a guided tour of mathematical physics (by roel snieder, department of geophysics, utrecht univers

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1、AGuidedTourofMathematicalPhysicsRoelSniederDept.ofGeophysics,UtrechtUniversity,P.O.Box80.021,3508TAUtrecht,TheNetherlandsPublishedbySamizdatPressGolden
WhiteRiverJunctioncSamizdatPress,1994SamizdatPresspublicationsareavailableviaInternetfromhttp://samizdat.mines.ed

2、uPermissionisgiventocopythesedocumentsforeducationalpurposesNovember16,1998Contents1Introduction52Summationofseries72.1TheTaylorseries.................................72.2Thebouncingball................................112.3Re ectionandtransmissionbyastackoflayers..

3、..............133Sphericalandcylindricalcoordinates173.1Introducingsphericalcoordinates........................173.2Changingcoordinatesystems..........................203.3Theaccelerationinsphericalcoordinates....................213.4Volumeintegrationinsphericalcoo

4、rdinates..................243.5Cylindercoordinates...............................264Thedivergenceofavectoreld314.1The uxofavectoreld.............................314.2Introductionofthedivergence..........................324.3Sourcesandsinks........................

5、.........344.4Thedivergenceincylindercoordinates.....................354.5Islifepossibleina5-dimensionalworld?....................375Thecurlofavectoreld415.1Introductionofthecurl.............................415.2Whatisthecurlofthevectoreld?......................4

6、25.3Therstsourceofvorticity rigidrotation...................445.4Thesecondsourceofvorticity shear......................455.5Themagneticeldinducedbyastraightcurrent...............475.6Sphericalcoordinatesandcylindercoordinates................476ThetheoremofGauss51

7、6.1StatementofGauss'law.............................516.2Thegravitationaleldofasphericallysymmetricmass............526.3Arepresentationtheoremforacousticwaves..................546.4Flowingprobability................................5512CONTENTS7ThetheoremofStokes59

8、7.1StatementofStokes'law.............................597.2Stokes'theoremfromthetheoremofGauss..................627.3Themagneticeldofacurrentinas