北大数学物理方法(A)-数学物理方程教案14积分变换

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Outline1›oùÈ©C†ÔnÆ2007cSC.S.Wu1›oùÈ©C†OutlineùLJ:1LaplaceC†A^Ã.\9D¯KÃ.uÅįK2FourierC†A^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩC†HankelC†MellinC†C.S.Wu1›oùÈ©C†OutlineùLJ:1LaplaceC†A^Ã.\9D¯KÃ.uÅįK2FourierC†A^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩC†HankelC†MellinC†C.S.Wu1›oùÈ©C†OutlineùLJ:1LaplaceC†A^Ã.\9D¯KÃ.uÅįK2FourierC†A^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩC†HankelC†MellinC†C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsReferencesÇÂÁ§5êÆÔn{6§119Ùù&œ§5êÆÔn{6§113ÙnÎ!X1Á§5êÆÔn{6§111ÙC.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringLaplaceCCC†††AAA^^^C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC†Œ^u¦)¹žm ‡©§½)¯KC†§gCþ‡ê'5~˜‡~X§5´xÚtü‡gCþ ‡©§½)¯K§C†ÒI¦)~‡©§(gCþx)½)¯K˜„`5§öo'N´¦)ù¦´©½)¯K)”¼ê§„7L‡ü§âU©¯K)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC†Œ^u¦)¹žm ‡©§½)¯KC†§gCþ‡ê'5~˜‡~X§5´xÚtü‡gCþ ‡©§½)¯K§C†ÒI¦)~‡©§(gCþx)½)¯K˜„`5§öo'N´¦)ù¦´©½)¯K)”¼ê§„7L‡ü§âU©¯K)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC†Œ^u¦)¹žm ‡©§½)¯KC†§gCþ‡ê'5~˜‡~X§5´xÚtü‡gCþ ‡©§½)¯K§C†ÒI¦)~‡©§(gCþx)½)¯K˜„`5§öo'N´¦)ù¦´©½)¯K)”¼ê§„7L‡ü§âU©¯K)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC†Œ^u¦)¹žm ‡©§½)¯KC†§gCþ‡ê'5~˜‡~X§5´xÚtü‡gCþ ‡©§½)¯K§C†ÒI¦)~‡©§(gCþx)½)¯K˜„`5§öo'N´¦)ù¦´©½)¯K)”¼ê§„7L‡ü§âU©¯K)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC†Œ^u¦)¹žm ‡©§½)¯KC†§gCþ‡ê'5~˜‡~X§5´xÚtü‡gCþ ‡©§½)¯K§C†ÒI¦)~‡©§(gCþx)½)¯K˜„`5§öo'N´¦)ù¦´©½)¯K)”¼ê§„7L‡ü§âU©¯K)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringùLJ:1LaplaceC†A^Ã.\9D¯KÃ.uÅįK2FourierC†A^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩC†HankelC†MellinC†C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^‡¢Sþ§Ã.«m§´˜‡ÔnþĖÏd§XJ‡/ѽ)¯K{§K„Ak.^‡u x→±∞→0C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^‡¢Sþ§Ã.«m§´˜‡ÔnþĖÏd§XJ‡/ѽ)¯K{§K„Ak.^‡u x→±∞→0C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^‡¢Sþ§Ã.«m§´˜‡ÔnþĖÏd§XJ‡/ѽ)¯K{§K„Ak.^‡u x→±∞→0C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^‡¢Sþ§Ã.«m§´˜‡ÔnþĖÏd§XJ‡/ѽ)¯K{§K„Ak.^‡u x→±∞→0C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞)ŠLaplaceC†-u(x,t);U(x,p)=Z∞0u(x,t)e−ptdtrU(x,p)w¤´x¼ê§p´ëꧤ±∂2u∂x2;d2U(x,p)dx2|^Щ^‡§k∂u∂t;pU(x,p)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞)ŠLaplaceC†-u(x,t);U(x,p)=Z∞0u(x,t)e−ptdtrU(x,p)w¤´x¼ê§p´ëꧤ±∂2u∂x2;d2U(x,p)dx2|^Щ^‡§k∂u∂t;pU(x,p)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞)ŠLaplaceC†-u(x,t);U(x,p)=Z∞0u(x,t)e−ptdtrU(x,p)w¤´x¼ê§p´ëꧤ±∂2u∂x2;d2U(x,p)dx2|^Щ^‡§k∂u∂t;pU(x,p)C.S.Wu1›oùÈ©C†ApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0u t=0=0−∞x∞)2?˜Ú-f(x,t);F(x,p)½)¯KÒC¤pU(x,p)−κd2U(x,p)dx2=F(x,p)3U x→±∞→0^‡e=Œ)(„Ö§~10.8)U(x,p)=121√κpZ∞−∞F(x0,p)exp−rpκ|x−x0|dx0C.S.

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