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1、March25,2009Time:04:39pmfm.texTHEMATHEMATICALMECHANICiMarch25,2009Time:04:39pmfm.texiiMarch25,2009Time:04:39pmfm.texMARKLEVITHEMATHEMATICALMECHANICusingphysicalreasoningtosolveproblemsPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDiiiMarch25,2009Time:04:39pmfm.tex
2、Copyrightc2009byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressCataloging-in-Publicat
3、ionDataLevi,Mark,1951–Themathematicalmechanic:usingphysicalreasoningtosolveproblems/MarkLevi.p.cm.Includesbibliographicalreferencesandindex.ISBN978-0-691-14020-9(cloth:alk.paper)1.Problemsolving.2.Mathematicalphysics.I.Title.QA63.L482009510–dc222009004861Brit
4、ishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinTimesPrintedonacid-freepaper.∞press.princeton.eduTypesetbySRNovaPvtLtd,Bangalore,IndiaPrintedintheUnitedStatesofAmerica10987654321ivMarch25,2009Time:04:39pmfm.texContents1Introduction1
5、1.1MathversusPhysics11.2WhatThisBookIsAbout21.3APhysicalversusaMathematicalSolution:AnExample61.4Acknowledgments82ThePythagoreanTheorem92.1Introduction92.2The“FishTank”ProofofthePythagoreanTheorem92.3ConvertingaPhysicalArgumentintoaRigorousProof122.4TheFundam
6、entalTheoremofCalculus142.5TheDeterminantbySweeping152.6ThePythagoreanTheorembyRotation162.7StillWaterRunsDeep172.8AThree-DimensionalPythagoreanTheorem192.9ASurprisingEquilibrium212.10PythagoreanTheorembySprings222.11MoreGeometrywithSprings232.12AKineticEnerg
7、yProof:PythagorasonIce242.13PythagorasandEinstein?253MinimaandMaxima273.1TheOpticalPropertyofEllipses283.2MoreabouttheOpticalProperty313.3LinearRegression(TheBestFit)viaSprings313.4ThePolygonofLeastArea343.5ThePyramidofLeastVolume363.6ATheoremonCentroids393.7
8、AnIsoperimetricProblem403.8TheCheapestCan443.9TheCheapestPot47March25,2009Time:04:39pmfm.texviCONTENTS3.10TheBestSpotinaDrive-InTheater483.11TheInscribedAngle513.12Fermat’sPrincipleandSne
