• 2022-06-19
     求泊松方程在矩形区域[tex=8.857x1.214]mR9aUUaAbYM2D78bFcQ2tQ==[/tex] 内的狄氏问题的格林函数.[p=align:center]
  • 解:其格林函数的定解问题为[tex=20.357x3.357]GE56u9QCDTqcLxZ66HADymkyxqBirFocvvKRM0qmMN8PDa8sXBNtX3HsKde8wJ8Qr/Y34nwDbOxb9zcDzeHRaR7K/Sk4oLX/UmPRG+YN2HDXmX+S95Chs7TA0d9uPpPNDnvhDkf8jD5ZWrPc7sEchJPpcv2Uc3r1k7Lc3spiFmrQQNCN64E9wsfvnhNUFLf2dc6JskpU9SqNeJpWC6+5VURuNFlFLWU1BaH225M8il1VC3waAEj1I8lbCMDclZbIbkCmNK2u1mG+EBjs7CWaaAIbGQFNYQYgwreiaednyfVtxMEejzP/WBhO/10vzR72kxFBHhgQlwGganmLiD/LkQ==[/tex]它是定解问题[tex=23.929x3.357]GE56u9QCDTqcLxZ66HADymkyxqBirFocvvKRM0qmMN8PDa8sXBNtX3HsKde8wJ8QJ5eENqtCu20ZGsPJOoJ4s7fStMqN1srouozYqnIEpeWzXG7XtX2rkBE1occt+Hs96XRuKYWTJB7k9LCla9Sd+T3sh6+Z5M4VIu4v00N5SsT5F6Q05IdFMA1F/elRlqinGupi1dgH2E5ZnGYeBGrtkuVitFJLQYAJh/kD9NG3VP4FLZo1b0Hbasf+GngGnStrcYvOvLuO/AoNegOBzljFR5KzREukNGYs80DyNQyXMsrVKGsDqXybMyxpHyUSKTjlnt+1dJru/n5BSUgqlUayKA==[/tex]       (3)当 [tex=2.429x1.0]tv0/A0DlvArlnDLq6FCi6g==[/tex]时的特例,而与定解问题(3)相应的本征值问题为[tex=15.357x3.357]GE56u9QCDTqcLxZ66HADymkyxqBirFocvvKRM0qmMN83AOWMzYWgaK3RIkorgTU4ouq2ouounvMC3yVLXopO82ZVRqSQzWWiHWF1iq/G9UGTQsl+NZWwecY4RM4t/17nN7GR9SvbgWV4i02DsXUI74gzNIuNS+61jV9fRzf4R4itJfyA8Wfn3P3d91Mo4cV5MAS6frftBu1eJtIaJtmxeAHVR6GNxcQP+GphXhKk7d7PzcKi15mpmbivyNJqS5OWNMyVuw1oxMzO+SgKHOFziZVMFvW6xbbCiH1hnP5rqz0=[/tex]它的本征值和片一化的本征函数分别是[tex=21.0x5.786]rZM5/OPAdr7aX+kNl9iwpEGPEAAVxCscgAoGGb9nLckyC+DsaPL8mXg9ASBUV2Luxek08pHrnub5FTmQLpossmdq3az4tVQXaC1mqYFJ9QrkTJTzmn0z448aS2wJHxZejxwMV5C+j1Ii6GpM9es4j/0dnNa+JdcJ8SfOcl0r4SH1VSK1wB9uFnzY1fswKbQa3pqRf4k2b3ZTxixkX6oKKT81N25s38a25bToutZsznrtt3QXhxK+5whImep1877hvPMHxE6fO2IlkSfNsToP3fX4FK6ygKANE0CoXBcJLaDzK9g2FOsjoQpK447FhO6l[/tex]其中[tex=8.857x2.143]iu7iqIL/Q+NdSjSZpwzHiFi9Eyjww7E5CxBUbT15zv4IayKjJctyORzT/BVp3qTwmLnVburR1lUNZmWnffITiQ==[/tex]在式(1)中[tex=5.143x1.214]bKpsY4/EF0M81KO/mygf+hi1kviviBRi0HzcmNiMUZ4=[/tex] 故 有[tex=22.857x3.429]//1ElSBxfK5GYN6GQdJg8B1pP4OWJs4LRy2XY1vkdKl2n0DOO212xHwify6Jyi2/yM3V5eBGSeNkvbPAwMHQv8RXMeOBUnCzsZEMM4xOHrO93NJ362ElTU3nZih6boyK+5x9RtkPxNkgSIrmjCL3dO+SAgG/JXZJlkDYUjaStR5sSuef+O1YkqVhSszNbiXoGkvJ2k5LgziaT+WEJXl9Cw31mayHxmnTIDqO9fp/Eog=[/tex]

    内容

    • 0

      求下列函数的拉氏逆变换.[p=align:center][tex=6.786x2.214]grkVa3S0YYflbCEUGFMx3wDqPKXl3n+tH7ZdpTo3VO4=[/tex]

    • 1

      求下列函数的拉氏逆变换.[p=align:center][tex=5.214x2.429]/7NYPJ52MLAPyRAkWElBQYBlrEA32w573V0WH40azKM=[/tex]

    • 2

      求下列函数的傅氏积分:[p=align:center][tex=12.0x3.643]G6kvWfpkGVYUDXDVCjlJ3wwebIX7aht5fS9lH+Su4souyi0bWa1B1GJ9pY8yRYfnMi5pJxHx1imNQNcu0gkZYYh+b9SkBeR+0zouG9tJRKQ=[/tex]

    • 3

      求下列函数的拉氏逆变换.[p=align:center][tex=6.857x2.714]m1TlWv5570Vmii14nY0qaCJrnYwUIwbks0rJpnpuE7U/TCbHThC2UezH6irFX49A[/tex]

    • 4

      求下列函数的拉氏逆变换.[p=align:center][tex=4.857x2.214]Ino7ZaxSbSMx0+Y39D0zvfR0ybFQi5hU0syPA/nx8AE=[/tex]