数学物理

图书标准信息

• 作者 [法]阿培（Walter Appel） 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 1
• ISBN 9787510050633
• 定价 129.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 642页
• 正文语种 简体中文

【内容简介】

　　Thereisafairlyfasbionablecurrentofthoughtthatboldsthattheuseofadvancedmathematicsisoflittlerealuseinphysics，andgoessometimesasfarastosaythatknowingconvincedthatmatbematicsisstikllaparecioussourceofinsight，notforstudentsofphysics，butalsoforresearchers.
　　Manyonlyseemathematicsasatool-andofcourse，itispartatool，buttheyshouldberemindedthat，asGalileosaid，thebookofNatureiswritteningiveexamplesthatknowingmathematicsprovidesthemeanstounderstandprecisephysicalnotions，tousethemmoreeasily，toestablishthemonasurefoundation，andevenmoreimportantly，todiscovernewones.

【目录】

Abook'sapoLogy
Indexofnotation

1Reminders：convergenceofsequencesandseries
1.1Theproblemoflimitsinphysics
1.1.aTwoparadoxesinvolvingkineticenergy
1.1.bRomeo,Juliet,andviscousfluids
1.1.cPotentialwallinquantummechanics
1.1.dSemi-infinitefilterbehavingaswaveguide
1.2Sequences
1.2.aSequencesinanormedvectorspace
1.2.bCauchysequences
1.2.cThefixedpointtheorem
1.2.dDoublesequences
1.2.eSequentialdefinitionofthelimitofafunction
1.2.fSequencesoffunctions
1.3Series
1.3.aSeriesinanormedvectorspace
1.3.bDoublyinfiniteseries
1.3.cConvergenceofadoubleseries
1.3.dConditionallyconvergentseries,absolutelyconvergentseries
1.3.eSeriesoffunctions
1.4Powerseries,analyticfunctions
1.4.aTaylorformulas
1.4.bSomenumericalillustrations
1.4.cRadiusofconvergenceofapowerseries
1.4.dAnalyticfunctions
1.5Aquicklookatasymptoticanddivergentseries
1.5.aAsymptoticseries
1.5.bDivergentseriesandasymptoticexpansions
Exercises
Problem
Solutions

2MeasurethearyandtheLebesgueintegral
2.1TheintegralaccordingtoMr.Riemann
2.1.aRiemannsums
2.1.bLimitationsofRiemann'sdefinition
2.2TheintegralaccordingtoMr.Lebesgue
2.2.aPrincipleofthemethod
2.2.bBorelsubsets
2.2.cLebesguemeasure
2.2.dTheLebesgue-algebra
2.2.eNegligiblesets
2.2.fLebesguemeasureonRn
2.2.gDefinitionoftheLebesgueintegral
2.2.hFunctionszeroalmosteverywhere,spaceL1
2.2.1Andtoday?
Exercises
Solutions

3Integralcalculus
3.1Integrabilityinpractice
3.1.aStandardfunctions
3.l.bComparisontheorems
3.2Exchangingintegralsandlimitsorseries
3.3Integralswithparameters
3.3.aContinuityoffunctionsdefinedbyintegrals
3.3.bDifferentiatingundertheintegralsign
3.3.cCaseofparametersappearingintheintegrationrange
3.4Doubleandmultipleintegrals
3.5Changeofvariables
Exercises
Solutions

4ComplexAnalysisⅠ
4.1Holomorphicfunctions
4.1.aDefinitions
4.2Cauchy'stheorem
4.3Propertiesofholomorphicfunctions
4.4Singularitiesofafunction
4.5Laurentseries
……
5ComplexAnalysisⅡ
6Conformalmaps
7DistributionsⅠ
8DistributionsII
9Hilbertspaces,Fourierseries
10Fouriertransformoffunctions
11Fouriertransformofdistributions
12TheLaplacetransform
13PhysicalapplicationsoftheFouriertransform
14Bras,kets,andallthatsortofthing
15Greenfunctions
16Tensors
17Differentialforms
18Groupsandgrouprepresentations
19Introductiontoprobabilitytheory
20Randomvariables
21Convergenceofrandomvariables：centrallimittheorem
Appendices
Tables