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本帖最后由 三T上人 于 2016-7-22 13:22 编辑 <br /><br />1. Simple Calculations with MATLAB .................................................. 1
1.1 IntroductionandaWordofWarning................................................. 1
1.2 ScalarQuantitiesandVariables ...................................................... 2
1.2.1 Rules forNamingofVariables...................................................... 4
1.2.2 Precedence: The Order in Which Calculations Are Per-formed........ 5
1.2.3 MathematicalFunctions............................................................. 8
1.3 Format:TheWayinWhichNumbersAppear ..................................... 12
1.4 Vectors inMATLAB..................................................................... 13
1.4.1 InitialisingVectorObjects.......................................................... 13
1.4.2 ManipulatingVectorsandDotArithmetic ...................................... 14
1.5 SettingUpMathematicalFunctions................................................. 17
1.6 SomeMATLABSpeci?cCommands ............................................... 20
1.6.1 LookingatVariablesandTheirSizes............................................ 22
1.7 Accessing Elements of Arrays ................................................... 23
1.8 Tasks .................................................................................... 24
2. Writing Scripts and Functions ..................................................... 27
2.1 CreatingScriptsandFunctions.................................................... 27
2.1.1 Functions ............................................................................. 30
2.1.2 BriefAside ............................................................................ 35
2.2 Plotting Simple Functions ......................................................... 36
2.2.1 Evaluating Polynomials and Plotting Curves ........... 41
2.2.2 More on Plotting ................................... 44
2.3 FunctionsofFunctions .................................... 49
2.4 Errors .................................................. 51
2.4.1 NumericalErrors................................... 51
2.4.2 UserError......................................... 54
2.5 Tasks ................................................... 57
3. Loops and Conditional Statements .......................... 63
3.1 Introduction ............................................. 63
3.2 LoopsStructures ......................................... 63
3.3 SummingSeries .......................................... 68
3.3.1 Sums of Series of the FormN j=1jp, p ∈ N............... 73
3.3.2 Summing In?nite Series ............................. 76
3.3.3 Summing Series Using MATLAB Speci?c Commands . . . 79
3.3.4 LoopsWithinLoops (Nested)........................ 82
3.4 Conditional Statements ................................... 83
3.4.1 Constructing Logical Statements ..................... 85
3.4.2 The MATLAB Command switch .................... 88
3.5 Conditional loops......................................... 90
3.5.1 The break Command............................... 92
3.6 MATLABSpeci?cCommands ............................. 92
3.7 ErrorChecking........................................... 94
3.8 Tasks ................................................... 97
4. Root Finding ............................................... 103
4.1 Introduction .............................................103
4.2 InitialEstimates .........................................104
4.3 Fixed Point Iteration .....................................109
4.4 Bisection ................................................113
4.5 Newton–RaphsonandSecantMethods ......................117
4.5.1 Derivationof theNewton–RaphsonMethod............117
4.6 RepeatedRootsofFunctions...............................123
4.7 ZerosofHigher-DimensionalFunctions(*) ...................125
4.8 MATLABRoutines forFindingZeros .......................128
4.8.1 RootsofaPolynomial ..............................128
4.8.2 The Command fzero ...............................128
4.9 Tasks ...................................................130
5. Interpolation and Extrapolation ............................ 133
5.1 Introduction .............................................133
5.2 Saving and Reading Data ..................................134
5.3 WhichPoints toUse?.....................................139
5.4 Newton Forward Di?erences and Lagrange Polynomials .......141
5.4.1 Linear Interpolation/Extrapolation ...................147
5.5 CalculatingInterpolatedandExtrapolatedValues ............148
5.6 Splines..................................................150
5.7 CurvesofBestFit........................................152
5.8 Interpolation of Non-Smooth Data ..........................155
5.8.1 Insu?cient Data Points .............................158
5.9 MinimisationofFunctionsandParameterRetrieval ...........161
5.9.1 ParameterRetrieval ................................163
5.9.2 Using fmins forParameterRetrieval..................164
5.10 Tasks ...................................................166
6. Matrices .................................................... 169
6.1 Introduction .............................................169
6.1.1 InitialisingMatricesWithinMATLAB ................169
6.1.2 MatrixOperations..................................174
6.1.3 OperationsonElementsofMatrices ..................180
6.1.4 MoreonSpecialMatrices............................182
6.1.5 MatricesContainingStrings .........................185
6.2 PropertiesofMatricesandSystemsofEquations .............186
6.2.1 DeterminantsofMatrices............................190
6.3 ElementaryRowOperations ...............................191
6.3.1 Solving Many Equations at Once .....................198
6.4 MatrixDecomposition ....................................199
6.5 EigenvaluesandEigenvectors ..............................204
6.6 Speci?cMATLABCommands .............................208
6.7 CharacteristicPolynomials ................................212
6.8 ExponentialsofMatrices ..................................214
6.9 Tasks ...................................................217
7. Numerical Integration ...................................... 225
7.1 Introduction .............................................225
7.2 IntegrationUsingStraightLines............................226
7.2.1 Errors intheTrapeziumMethod .....................229
7.3 IntegrationUsingQuadratics ..............................230
7.4 IntegrationUsingCubicPolynomials........................235
7.5 IntegratingUsingMATLABCommands.....................237
7.6 Speci?cExamplesof Integrals..............................238
7.6.1 In?nite Integrals and Removable Singularities ..........238
7.6.2 Inde?niteIntegrals .................................240
7.7 Tasks ...................................................242
8. Solving Di?erential Equations .............................. 247
8.1 Introduction .............................................247
8.2 Euler’sMethodandCrank–Nicolson ........................247
8.2.1 AnalyticalComparisons .............................253
8.3 BandedMatrices .........................................259
8.4 Runge–KuttaMethods ....................................263
8.5 Higher-OrderSystems.....................................266
8.5.1 Second-OrderSystems ..............................266
8.5.2 Bessel’s equation ...................................270
8.5.3 Airy’sEquation ....................................273
8.5.4 ShootingMethods ..................................274
8.6 Boundary-Value Problems .................................278
8.7 PopulationDynamics .....................................282
8.8 EigenvaluesofDi?erentialSystems .........................285
8.9 Tasks ...................................................286
9. Simulations and Random Numbers ......................... 291
9.1 Introduction .............................................291
9.2 Statistical quantities ......................................291
9.2.1 Averages ..........................................291
9.2.2 Other Statistical Measures ...........................293
9.3 RandomNumbersandDistributions ........................295
9.3.1 NormalDistribution ................................298
9.3.2 Calculating Probabilities ............................299
9.3.3 Permutations ......................................300
9.4 MapsandWhiteNoise....................................300
9.4.1 Modelling Discrete Systems ..........................307
9.4.2 PeriodicityandChaos...............................309
9.4.3 RandomMotion....................................316
9.5 Tasks ...................................................319
A. A Mathematical Introduction to Matrices .................. 323
A.1 SpecialMatrices..........................................330
A.2 InversesofMatrices.......................................331
B. Glossary of Useful Terms ................................... 335
B.1 Arithmetic and Logical Operators ..........................335
B.2 Symbols.................................................343
B.3 Plotting Commands ......................................347
B.4 GeneralMATLABCommands .............................365
C. Solutions to Tasks .......................................... 389
C.1 Solutions forTasks fromChapter1 .........................389
C.2 Solutions forTasks fromChapter2 .........................394
C.3 Solutions forTasks fromChapter3 .........................400
C.4 Solutions forTasks fromChapter4 .........................408
C.5 Solutions forTasks fromChapter5 .........................414
C.6 Solutions forTasks fromChapter6 .........................418
C.7 Solutions forTasks fromChapter7 .........................429
C.8 Solutions forTasks fromChapter8 .........................436
C.9 Solutions forTasks fromChapter9 .........................454
Index ........................................................... 459
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