文件名称:
Computing with Mathematica
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上传时间: 2009-05-26
详细说明： Part I Learning the Basics 1 Mathematica Basics: An Introduction 3 Introduction 3 Arithmetic 3 MathematicalFunctions 5 SymbolicComputations 6 ExactandApproximateSolutionsforEquations 7 Graphsof FunctionsofOneVariable 9 Graphsof ParametricEquations 10 Graphsof Su rfacesinThreeDimensions 11 Graphsof ContourCurves forSurfaces 11 Matrix Algebra 12 RandomNumbers 13 Exercises 14 Mathematica Basics: Help 19 Introduction 19 The?and ??Operators 19 TheHelpBrowser 20 InterruptingMathematica Computations 21 MemoryManagementinMathematica 21 Exercises 22 v vi Contents Mathematica Basics: Notebooks 25 Introduction 25 NotebookToolbars 25 FormatPreferences 25 PageBreakPreferences 26 CellGroupings 26 TagNames 27 Links 28 In/OutNames 28 HyperlinkstoDocumentation 29 Exercises 29 Associated NotebookonCD-ROM:Cell Hierarchy CellHierarchy.nb Mathematica Basics: Text and Typesetting 31 Introduction 31 The BasicTypesettingandCompleteCharacters Palettes 31 AlgebraicManipulationPalette 33 BasicInputPalette 34 BasicCalculationsPalette 34 Exercises 35 Mathematica Basics: Packages 37 Introduction 37 LoadingStandardPackages 37 ForgettingtoLoadaPackage 39 Exercises 41 Part II Designing Functions 43 Values, Variables, and Assignments 45 Introduction 45 The ImmediateAssignmentOperator =for Values 46 The Delayed AssignmentOperator := for Functions 49 Evaluation Issues fortheImmediate and Delayed AssignmentOperators 53 Contents vii Computational EfficiencyandtheAssignmentOperators 56 Exercises 58 Functions 63 Introduction 63 FunctionswithaSingleArgument 63 FunctionswithSeveralArguments 69 FunctionswithStructuredArguments 71 FunctionswithDefault Valuesfor Arguments 75 FunctionswithaVaryingNumberof Arguments 80 Exercises 81 Recursive Definitions 87 Introduction 87 FunctionswithaSingleRecursiveArgument 87 FunctionswithSeveralRecursiveArguments 92 Limitationsto RecursiveComputations 95 Exercises 99 Substitution Rules and Optional Arguments 107 Introduction 107 SubstitutionRulesandthe Replacement Mechanism 107 SubstitutionRulesandInteractiveComputations 110 OptionsforBuilt-inFunctions 111 Defining anOptionforaFunction 114 Exercises 117 Four Spheres Packing Problem 119 Introduction 119 AnalysisoftheProblem 119 Computational Solutionof the Problem 120 GraphicRenderingof the Solution 121 Exercises 123 Associated NotebookonCD-ROM:Two-dimensionalViews oftheSpheres Views2D.nb Cross-sectionalViewofTwoTouching Spheres VerticalProjectionofThree Touching Spheres viii Contents Associated FolderonCD-ROM: FourSpheresDrawings Views2D-Drawings.nb EvaluationofViews2D.nb SphereDrawings.nb Evaluationof“GraphicRenderingof Solution” Part III Designing Programs 125 List Processing Functions 127 Introduction 127 ProcessingListswiththeMap[]Function 127 ApplicationsoftheMap[]Function to Graphics Objects 134 ListManipulation,ElementExtraction,and the Fold[]Function 140 TheFunctionsHead[],Apply[],Outer[],Depth[],andPosition[] 146 Exercises 153 Iterations with Loops 159 Introduction 159 UsingtheDo[]Loop:Basics 159 UsingtheDo[]Loop:AHulaHoop Animation 163 UsingtheWhile[]Loop:Basics 165 UsingtheWhile[]Loop:Termination Conditions and the Bisection Method 167 UsingtheFor[]Loop:Basics 170 UsingListProcessingFunctionsas Alternatives for Loops 173 The CollatzFunction 175 Exercises 176 Computations with Modules and Local Variables 181 Introduction 181 UsingtheModule[]Function:Basics 181 UsingtheModule[]Function:ReturningNumbersand Lists 184 UsingtheModule[]Function:Rendering GraphicsObjects 188 Exercises 191 Contents ix Part IV Exploring Advanced Features 197 Advanced Mathematica: Options 199 Introduction 199 Defining aSingleOptionfor aFunction 199 Defining SeveralOptionsfora Function 204 UsingBuilt-inGraphicsOptions in User-Defined Functions 208 Defining OptionsforOneFunction ThatAreOptions inSeveral OtherFunctions 211 Exercises 216 Advanced Mathematica: Hyperlinks and Buttons 221 Introduction 221 Hyperlinkswithina Notebook 221 JumpswithinaNotebook withoutHyperlinks 222 HyperlinksbetweenNotebooks 222 Hyperlinkstothe HelpBrowser 222 HyperlinkstoInternetResources 223 Hyperlinksas Buttons 224 CreatingaTypesettingPalette 225 CreatingaPalette of Expressions 227 CreatingaPalette of Characters and Expressions 228 CreatinganEvaluationPalette 229 PrintingaPalette 231 Exercises 231 Associated NotebookonCD-ROM:Targetofa Hyperlink JumpTarget.nb Associated FolderonCD-ROM: SamplePalettes n-CompleteCharacters.nb p-Pi.nbandn-Pi.nb p-Trig.nbandn-Trig.nb p-Logic.nbandn-Logic.nb p-Evaluate.nbandn-Evaluate.nb Advanced Mathematica: Packages 233 Introduction 233 ContextsandNames 233 x Contents InitializationCells 236 The BasicSchemeofaPackage 236 PackageFiles 244 APackageforanIterationFunction 247 APackageforGram-SchmidtOrthogonalization 250 LoadingPackages 254 Exercises 256 Associated FolderonCD-ROM: PackagesSupport InitCellA.nbandInitCellA.m InitCellM.nbandInitCellM.m Template.nbandTemplate.m Thermometer.nbandThermometer.m Iteration.nbandIteration.m GramSchmidt.nband GramSchmidt.m Advanced Mathematica: Files, Data Exchange, and Conversions 261 Introduction 261 DirectoriesandFilePaths 262 ImportandExport ofData 263 ConversionstoOtherFileFormats 266 ProtectedFunctions 267 Exercises 270 Associated FolderonCD-ROM:DataTests Survey.xls Filesgeneratedfromthenotebook: GoodAges.dat SortedAges.dat Std100CSV Std100Lines Std100List Std100Table Std100.xls SortedAges.xls Associated FolderonCD-ROM: HTMLDemos SphereCenters.nb SphereCentersFolder: contains thefilesgeneratedby Mathematica SphereDrawings.nb Contents xi SphereDrawings Folder: containsthefilesgeneratedbyMathematica Views2D-Drawings.nb Views2D-DrawingsFolder: containsthefilesgeneratedbyMathematica Part V Student Projects 273 Student Projects 275 Introduction 277 Arnold’sCatMap and ChaoticMapping 280 BouncingBalls 281 Collatz’sFunction 282 Conway’sChallengeSequence 283 ExponentiallyDamped Surfaces 284 FiniteAutomata 285 FractalsandChaoticBoundary Sets 286 FractalsandIteratedFunction Systems 288 GeometricOpticsandLens Systems 289 GroupsofRigidMotions 290 GrowthRatesofFunctions 291 HarmonicCoupledOscillations 292 HiddenPatterns 293 ImplementationofaPackage 294 InterpolationofCurveswith CubicSplines 295 JugglingBalls 296 LeasingaCar 297 MarkovChainsandDynamic Models 298 MoiréFringes 299 OscillatingMass System 301 Pell’sEquation 302 PublicKey Cryptography 303 Rainbows 305 RecurrenceRelations 306 SpanningTreesofaGraph 307 Associated FolderonCD-ROM: ProjectsSupport DeterministicFiniteAutomata: xii Contents DFAIntro.nbandDFA.m IteratedFunctionSystems IFSIntro.nbandIFS.m LocalParametricSplines LPSIntro.nbandLPS.m PublicKey Cryptography RSAIntro.nbandRSA.m Index 309 ...展开收缩
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