在半平面[tex=2.357x1.214]lIwqpLgUWMISXegKMxjITA==[/tex]内求解拉普拉斯方程的第一边值问题[tex=12.571x1.5]sZXbmOIo1anR9COwJKuoOyNp1hu4jgnnBMd6jr4j+oxPuCrOnvetsN2d3SGJid/L[/tex]

2022-06-19

在半平面[tex=2.357x1.214]lIwqpLgUWMISXegKMxjITA==[/tex]内求解拉普拉斯方程的第一边值问题[tex=12.571x1.5]sZXbmOIo1anR9COwJKuoOyNp1hu4jgnnBMd6jr4j+oxPuCrOnvetsN2d3SGJid/L[/tex]

答案：

解：由平面第一边值问题的格林函数满足[tex=17.214x3.357]fnpmC2J6JmQBLyo5NmGAzxCZJVX+7fLkh7381dsdXUjjmUVKECjBshr9Tw1jSXL4TfvvpF4ZyRijIyQYqQ8n3POE/sTUvEpCKSoIzuxZrawtlj3XLbqpQ+QLmTOfATwV5fE9v0uOXXg6Juk3t2l9LIUn5kMf+D3wE2fJrNY2rEX06jKq0su1ccKC0JWiqqCIzwdoQqyCVLs56Twasrxb34Li62lL6W7k5trJjdWkbiH9Mb35Yu5YHkj7S932dDCq[/tex]的解为[tex=18.929x2.786]8KB19ch3pl1b5vQW++2+WIFuoLCC4PSdumNEwXbuHtFmRL9fudPXZ1EBptxPzArXOkXb97YpH5BbzQFfs5MYka5RdbqpO27uH3bNwV7QEEQ5nGpvPubH6OX6IZ8MxXrpyZ3ROG3Xah3PwIy6eVbCGSny1dhiH20IGaLsV9O1LWs=[/tex]其中[tex=29.286x2.214]ojRw8qNtDN7d7CIkpwGDisAgSsyIyVR9RZwzVOdT+TuFrorKJnbI8t0CGiDbmkiffYvvf+adIclbTd7728+w/DaPdarkMcjEoHK7ORqv6t+KMG4uDn/TzwLtpakaxrahcMkUj3N9f0gvdsjarFnPrnrvcheXSOD2CvXT4JeswHTAVVrh39Z/rvfnqlBgGS/NXBvQR6/plQ4kcugUonCEXLNZrGQkCVjlBnBAgJHQYk2ci3mBagLTsYmn9ZNW8CeMN4joLZrUx6NpjrtZ0bOU8cq85zbDyfvwT8pOoeIIEyo=[/tex][tex=33.571x6.071]Ck4j1YFlvVH5wCAykOEMixZQAoSw8zga3CMoRd/IIVbFs0wZnpJ7FLBkS+zoyjkA+7AN9xUGyFqFXLEPOu+v4hft27TsRagk0X38VFEeqNnTOCeB+GmqGpU1GFgC4z9Fv58vTzBiv/JC53G7T4eMCbrAjzwlcME7MoCo934s0K3CXZ9F0w/oPlUgiyClf9M9ByDqB34orASCKMABeDOBkiBTQZrRKqAJIxnZrgKs70hJ8rJl+dt3xZSeI+iztGbmNCHkZXOTL82WxorMR65bTrB+98jQl+tiHUzzcNDbuHFIQq+8jZXCA47Kk9Vswm05VzuyIsQrbNnYi/xz6RCCRT0xp6ZQJfY4zIcVAI/kCkGtarLjvtfSRecPsN2FJJIJ5Z5kANaPTv7K7zDqsAWqEd8sMqJAtw+uOIoG+D1AOlMjNJMv9Thnqz2FyJzfkyNDNvn/D1nlPxngGJXrOdlDya+SdaJIaBRSI15LgTvwu+I=[/tex]代人积分公式可得[br][/br][tex=16.286x2.857]1UMCqUmoaCR9IhjwYbl5hfH1C9PkOK517mqnUw+9yRVaH6vXPw5ifEBMUtvS13GbgPHXo8iycpN5db7AELDngLNanCAhhpjk8xHjroseCprhlA7kvr/l0qYjmpIj1U2I6ZBobgujQpKnoqYe6E4H8RBZfc2qTNCQU17oEIxwmLRsevIT95G39YTf6G9Y3wuY[/tex]

举一反三

内容

0
已知[tex=10.786x1.357]oPxEQGciaJq0uWonaJqXssvTKx2aAMqoshLd51U2O4M=[/tex]，若[tex=2.0x1.214]IENxQEh5u4RdnCaqHm72Xg==[/tex]相互独立，则[tex=3.0x1.357]cl60lRnHnAb2Fyha9FYNvw==[/tex] A: 1/2 B: 1/3 C: 2/3 D: 3/4
1
[tex=2.214x1.0]Z8GWW72u+MH/mjafnp+83A==[/tex]丙酮酸经过丙酮酸脱氢酶系和柠檬酸循环产生[tex=4.0x1.214]EPDWVFNjIR8daNoozaWRDg==[/tex],生成的[tex=3.214x1.0]1AqDCKqjaAug6buHS5Z0tQ==[/tex]、[tex=3.429x1.214]HYAn2+I9AZQLWcA3ajoPaw==[/tex]和[tex=2.143x1.0]qQANfGnLx7pE5mcaEibuNg==[/tex](或[tex=2.071x1.0]YGdeb/NAM7yg+XY6SY16Fg==[/tex])的摩尔比是( )。未知类型：{'options': ['3:2:0', '4:2:1', '4:1:1', '3:1:1', '2: 2:2'], 'type': 102}
2
9判别下列函数是否是周期函数,若是周期函数,求其周期 :(1) [tex=8.357x1.357]jijpvC8Aw74QOOOJh5Va05j3PtA64Pms1Q5qDGlqeN4=[/tex](2) [tex=5.643x1.357]TG5DUF3HrCbhIJWDEcp5Pj9u3e2PUgpbN4NJQ6DZXLw=[/tex](3) [tex=5.714x1.357]SBxtvKszj8+jJcycMEKn5vqfhi5GLWqH4Gac9QRbIHc=[/tex](4) [tex=6.929x1.357]NZ5EVFRfE4pFsgkbEOhFkNg5/qZx8geAT5eL+yzbq1Q=[/tex]
3
在矩形区域[tex=8.857x1.214]8uiQoSOJkMmOQsq0h09plA==[/tex]上求解拉普拉斯方程[tex=2.714x1.0]XZxNuDBDKDChdvMyVUROEg==[/tex]，使满足如下边界条件，其中A，B为常数[tex=6.857x1.357]WfzXYNdOb3O1ndzxlvYEHnMpo5FsSbgx3aFZTr7uEps=[/tex]在矩形区域[tex=8.857x1.214]8uiQoSOJkMmOQsq0h09plA==[/tex]上求解拉普拉斯方程[tex=2.714x1.0]XZxNuDBDKDChdvMyVUROEg==[/tex]，使满足如下边界条件，其中A，B为常数[tex=3.643x1.357]WfzXYNdOb3O1ndzxlvYEHsKiAdLL4XLKHB0nve3QZbY=[/tex]在矩形区域[tex=8.857x1.214]8uiQoSOJkMmOQsq0h09plA==[/tex]上求解拉普拉斯方程[tex=2.714x1.0]XZxNuDBDKDChdvMyVUROEg==[/tex]，使满足如下边界条件，其中A，B为常数[tex=6.786x2.143]WfzXYNdOb3O1ndzxlvYEHiABdUA3ykZtcmOVGU4uAjeseETAXJruXfdgrNdSjIM/[/tex][br][/br]在矩形区域[tex=8.857x1.214]8uiQoSOJkMmOQsq0h09plA==[/tex]上求解拉普拉斯方程[tex=2.714x1.0]XZxNuDBDKDChdvMyVUROEg==[/tex]，使满足如下边界条件，其中A，B为常数[tex=3.5x1.5]WfzXYNdOb3O1ndzxlvYEHsMfkLaQGw4GGtDXzCjdZk0=[/tex]
4
用拉普拉斯变换求解高阶方程 [tex=10.143x1.429]rjzw0bBUODiY66l+Mq83xBnMF36gtfOUrjWP9Dn7D5oFd9H7kzGSi9GO+66Kpz6LRfygNLRQY+Ap8H8hdlPW+zm2TDafO0olzQXlpIxrOR424HBT5iNvEXp3bcV6VHN8[/tex] [tex=9.143x1.429]HSop7NHcHBRBRymD+K4eqzoYVPGc3dRRuqWq12iZO4bgcmlHdEcChnFZjA01B7Bp[/tex]