Outline1oùÈ©CÔnÆ2007cSC.S.Wu1oùÈ©COutlineùÇ:1LaplaceCA^Ã.\9D¯KÃ.uÅįK2FourierCA^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩCHankelCMellinCC.S.Wu1oùÈ©COutlineùÇ:1LaplaceCA^Ã.\9D¯KÃ.uÅįK2FourierCA^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩCHankelCMellinCC.S.Wu1oùÈ©COutlineùÇ:1LaplaceCA^Ã.\9D¯KÃ.uÅįK2FourierCA^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩCHankelCMellinCC.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsReferencesÇÂÁ§5êÆÔn{6§119Ùù&§5êÆÔn{6§113ÙnÎ!X1Á§5êÆÔn{6§111ÙC.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringLaplaceCCCAAA^^^C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC^u¦)¹m ©§½)¯KC §gCþê'5~~X§5´xÚtügCþ ©§½)¯K§C ÒI¦)~©§(gCþx)½)¯K`5§ öo'N´¦)ù¦´©½)¯K)¼ê§7Lü§âU©¯K)C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC^u¦)¹m ©§½)¯KC §gCþê'5~~X§5´xÚtügCþ ©§½)¯K§C ÒI¦)~©§(gCþx)½)¯K`5§ öo'N´¦)ù¦´©½)¯K)¼ê§7Lü§âU©¯K)C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC^u¦)¹m ©§½)¯KC §gCþê'5~~X§5´xÚtügCþ ©§½)¯K§C ÒI¦)~©§(gCþx)½)¯K`5§ öo'N´¦)ù¦´©½)¯K)¼ê§7Lü§âU©¯K)C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC^u¦)¹m ©§½)¯KC §gCþê'5~~X§5´xÚtügCþ ©§½)¯K§C ÒI¦)~©§(gCþx)½)¯K`5§ öo'N´¦)ù¦´©½)¯K)¼ê§7Lü§âU©¯K)C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringÚóLaplaceC^u¦)¹m ©§½)¯KC §gCþê'5~~X§5´xÚtügCþ ©§½)¯K§C ÒI¦)~©§(gCþx)½)¯K`5§ öo'N´¦)ù¦´©½)¯K)¼ê§7Lü§âU©¯K)C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteStringùÇ:1LaplaceCA^Ã.\9D¯KÃ.uÅįK2FourierCA^ÄnÃ.\9D¯KÃ.uÅįK3٧ȩCHankelCMellinCC.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^¢Sþ§Ã.«m§´ÔnþÄÏd§XJ/ѽ)¯K{§KAk.^ux→±∞→0C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^¢Sþ§Ã.«m§´ÔnþÄÏd§XJ/ѽ)¯K{§KAk.^ux→±∞→0C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^¢Sþ§Ã.«m§´ÔnþÄÏd§XJ/ѽ)¯K{§KAk.^ux→±∞→0C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞`²3ù«Ã.«m½)¯K¥§¿Ø²(Ñ.^¢Sþ§Ã.«m§´ÔnþÄÏd§XJ/ѽ)¯K{§KAk.^ux→±∞→0C.S.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞)LaplaceC-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.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞)LaplaceC-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.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞)LaplaceC-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.Wu1oùÈ©CApplicationofLaplaceTransformApplicationofFourierTransformOtherIntegralTransformsHeatConductionwithinInfiniteRodWavePropagationwithinanInfiniteString~14.1¦)Ã.\9D¯K∂u∂t−κ∂2u∂x2=f(x,t)−∞x∞t0ut=0=0−∞x∞)2?Ú-f(x,t);F(x,p)½)¯KÒC¤pU(x,p)−κd2U(x,p)dx2=F(x,p)3Ux→±∞→0^e=)(Ö§~10.8)U(x,p)=121√κpZ∞−∞F(x0,p)exp−rpκ|x−x0|dx0C.S.