nayfeh a.h., chin c.-m. perturbation methods with mathematica (draft, 1999)(346s)

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1、TableofContents--------------------------Chapter1:Introduction--------------------------·1.1PreliminaryRemarks·1.2SymbolicComputation·1.2.1GlobalRules·1.2.2LocalRules·1.2.3PatternMatching·1.2.4UsingPatternsinRules·1.2.5RestrictingPatternMatchingwithPredicates·1.2.6PureFunctions·

2、1.2.7MapandApply·1.2.8NestandFold-------------------------------------Chapter2:TheDuffingEquation-------------------------------------·2.1TheDuffingEquation·2.2StraightforwardExpansion·2.3TheLindstedt-PoincaréTechnique·2.4TheMethodofMultipleScales·2.4.1Second-OrderReal-ValuedSys

3、tem·2.4.2First-OrderReal-ValuedSystem·2.4.3First-OrderComplex-ValuedSystem·2.5VariationofParameters·2.6TheMethodofAveraging-------------------------------------------------------------------Chapter3:SystemswithQuadraticandCubicNonlinearities--------------------------------------

4、-----------------------------·3.1NondimensionalEquationofMotion·3.2StraightforwardExpansion·3.3TheLindstedt-PoincaréTechnique·3.4TheMethodofMultipleScales·3.4.1Second-OrderReal-ValuedSystem·3.4.2First-OrderReal-ValuedSystem·3.4.3First-OrderComplex-ValuedSystem·3.5TheMethodofAver

5、aging·3.6TheGeneralizedMethodofAveraging·3.7TheKrylov-Bogoliubov-MitropolskyTechnique·3.8TheMethodofNormalForms-------------------------------------------------------------Chapter4:ForcedOscillationsoftheDuffingEquation------------------------------------------------------------

6、-·4.1StraightforwardExpansion·4.2TheMethodofMultipleScales·4.2.1Preliminaries·4.2.2PrimaryResonance·4.2.3SecondaryResonancesDuetoCubicNonlinearities·4.2.4SecondaryResonancesDuetoQuadraticNonlinearities·4.2.5First-OrderReal-ValuedSystem·4.2.6First-OrderComplex-ValuedSystem·4.2.7T

7、heFunctionMMS1·4.3TheGeneralizedMethodofAveraging·4.4TheMethodofNormalForms-----------------------------------------------------------------------------------------Chapter5:Higher-OrderApproximationsforSystemswithInternalResonances------------------------------------------------

8、-----------------------------------------·5.1Eu