北大数学物理方法(A)-数学物理方程教案02分离变量法1

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

Outline1ù©lCþ{(˜)®ŒÆÔnÆ2007cSC.S.Wu1ù©lCþ{(˜)OutlineùLJ:1üà½ugdÄ©lCþ{¼ê5y²o(2eZ­‡µã¼ê5)˜5C.S.Wu1ù©lCþ{(˜)OutlineùLJ:1üà½ugdÄ©lCþ{¼ê5y²o(2eZ­‡µã¼ê5)˜5C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksReferencesÇÂÁ§5êÆÔn{6§§14.1ù&œ§5êÆÔn{6§§8.1nÎ!X1Á§5êÆÔn{6§§10.3C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksReferencesÇÂÁ§5êÆÔn{6§§14.1ù&œ§5êÆÔn{6§§8.1nÎ!X1Á§5êÆÔn{6§§10.3C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksReferencesÇÂÁ§5êÆÔn{6§§14.1ù&œ§5êÆÔn{6§§8.1nÎ!X1Á§5êÆÔn{6§§10.3C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚó/d ‡©§Ï)¦‡½)¯K)0§ù«{3õꜹe¿Ø¢^éu9p ‡©§½)¯K§=¦Œ±k¦Ñ ‡©§Ï)§duÏ)¥¹k–½¼ê§˜„`5§J±†Šâ½)^‡½Ñ ‡©§Ï)(§‘gCþê8O\²wE,§OŽþ:ìOŒC.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚó/d ‡©§Ï)¦‡½)¯K)0§ù«{3õꜹe¿Ø¢^éu9p ‡©§½)¯K§=¦Œ±k¦Ñ ‡©§Ï)§duÏ)¥¹k–½¼ê§˜„`5§J±†Šâ½)^‡½Ñ ‡©§Ï)(§‘gCþê8O\²wE,§OŽþ:ìOŒC.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚó/d ‡©§Ï)¦‡½)¯K)0§ù«{3õꜹe¿Ø¢^éu9p ‡©§½)¯K§=¦Œ±k¦Ñ ‡©§Ï)§duÏ)¥¹k–½¼ê§˜„`5§J±†Šâ½)^‡½Ñ ‡©§Ï)(§‘gCþê8O\²wE,§OŽþ:ìOŒC.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚók.«mþÅЧ½)¯Kº9D§Ï)ºk7‡Ïé¦) ‡©§½)¯K#{Fù«¦){·^‰Œ2©lCþ{´¦) ‡©§½)¯K~^{±/üà½ugdÄ0~C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚók.«mþÅЧ½)¯Kº9D§Ï)ºk7‡Ïé¦) ‡©§½)¯K#{Fù«¦){·^‰Œ2©lCþ{´¦) ‡©§½)¯K~^{±/üà½ugdÄ0~C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚók.«mþÅЧ½)¯Kº9D§Ï)ºk7‡Ïé¦) ‡©§½)¯K#{Fù«¦){·^‰Œ2©lCþ{´¦) ‡©§½)¯K~^{±/üà½ugdÄ0~C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚók.«mþÅЧ½)¯Kº9D§Ï)ºk7‡Ïé¦) ‡©§½)¯K#{Fù«¦){·^‰Œ2©lCþ{´¦) ‡©§½)¯K~^{±/üà½ugdÄ0~C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚók.«mþÅЧ½)¯Kº9D§Ï)ºk7‡Ïé¦) ‡©§½)¯K#{Fù«¦){·^‰Œ2©lCþ{´¦) ‡©§½)¯K~^{±/üà½ugdÄ0~C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚók.«mþÅЧ½)¯Kº9D§Ï)ºk7‡Ïé¦) ‡©§½)¯K#{Fù«¦){·^‰Œ2©lCþ{´¦) ‡©§½)¯K~^{±/üà½ugdÄ0~C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚóÆS¥A5¿¯KÏLäN¢~§Ýº©lCþ{Ä°†)KÚ½²(©lCþ{n؝â(y3´JѯK)k¿Â­‡(ØäNOŽE|C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚóÆS¥A5¿¯KÏLäN¢~§Ýº©lCþ{Ä°†)KÚ½²(©lCþ{n؝â(y3´JѯK)k¿Â­‡(ØäNOŽE|C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚóÆS¥A5¿¯KÏLäN¢~§Ýº©lCþ{Ä°†)KÚ½²(©lCþ{n؝â(y3´JѯK)k¿Â­‡(ØäNOŽE|C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksÚóÆS¥A5¿¯KÏLäN¢~§Ýº©lCþ{Ä°†)KÚ½²(©lCþ{n؝â(y3´JѯK)k¿Â­‡(ØäNOŽE|C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsüà½u(ul)gdĽ)¯K∂2u∂t2−a2∂2u∂x2=00xl,t0u x=0=0u x=l=0t≥0u t=0=φ(x)∂u∂t t=0=ψ(x)0≤x≤lC.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsüà½u(ul)gdĽ)¯K∂2u∂t2−a2∂2u∂x2=00xl,t0u x=0=0u x=l=0t≥0u t=0=φ(x)∂u∂t t=0=ψ(x)0≤x≤lC.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsùLJ:1üà½ugdÄ©lCþ{¼ê5y²o(2eZ­‡µã¼ê5)˜5C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusions½)¯Kďl!üà½ugdħ§9½)^‡∂2u∂t2−a2∂2u∂x2=00xl,t0u x=0=0u x=l=0t≥0u t=0=φ(x)∂u∂t t=0=ψ(x)0≤x≤lF¦A)äk©lCþ/ª§=u(x,t)=X(x)T(t)C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=0C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=0=⇒X(x)T00(t)=a2X00(x)T(t)C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=0=⇒X00(x)X(x)=1a2T00(t)T(t)C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=0=⇒X00(x)X(x)=1a2T00(t)T(t)=−λC.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=0=⇒X00(x)+λX(x)=0T00(t)+λa2T(t)=0C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=0=⇒X00(x)+λX(x)=0T00(t)+λa2T(t)=0u x=0=0C.S.Wu1ù©lCþ{(˜)FreeVibrationinaStringFixedatBothEndsImportantRemarksSeparationofVariablesOrthogonality:ProofSummaryConclusionsÏé©lCþ/ªu(x,t)=X(x)T(t))∂2u∂t2−a2∂2u∂x2=

1 / 158
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