北大数学物理方法(A)-复变函数教案14Laplace变换

整理文档很辛苦,赏杯茶钱您下走!

免费阅读已结束,点击下载阅读编辑剩下 ...

阅读已结束,您可以下载文档离线阅读编辑

资源描述

Outline1›oùLaplaceC†ÔnÆ2007cSC.S.Wu1›oùLaplaceC†OutlineùLJ:1LaplaceC†½ÂLaplaceC†Ä5Ÿ2LaplaceC†‡üLaplaceC†”¼ê7‡^‡LaplaceC†‡üÊH‡üúªC.S.Wu1›oùLaplaceC†OutlineùLJ:1LaplaceC†½ÂLaplaceC†Ä5Ÿ2LaplaceC†‡üLaplaceC†”¼ê7‡^‡LaplaceC†‡üÊH‡üúªC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformReferencesÇÂÁ§5êÆÔn{6§19Ùù&œ§5êÆÔn{6§16ÙnÎ!X1Á§5êÆÔn{6§§6.1,6.2,6.3C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformLaplaceC†({¡.¼C†)´~^˜«È©C†©3êÆ!Ôn9ó§‰Æ¥k2A^!0 LaplaceC†½Â9ÙÄ5ŸC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformLaplaceC†({¡.¼C†)´~^˜«È©C†©3êÆ!Ôn9ó§‰Æ¥k2A^!0 LaplaceC†½Â9ÙÄ5ŸC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformùLJ:1LaplaceC†½ÂLaplaceC†Ä5Ÿ2LaplaceC†‡üLaplaceC†”¼ê7‡^‡LaplaceC†‡üÊH‡üúªC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dtùpt´¢ê§p´Eê§p=s+iσF(p)¡f(t)Laplace†ª§{¡.¼†ªe−pt´LaplaceC†ØC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dtùpt´¢ê§p´Eê§p=s+iσF(p)¡f(t)Laplace†ª§{¡.¼†ªe−pt´LaplaceC†ØC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dtùpt´¢ê§p´Eê§p=s+iσF(p)¡f(t)Laplace†ª§{¡.¼†ªe−pt´LaplaceC†ØC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dtùpt´¢ê§p´Eê§p=s+iσF(p)¡f(t)Laplace†ª§{¡.¼†ªe−pt´LaplaceC†ØC.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dt¶¡µf(t)LaplaceC†¼êF(p)LaplaceC†”¼ê{PÒF(p)=L{f(t)}½F(p):f(t)f(t)=L−1{F(p)}½f(t);F(p)C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dt¶¡µf(t)LaplaceC†¼êF(p)LaplaceC†”¼ê{PÒF(p)=L{f(t)}½F(p):f(t)f(t)=L−1{F(p)}½f(t);F(p)C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformDefinitionLaplaceC†´˜«È©C†§§rf(t)C†F(p)F(p)=Z∞0e−ptf(t)dt¶¡µf(t)LaplaceC†¼êF(p)LaplaceC†”¼ê{PÒF(p)=L{f(t)}½F(p):f(t)f(t)=L−1{F(p)}½f(t);F(p)C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform~14.1¼êf(t)=1Laplace†ª1;Z∞0e−ptdt=−1pe−pt ∞0=1pRep0ùp›^‡Rep0´yÈ©Âñ§½ö`§´LaplaceC†3^‡C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform~14.1¼êf(t)=1Laplace†ª1;Z∞0e−ptdt=−1pe−pt ∞0=1pRep0ùp›^‡Rep0´yÈ©Âñ§½ö`§´LaplaceC†3^‡C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform~14.2¼êf(t)=eαtLaplace†ªeαt;Z∞0e−pt·eαtdt=−1pe−(p−α)t ∞0=1p−αRepReαùp›^‡RepReαÓ´yÈ©Âñ§=LaplaceC†3C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform~14.2¼êf(t)=eαtLaplace†ªeαt;Z∞0e−pt·eαtdt=−1pe−(p−α)t ∞0=1p−αRepReαùp›^‡RepReαÓ´yÈ©Âñ§=LaplaceC†3C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform?Øl~14.1Ú~14.2Œ±wѧduLaplaceC†Ø´e−pt§¤±éuƒ2¼êf(t)§Ù.¼†ªÑ3$–t→∞,f(t)→∞ž§f(t).¼†ªŒU3LaplaceC†3^‡Ò´È©Z∞0e−ptf(t)dtÂñ^‡C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform?Øl~14.1Ú~14.2Œ±wѧduLaplaceC†Ø´e−pt§¤±éuƒ2¼êf(t)§Ù.¼†ªÑ3$–t→∞,f(t)→∞ž§f(t).¼†ªŒU3LaplaceC†3^‡Ò´È©Z∞0e−ptf(t)dtÂñ^‡C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform?Øl~14.1Ú~14.2Œ±wѧduLaplaceC†Ø´e−pt§¤±éuƒ2¼êf(t)§Ù.¼†ªÑ3$–t→∞,f(t)→∞ž§f(t).¼†ªŒU3LaplaceC†3^‡Ò´È©Z∞0e−ptf(t)dtÂñ^‡C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransform?Øl~14.1Ú~14.2Œ±wѧduLaplaceC†Ø´e−pt§¤±éuƒ2¼êf(t)§Ù.¼†ªÑ3$–t→∞,f(t)→∞ž§f(t).¼†ªŒU3LaplaceC†3^‡Ò´È©Z∞0e−ptf(t)dtÂñ^‡C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformLaplaceC†3¿©^‡3ýŒõê¢S¯K¥§f(t)ÑU÷v1f(t)3«m0≤t∞¥Ø1˜amä: Ñ´ëY§…këYê§3?Ûk«m¥ù«mä:ê8´k2f(t)kkOê§=3êM09s0≥0§¦éu?ÛtŠ(¢Sþ§‡éuvŒtŠ)§|f(t)|Mes0tXJs03{§§˜½¿Ø˜§Ï's0Œ?ÛêÎ܇¦s0e(.¡ÂñîI§Ps0C.S.Wu1›oùLaplaceC†LaplaceTransformInverseLaplaceTransformDefinitionofLaplaceTransformPropertiesofLaplaceTransformLaplaceC†3¿©^‡3ýŒõê¢S¯K¥§f(t)ÑU÷v1f(t)3«m0≤t∞¥Ø1˜amä: Ñ´ëY§…këYê§3?Ûk«m¥ù«mä:ê8´k2f(t)kkOê§=3êM09s0≥0§¦éu?ÛtŠ(

1 / 117
下载文档,编辑使用

©2015-2020 m.777doc.com 三七文档.

备案号:鲁ICP备2024069028号-1 客服联系 QQ:2149211541

×
保存成功