• 2022-07-26
    求所给微分方程初值问题在指定区间上的近似解(计算到三位小数):[tex=4.929x1.571]/XRz+DqgRcOprHi3GjhTpyxgV87r8YyX+2vVlvUBNTE=[/tex],[tex=5.357x1.357]GD62fUMGXAiRkEnEziGW1S2Xs91QttA3/S/bgqtBUf0=[/tex];按[tex=3.143x1.0]+MV2oelKjQjW1gi2HJe2gg==[/tex] 在[tex=3.571x1.357]ZnulbN4u/yBcahEJCwEKCw==[/tex]上求近似解。
  • [b]解[/b]     计算数据与公式为:[tex=3.0x1.214]nfo0TtDiwot/UYs0epyJlQ==[/tex],[tex=4.429x1.214]d6fqFWc7YHInK0TVOBJD8OkhecnBgGLsI5YJmS+dWSA=[/tex],[tex=4.143x1.0]aTUXmNNOIvY3rGafGSARPA==[/tex],[tex=5.786x1.214]R3epBTz5sIiY2Gx2YFCMuK1aK/tJgrT7uMjnyhZ0Iao=[/tex], [tex=9.5x1.286]mzDcxmcX60DK5hqz1uHfe2s+eorY12UXi7R9+g6EpMa9JPJEixCAuMawE+Mvc0zR[/tex][tex=6.5x1.286]B7QFWKNCfE/FAHJICrKXkMr6PcxvSW83afPS7DSgDnKl/DNguNqwbkcAuj6hMIdz[/tex] .列表计算如下:[img=405x154]177230bb5f38b8f.png[/img]其中[tex=2.0x1.0]CEUpxzXMsNTzJgpD5c1lkQ==[/tex]两列是近似解的函数表。

    举一反三

    内容

    • 0

      利用微分,求下列近似值:(1)[tex=2.571x2.0]1gkPHMmDFl17xiZlURulcg==[/tex](2)[tex=2.429x1.429]USggBAjFomMY4e0NLutPiA==[/tex](3)[tex=2.143x1.214]042jw9WE645b3wxL0waCXw==[/tex](4)[tex=2.786x1.0]zIDxscziz4XQWvCmOgHhvQ==[/tex]

    • 1

      求下列函数的导函数:(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]

    • 2

      比较求[tex=7.143x1.286]MhzkFqxktyJdcqaQ8GqG+X54rtFJ4SRaN9b1lx8TAu0=[/tex]的根到三位小数所需的计算量:(1)在区间[tex=1.929x1.286]5WiKxiqIs2aMQ1aNQurkGw==[/tex]内用二分法;(2)用迭代法[tex=6.571x2.0]2f0fZcitv6XcvzH28Y2+VAayndeevS2dJr1StXZHw+nDHIKJOSJxhwTSJTJ/m67U[/tex],取初值[tex=2.786x1.286]LRJDQR+Dj4Mau2RMgM4FUg==[/tex]。

    • 3

      设矩阵[p=align:center][tex=22.143x3.643]+HNIZcMaSzNwCe0LO7bsUq/nNqiD9uPVTX2/0HTi4M1ZunAEz7qfA0Rd4ovBDZfbF0GGptIGukHKOpbU4T80nTzErVwKYTs47PXy7I1XE++qtUmsh208vGDr7MXpYVMuue4tfvhHRJLpbtyk1c9gflSH5Tkz0UMsPjui7wPzKBU08/vB+N4sKYnD/Q0clHeQK7pT2y7o9KK3BmOLD7xVrZgRj2iFXMh2GeWPZ6MQh2cc/+VI9kCbffCxY/5NFhhEg5peWRqbWgbcZiOGAvr4nJHWN3qjueDxOqTvbDaTM3I=[/tex](1) 求 [tex=3.357x1.214]03ql8P+0CvRd0jLgTuf2VbT/wkB2igrddY7J5Strl0NU0hh6vIeN8jScC63B9GnL[/tex](2) 解矩阵方程 [tex=5.0x1.214]zvhQGTB3bj6p1+G/NgyQR3d8RUTq+KWJyJoscsNb5yO4fheydfGUyOSeXl9e1m/p[/tex] 求 [tex=1.286x1.214]J9ANNFCyxpObx83w0Vdt38yleCTlTu8vvnAXkiBZ7K0=[/tex](3)解矩阵方程 [tex=11.786x1.357]hbnRNbrpLcfkctuGfn+sleqQROrTrwqqWds6OPLk7Wdn4vtQb1+Muj1i2/7A1FkoB4neXMMMBk0saIAf9uWaRm+qUEsJaMS5QeVJeBYZxhkTnaWiAitNyge3msYgxeJV[/tex] 求 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex].

    • 4

      求初值问题[tex=6.857x4.214]7EJHVCtO2IWq3KpdB+jQsn3y6ZMwO3fGndEVwnd2fzkT1kybglXawWTOSbgnWC1cxVHtSLIaUVZrABJsXSA/cqs3qlTtljO6zFByOgfPeEwaOzg5Kp8cY2z68ZMvtkGU[/tex],[tex=8.357x1.357]cFqNBYljekuif9uTbfDV0sk2Dl9jSw/9BwPYyjwly6g=[/tex]的解的存在区间.并求第二次近似解,给出在解的存在区间的误差估计.