210 for Plot, 184 for Plot3D, 210 for Regress•, 1031 for Simplify, 423 for TableForm, 468 for cell frames, 68 for cells, 67 for controls, 374 for fonts, 65 for formatting, 66 for frame boxes, 67 for front end, 61 for numerical routines, 409 for printing, 69 for text layout, 65 for views, 364 in packages, 538 information about, Options, 181 setting, SetOptions, 180 using, 180 Options, 181, 538 OptionsPattern, 538 OptionValue, 538 Or H»»L, 433 Orange, 169 Ordering, 458, 766, 782 OrOpt, 777 Orthogonal decompositions of matrices, 706 polynomials, 439 vectors, 685 Orthogonalize, 685 OrZweig, 777 Oscillatory integrands, 658 OscillatorySelection, 647, 660 Out, 8, 414 Outer, 456, 466 Outer products, KroneckerProduct, 683 Outer products, Outer, 683 Outliers, 265, 822 Output 1D, 70 Index 2D, 70 editing, 24, 52 in TEX form, TeXForm, 111 in C form, CForm, 111 in Fortran form, FortranForm, 111 in framed form, Framed, 72 in input form, InputForm, 70 in internal form, FullForm, 426 in labeled form, Labeled, 72 in output form, OutputForm, 70 in pane form, Pane, 72 in panel form, Panel, 72 in shallow form, Shallow, 425 in short form, Short, 425 in standard form, StandardForm, 70 in traditional form, TraditionalForm, 70 suppressing, ;, 33 Output from Above Hmenu commandL, 24 OutputForm, 70 Overdetermined linear systems, 714 Overlaps, 508 p values, 1024 Packages contexts in, 537 extra, 97 forgetting to load, 533 from notebooks, 535 legacy, 98 loading, 94 loading automatically, 96 loading with Get HL, 110 PutAppend H>>>L, 110 q|difference equations, 928 q|q plots, QuantilePlot•, 252 QRDecomposition, 706 QuadraticFormDistribution•, 984 Quadrature, 644 Quadrature rules, 652 Quantifiers, 728 Quantile, 967, 1004 Quantile-quantile plots, 252 QuantilePlot•, 252 Quantiles of multivariate distributions, EllipsoidQuantile•, 985 of univariate data, Quantile, 1004 of univariate distributions, Quantile, 967 Quartics, 703, 721, 724 QuartileDeviation, 1005 Quartiles, 265, 1004 Quartiles, 1004 QuartileSkewness, 1005 Quasi|linear partial differential equations, 886 QuasiMonteCarlo, 647, 662 QuasiNewton, 763, 822 Quaternions, 16 1102 Queue process, 1000 Quiet, 540 Quit, Quit Kernel Hmenu commandL, 7, 114 Quotient, 397 QuotientRemainder, 397 Radical equations, Solve, Reduce, 723 optimization, Minimize, 743 RadioButtonBar, 332, 380 Ramanujan, Srinivasa, 395, 398 RamanujanTau, 398 RamanujanTauL, 398 RamanujanTauTheta, 398 RamanujanTauZ, 398 Random lines, 684 numbers, generating with quantiles, 984 numbers, generation of, RandomInteger, RandomReal, 968 numbers, seeds for, SeedRandom, 963 numbers, uniformly distributed, RandomReal, etc., 962 permutations, RandomSample, 966 primes, RandomPrime, 396 processes, 987 variables, sums of, 602-603 walk Metropolis method, 1057 walks, 683, 987 RandomChoice, 965, 987 RandomComplex, 962 RandomInteger, 31, 962, 968, 973 RandomPrime, 396, 962 RandomReal, 31, 962, 968, 973, 976 RandomSample, 965-966 RandomSearch, 749 RandomSeed, 751 randomWalk, 987 Range of characters, CharacterRange, 434 of numbers, Range, 36, 446 Range, 36, 446, 678 Rank of matrices, MatrixRank, 703 Raster, 154, 169-170 Rasterize, 105 Rational approximation of reals, Rationalize, 400 Chebyshev approximation, RationalInterpolation•, 806, 826 expressions, 427 interpolation, RationalInterpolation•, 806 numbers, 396 numbers, domain of, Rationals, 420 Mathematica Navigator RationalInterpolation•, 806, 826 Rationalize, 400 Rationals, 420 RayleighDistribution, 977 Re, 137, 400, 430 Read, 104 Reading data, Import, 100 graphics, Import, 105 interactive inputs, Input, 564 results, Get HL, 584 RulerUnits, 69 Rules, 584 applying in all possible ways, ReplaceList, 495, 994 applying once, ReplaceAll Hê.L, 32, 416, 494 applying repeatedly, ReplaceRepeated Hêê.L, 418, 494, 596 base of, 586 dispatching, 588 downvalues, 588 global delayed, SetDelayed H:=L, 584 global immediate, Set H=L, 584 in programming, 584 local delayed, RuleDelayed H:>L, 584 local immediate, Rule H->L, 416, 584 names of, 418 upvalues, 588 Run|length encoding, 461, 613 Runge-Kutta methods, 866, 871, 917 rungeKuttaSolve, 872 runLengthDecoding, 574 runLengthDecoding2, 613 runLengthEncoding, 574 runLengthEncoding2, 613 Runs, Split, 450, 993 Ruskeepää H2007L, 677 Ruskeepää H2008aL, 395 Ruskeepää H2008bL, 395 Saddle points, 617, 769 Salmon, 134 Same expressions testing for with Equal H==L, 43, 431-432 testing for with SameQ H===L, 431-432, 578 testing for with random numbers, 964 SameQ H===L, 431, 578 SameTest, 459, 578, 737-738, 767, 988 Mathematica Navigator Sampling Gibbs, 1054 in function interpolation, InterpolationPoints, 808 in optimization, SearchPoints, 751 Markov chain Monte Carlo, 1057 with replacement, RandomChoice, 965 without replacement, 554, 577 without replacement, RandomSample, 965 Sandefur H1990L, 923 Save Hmenu commandL, 52 Save, 110 Save As Hmenu commandL, 52, 78 Save As Special Hmenu commandL, 52 Save Selection As Hmenu commandL, 100, 105 SaveDefinitions, 348, 353 Saving memory, 114 notebooks, 52 results, Put H>>L, 110 time, 112 Scalar product, Dot H.L, 683, 699 ScalarTripleProduct•, 620 Scale, 160 Scale•, 621, 632 Scaled, 165 ScaleFactor•, 144 ScaleFunction•, 144 ScalingFactor, 752 ScalingTransform, 160, 686 Scan, 462 Scatter plot matrix, PairwiseScatterPlot•, 251 SchurDecomposition, 707 Schwalbe and Wagon H1997L, 830 ScientificForm, 399 Scoping constructs, 520 with Block, 522 with Function, 520 with Module, 521 with With, 522 Screen environments, 55 ScriptMinSize, 67 ScriptSizeMultipliers, 67 Search path for contexts, $ContextPath, 532 for files, $Path, 107 Searching elements, Select, etc., 457 positions, Position, 458 with patterns, 493 SearchPoints, 751 Sec, 11, 435 Secant, 735 Index Secant method, 733, 739 secantSolve, 739 secantSolve2, 740 Sech, 435 Sections, automatic numbering of, 91 SeedRandom, 963 Select, 3, 401, 457, 493, 520, 609, 680, 774, 1047 SelfLoopStyle, 268 SemialgebraicComponentInstances, 727 Sensitivity to initial conditions, 862, 937 to numerical inaccuracies, 861, 936 Separation of variables, 893, 906 Sequence, 180, 463 SequenceLimit•, 632 Sequences, 463 SequentialSumOfSquares•, 1031 Series, 40, 624, 825 Series expansions, Series, 40, 624 Series solutions to differential equations, 630, 843 to partial differential equations, 893 SeriesCoefficient, 627, 928, 931 SessionTime, 112 Set H=L, 9, 414, 584 Set operations, 459 SetAttributes, 531, 624 SetCoordinates•, 620 SetDelayed H:=L, 512, 584 SetDirectory, 108 SetOptions, 180, 193 SetPrecision, 406, 544 SetSystemOptions•, 881 SetterBar, 332, 380 ShadowBackground•, 210 Shadowing of names, 96, 534 Shallow, 425 Shape statistics, 1005 Share, 114 Shaw and Tigg H1994L, 13, 822 ShearingTransform, 160, 686 Shooting, 866, 876 Shooting method, 875 Short, 34, 425 Shortest, 504 Shortest path problem, 781 ShortestPath•, 742 Show in changing options, 180 in superimposing plots, 26, 121, 221 options for, 181 Show Cell Tags Hmenu commandL, 90 Show Expression Hmenu commandL, 60 Show Page Breaks Hmenu commandL, 54 1105 Show Toolbar Hmenu commandL, 54 ShowCellLabel, 67 showConfidenceIntervals, 1022 showError, 824 showFit, 814 showIterations, 767 ShowLegend•, 210 showLocalResiduals, 1041 showPValues, 1026 showResiduals, 815 ShrinkingDelay, 353, 373 ShrinkRatio, 752 SI•, 402 Sieve of Eratosthenes, 555 Sign, 430, 438 SignificanceLevel•, 1024 Significant digits, 403-404 Simplex, 757 Simplify, 32, 419 options for, 423 Simplifying expressions, Simplify, 32, 419 special functions, FullSimplify, 32, 419 SimulatedAnnealing, 749, 777 Simulating stochastic processes, 987 Simultaneous difference equations, RSolve, 929 differential equations, DSolve, NDSolve, 836, 852, 860 linear equations, Solve, LinearSolve, 710 partial differential equations, NDSolve, 909 polynomial equations, Solve, NSolve, 718 transcendental equations, FindRoot, 734 Sin, 11, 435 Sinc, 435 Single|image stereograms, SIS•, 146 SinglePredictionCITable•, 1031, 1034, 1036 Singular values, 701 Singularities with NDSolve, 869 with NIntegrate, 644, 655 with Series, 626 SingularityHandler, 656 SingularValueDecomposition, 701, 706 SingularValueList, 701-702 Sinh, 435 SinhIntegral, 440 SinIntegral, 440 SIS•, 146 Size of Mathematica, 4-5 of expressions, ByteCount, 114 of fonts, FontSize, 193 1106 of graphics, 120 of graphics, ImageSize, 105, 120, 189 of points, PointSize, 155 Skeel and Keiper H2001L, xii Skewness, 967, 973, 1005 Skip, 104 Slide shows, 58 Slider, 319, 377 Slider2D, 324, 378 Sliders, 318, 375 SlideView, 362 Slot HÒL, 520 SlotSequence HÒÒL, 520 Small, 155, 165, 192 Smaller, 165, 192 Smith and Blachman H1995L, 116 Smoothing, 1041 with a kernel, ListCorrelate, 1041 with discrete Fourier transform, Fourier, 1045 with exponential smoothing, ExponentialMovingAverage, 1044 with local regression, 1044 with moving averages, MovingAverage, 1044 with moving medians, MovingMedian, 1044 Social network, 273 Solve, 712 for linear equations, 43, 710 for polynomial equations, 43, 716, 718 for radical equations, 723 for transcendental equations, 730 SolveAlways, 719, 848, 956 SolveDelayed, 866, 917 Solving difference equations, RSolve, 924 differential equations, DSolve, NDSolve, 830 integral equations, 847 linear equations, Solve, LinearSolve, 710 partial differential equations, DSolve, NDSolve, 886 polynomial equations, Solve, NSolve, Reduce, 716 poynomial inequalities, Reduce, 725 radical equations, Solve, NSolve, Reduce, 723 transcendental equations, Solve, FindRoot, 730, 732 sort, 613 Sort, 34, 434, 452, 681, 1022 SortBy, 452, 681 Sorting, 613 according to a given criterion, 452, 1022 with Sort, 34, 452, 681 with SortBy, 452, 681 with Union, 452 Sound, 310 Mathematica Navigator Sound, Play, 121 Sow, 412, 564, 649 Spacings above headers, PageHeaderMargins, 69 around boxes, FrameMargins, 67 around cells, CellMargins, 67 between a cell frame and the labels, CellFrameLabelMargins, 68 between lines, LineSpacing, 66 between paragraphs, ParagraphSpacing, 66 between tabs, TabSpacings, 66 in grid boxes, Spacings, 471 inside cell frames, CellFrameMargins, 68 Spacings, 124, 471, 479 Span, ;;, 448, 679, 692 SpanFromAbove, 488 SpanFromBoth, 488 SpanFromLeft, 488 Sparse arrays, 689 Sparse linear systems, Solve, 711 SparseArray, 678, 687, 689, 705, 714 SpatialDiscretization, 918 Special characters, 74 Special functions, 439 expansion of, FunctionExpand, 424 simplification of, FullSimplify, 419 SpecialCharacters palette, 16 Spectrums, 675 Specularity, 178 Speeding up calculations, 112, 569-570 functions, Compile, 528 Spelling checking, 24, 53 errors, 53 Spelling Language Hmenu commandL, 53 SpellingOptions, 53, 69 Sphere, 177 Spherical•, 620 SphericalPlot3D, 143 SphericalRegion, 212, 217 Spiegel H1971L, 923, 928 Spiegel H1999L, 639, 671, 893, 964 Splice, 111 Spline•, 154, 163 SplineDivision•, 163 SplineDots•, 163 SplineFit•, 803 SplineFunction•, 804 SplinePoints•, 163 Splines in graphics, Spline•, 163 in interpolation, SplineFit•, 803 Splines` package, 163, 803 Index Split, 450, 567, 574, 681, 993 Sqrt, 11, 421, 435 Square brackets, 14 Square roots, Sqrt, 11, 421 SquaredEuclideanDistance, 684 StackedBarChart•, 256 Standard error of sample mean, 1005 StandardDeviation, 36, 967, 973, 1005 StandardForm, 70 StandardizedResiduals•, 1031, 1036 Start Kernel Hmenu commandL, StartingParameters•, 1036 StartingStepSize, 866, 917 StartOfLine, 510 StartOfString, 510 stationaryDistribution, 995 Statistical distributions, 979 StatisticalPlots` package, 251-252, 259 Statistics descriptive multivariate, 1008 descriptive univariate, 36, 1004 dispersion, multivariate, 1008 dispersion, univariate, 1005 location, univariate, 1004 shape, univariate, 1005 StausArea, 363 steadyStateAverages, 1001 stehfestILT, 672 StemLeafPlot•, 259 Step function, UnitStep, 438 StepDataPlot•, 868 StepMonitor, 411, 735, 749, 763, 822, 866, 868, 917-918 Stereograms single|image, SIS•, 146 two|image, 145, 149, 863 Stiff differential equations, 866 Stirling numbers, 464 StirlingS1, 437 stirlingS2, 465 StirlingS2, 437 Stochastic processes, 987 birth-death process, 272, 888, 999 Brownian motion, brownianMotion, 991 coin tossing, coinTossing, 988 continuous|time Markov chain, ctMarkovChain, 998 discrete|time Markov chain, dtMarkovChain, 992 gambler‘s ruin, gamblersRuin, 988 MêMê1 queue, 1000 Poisson process, poissonProcess, 997, 999 random walk, 1D, randomWalk, 987 random walk, 2D, 989 1107 random walk, 3D, 990 Wiener process, 991 Stopping criteria, for numerical methods, 411 Stopping criteria, SameTest, 578 Stratified Monte Carlo method, 663 String expressions, 506 StringCases, 507 StringCount, 507 StringDrop, 434 StringExpression, 507 StringFreeQ, 507 StringInsert, 434 StringJoin HL, 434 StringLength, 434 StringMatchQ, 507 StringPosition, 507 StringQ, 431, 434 StringReplace, 509 StringReplaceList, 509 StringReplacePart, 434 StringReverse, 434 Strings manipulating of, 433, 550 patterns in, 505 reading and writing, 103 replacing in, 509 searching in, 507 StringSplit, 509 StringTake, 434 StudentizedResiduals•, 1031 StudentNewmanKeuls•, 1029 StudentTCI•, 1020 StudentTDistribution, 979 StudentTPValue•, 1024 Style Hmenu commandL, 54 Style, 71, 164, 183, 193, 339 Style sheets, 55, 78 creating new, 64 editing, 63 nonstandard, 99 Styles for cells, 54 for curves in graphics, PlotStyle, 203 for graphics, 200 for notebooks, 55 for outputs, 70 for outputs, Style, 71 for text in graphics, Style, 164 Stylesheet Hmenu commandL, 55, 63 Subfactorial, 437 Sublists generation of, Partition, 450 removal of, Flatten, 450 Subscript, 447 ... can be used to edit the input; arrow keys may not function Using special editing commands such as Edit together with an editor such as Emacs can help a lot in plain Unix .) ‡ Quitting Mathematica. . .Mathematica ® Navigator This page intentionally left blank Mathematica ® Navigator Mathematics, Statistics, and Graphics THIRD EDITION Heikki Ruskeepää Department of Mathematics University... write Show[Plot[…], Plot[…]]; the DisplayFunction option is no longer needed • Graphics and Graphics3 D no longer need Show to display the graphics Thus, write Graphics[ {…}] instead of Show [Graphics[ {…}]
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