MATLAB经典教程:MATLAB编程与数值方法导论

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MATLAB经典教程:MATLAB编程与数值方法导论,(英文版) 目录如下: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 SomeMATLABSpecificCommands ........................ 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 .................................................. 512.4.1 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 Form
N

j=1
jp, p ∈ N............... 73
3.3.2 Summing Infinite Series ............................. 76
3.3.3 Summing Series Using MATLAB Specific 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 MATLABSpecificCommands ............................. 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 Differences and Lagrange Polynomials .......141
5.4.1 Linear Interpolation/Extrapolation ...................1475.5 CalculatingInterpolatedandExtrapolatedValues ............148
5.6 Splines..................................................150
5.7 CurvesofBestFit........................................152
5.8 Interpolation of Non-Smooth Data ..........................155
5.8.1 Insufficient 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 SpecificMATLABCommands .............................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 SpecificExamplesof Integrals..............................238
7.6.1 Infinite Integrals and Removable Singularities ..........238
7.6.2 IndefiniteIntegrals .................................240
7.7 Tasks ...................................................2428. Solving Differential 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 EigenvaluesofDifferentialSystems .........................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 .............................365C. 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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