北大数学物理方法(A)-复变函数教案15δ函数

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Outline1›Êùδ¼êÔnÆêÆÔn{‘§|2007cSC.S.Wu1›Êùδ¼êOutlineùLJ:1δ¼ê½Â:—ݼêδ¼êÄ$Ž5K‘Ún‘δ¼ê2~‡©§Green¼ê~‡©§Green¼êµÐŠ¯K~‡©§Green¼êµŠ¯K3Green¼êŒUé¡5Њ¯KŠ¯KC.S.Wu1›Êùδ¼êOutlineùLJ:1δ¼ê½Â:—ݼêδ¼êÄ$Ž5K‘Ún‘δ¼ê2~‡©§Green¼ê~‡©§Green¼êµÐŠ¯K~‡©§Green¼êµŠ¯K3Green¼êŒUé¡5Њ¯KŠ¯KC.S.Wu1›Êùδ¼êOutlineùLJ:1δ¼ê½Â:—ݼêδ¼êÄ$Ž5K‘Ún‘δ¼ê2~‡©§Green¼ê~‡©§Green¼êµÐŠ¯K~‡©§Green¼êµŠ¯K3Green¼êŒUé¡5Њ¯KŠ¯KC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sReferencesÇÂÁ§5êÆÔn{6§§10.1—10.4ù&œ§5êÆÔn{6§§5.3nÎ!X1Á§5êÆÔn{6§§6.5C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsÚó0 ˜«#“¼ê”δ¼êdÔnÆ[DiracÚ?Œ^u£ÔnÆ¥:þ§~X:Ÿþ§:Ö§óÀ3C“ÔnÆ¥kX2A^3êÆþ,δ¼êáu2¼ê§EŒ±ŠÊϼê˜?1$Ž§XOŽ‡©ÚÈ©§$–A^u¦)‡©§Œ±·‚?nk'êÆÔn¯K,‘54ŒB|C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsÚó0 ˜«#“¼ê”δ¼êdÔnÆ[DiracÚ?Œ^u£ÔnÆ¥:þ§~X:Ÿþ§:Ö§óÀ3C“ÔnÆ¥kX2A^3êÆþ,δ¼êáu2¼ê§EŒ±ŠÊϼê˜?1$Ž§XOŽ‡©ÚÈ©§$–A^u¦)‡©§Œ±·‚?nk'êÆÔn¯K,‘54ŒB|C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsÚó0 ˜«#“¼ê”δ¼êdÔnÆ[DiracÚ?Œ^u£ÔnÆ¥:þ§~X:Ÿþ§:Ö§óÀ3C“ÔnÆ¥kX2A^3êÆþ,δ¼êáu2¼ê§EŒ±ŠÊϼê˜?1$Ž§XOŽ‡©ÚÈ©§$–A^u¦)‡©§Œ±·‚?nk'êÆÔn¯K,‘54ŒB|C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsÚó0 ˜«#“¼ê”δ¼êdÔnÆ[DiracÚ?Œ^u£ÔnÆ¥:þ§~X:Ÿþ§:Ö§óÀ3C“ÔnÆ¥kX2A^3êÆþ,δ¼êáu2¼ê§EŒ±ŠÊϼê˜?1$Ž§XOŽ‡©ÚÈ©§$–A^u¦)‡©§Œ±·‚?nk'êÆÔn¯K,‘54ŒB|C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsÚó0 ˜«#“¼ê”δ¼êdÔnÆ[DiracÚ?Œ^u£ÔnÆ¥:þ§~X:Ÿþ§:Ö§óÀ3C“ÔnÆ¥kX2A^3êÆþ,δ¼êáu2¼ê§EŒ±ŠÊϼê˜?1$Ž§XOŽ‡©ÚÈ©§$–A^u¦)‡©§Œ±·‚?nk'êÆÔn¯K,‘54ŒB|C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsÚó0 ˜«#“¼ê”δ¼êdÔnÆ[DiracÚ?Œ^u£ÔnÆ¥:þ§~X:Ÿþ§:Ö§óÀ3C“ÔnÆ¥kX2A^3êÆþ,δ¼êáu2¼ê§EŒ±ŠÊϼê˜?1$Ž§XOŽ‡©ÚÈ©§$–A^u¦)‡©§Œ±·‚?nk'êÆÔn¯K,‘54ŒB|C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsùLJ:1δ¼ê½Â:—ݼêδ¼êÄ$Ž5K‘Ún‘δ¼ê2~‡©§Green¼ê~‡©§Green¼êµÐŠ¯K~‡©§Green¼êµŠ¯K3Green¼êŒUé¡5Њ¯KŠ¯KC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsŠδ¼êÔnµ§k?Ø:!~X:Ö֩ٗݼêêÆL«{ü儧k?ؘ‘œ/3ᆂþ0xl«mSkþ!Ö©Ù§oÖþ1‡ü §3«m ÃÖ§K֗ݼêδl(x)=0x−l/21l−l/2xl/20xl/2C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsŠδ¼êÔnµ§k?Ø:!~X:Ö֩ٗݼêêÆL«{ü儧k?ؘ‘œ/3ᆂþ0xl«mSkþ!Ö©Ù§oÖþ1‡ü §3«m ÃÖ§K֗ݼêδl(x)=0x−l/21l−l/2xl/20xl/2C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3DδfunctionsŠδ¼êÔnµ§k?Ø:!~X:Ö֩ٗݼêêÆL«{ü儧k?ؘ‘œ/3ᆂþ0xl«mSkþ!Ö©Ù§oÖþ1‡ü §3«m ÃÖ§K֗ݼêδl(x)=0x−l/21l−l/2xl/20xl/2C.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionse-l→0§òŸo(JºC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionse-l→0§òŸo(JºC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionsδl(x)=0x−l/21l−l/2xl/20xl/2liml→0δl(x)=(0x6=0∞x=0ePliml→0δl(x)=δ(x)§δ(x)kŸo¿ÂºC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionsδl(x)=0x−l/21l−l/2xl/20xl/2liml→0δl(x)=(0x6=0∞x=0ePliml→0δl(x)=δ(x)§δ(x)kŸo¿ÂºC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionsδl(x)=0x−l/21l−l/2xl/20xl/2liml→0δl(x)=(0x6=0∞x=0ePliml→0δl(x)=δ(x)§δ(x)kŸo¿ÂºC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionsδl(x)=0x−l/21l−l/2xl/20xl/2liml→0δl(x)=(0x6=0∞x=0ePliml→0δl(x)=δ(x)§δ(x)kŸo¿ÂºC.S.Wu1›Êùδ¼êDiracδfunctionGreenFunctionsofODEPossibleSymmetricPropertiesofGF’sDensityDistributionofAPointSourceBasicOperationRules2D&3Dδfunctionsδ(x)¿Âéu?¿˜‡3−l/2xl/2SëY¼êf(x)§Šâ¥Š½n§kZ∞−∞f(x)δl(x)dx=f(θl)−1/2≤θ≤1/24l→0§éu?¿˜‡3x=0:ëY¼êf(x)§kZ∞−∞f(x)δ(x)dx=f(0)AO´Z∞−∞δ(x)dx=1C.S.Wu1›Êùδ¼êDira

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