求一个分式线性映射[tex=3.286x1.357]ySGySJBkLne3ga0KuR9uXg==[/tex], 它将圆[tex=4.143x1.357]j/i77tFicZzOI+vXwa3/BA==[/tex]映到圆[tex=5.143x1.357]bn6M3+WaSxIiB2/GnqdRgFN9XXIvaScAGiDM3HmL05c=[/tex],且满足条件[tex=9.357x1.429]7LeQc82aqJBwP0caqbuyBRBlwVRFUFTi875epBeFcYEnpVPUowfLkRSVSJrH5Z5+[/tex]

2022-05-28

求一个分式线性映射[tex=3.286x1.357]ySGySJBkLne3ga0KuR9uXg==[/tex], 它将圆[tex=4.143x1.357]j/i77tFicZzOI+vXwa3/BA==[/tex]映到圆[tex=5.143x1.357]bn6M3+WaSxIiB2/GnqdRgFN9XXIvaScAGiDM3HmL05c=[/tex],且满足条件[tex=9.357x1.429]7LeQc82aqJBwP0caqbuyBRBlwVRFUFTi875epBeFcYEnpVPUowfLkRSVSJrH5Z5+[/tex]

答案：

解 令[tex=9.929x2.357]L5nqyCf0beeDgefAcGkyHaICEt+hhZ67V0/EGFW/XjWi09xx8CQ5WA75XcQ6mC4K[/tex]因此先求函数 [tex=4.143x1.357]2KUEoXG6jLCgR7H2X/ZEzw==[/tex],它将[tex=2.857x1.357]zTrgOiehoAQAolNEleJIkA==[/tex]映到 [tex=3.5x1.357]r71P5PIuujFIbfaDQEhQVa8HQrei8Nu9k4iIzqjpF/Y=[/tex], 此外由上面条件知,还要求它将 [tex=1.786x1.214]EU5yfouSi1pnXTS24RsRzQ==[/tex]映到[tex=8.0x2.357]fF1+imfr8xpaVQQ1V77yBpucdkNre3sBGtXt31OntPBd0gmH4dFIaAtwgxRYbl8WLBljlJdhrmxBWoC2mF/JjQ0bUGGFSEd3MepzIdId9fA=[/tex]. 因此由典型映射得[tex=4.143x1.357]t8rN+aRfWC5EpF5Mendgfpv/7dWkL20VMKUUtzJAWDE=[/tex]的反函数[tex=5.286x1.5]8z57fPy0+LSUOuA3FoNWFFDN2sjIELsDRs4WATqOVok=[/tex]为[tex=7.286x2.714]bH3Yuad2Ker/U6aWsVID+EkZjMXUQp/7Udzc1RIOnPD7ffxUmBIjqzYHbcw+BbhaGK4LXXGov6IJyhfVd36lMzCMb65y8Qr0/0c/WLEtJjlxdGNFuZaEaqVCOLLhSlrW[/tex]即[tex=9.857x3.071]gVZMZ++gnLe5xe2RxUSDs15bT5xttFTl5XzorxidWnzgSBQCeKNe3KPHcYqp0f0j00MGsBHS8BH4gF57UNoQk+oQCiztGmbBKrFJ4PYJrLew725xHOYchdEPVBZ1hDtH7yHuCyY02Xj3sUk1nRAEXCYWx/aNVJfktVGMwkMN+Gc7/dayQn7Z9VGQ/Sq9vZ5iOKCeydF8GDdFuKB8WHpucw==[/tex][tex=13.571x5.786]rZM5/OPAdr7aX+kNl9iwpOjZOUW77JIo1o4RlCUCNnioZSJ44pRV8d3EBSJlfKJ6i2os6hj85d7yJ0ogTUMzlaq/bYBLUsdXwbIgwb0w/Nk6rVg1lgkLA5r7zEdLG4SkedMuPQiMkAKUynARUHs2N1eNrt/ZVOuwPz2w5i6JyTS11385OySeRt6q+JwK7KmZig3EIJeB1I6q0nZsDRuw5zATLxp7Bv0+62VdYRFY9EnRVL98OLiuiBTuNWU5F30/IOBFhmZ71UUwKNRXTf5jjA==[/tex]由条件[tex=5.5x1.429]/1HKKkd0iIGXMNSiaO8H7AemmLhkSGbMS1nDDK2qt8A=[/tex]知[tex=15.786x7.357]rZM5/OPAdr7aX+kNl9iwpIx60FQa+1YIk9mSYAYIydqk7vteEG6yDbrOvy2v+4RLyB2CpbhuLhQQZxqRjo78uM9nJ20lshBkfRAaU+8LgyQ3GOfYy+6AQg57GnLNZb5UeU2KRw/DFsdaRui965ree5Ut9WJMHIae16t3ZTYo235+BWrFA8FyjIUydaZdxOd7nKLxGW1DxvTLydBMSSlsadNyxbu8TN5zgB+3oiA8VJBLAL4O7GD6bh495ESileoNUhuBiONNcxUP4UzXYjLQVkeil5QIi/RNe16tlSrvzeZd9+MlpFRqgZ1OLsKQTlWAaV9Pw1u4XjM0rYYFpxDKxxOGrXLl9LSPcV6sihJbWhuoFQWve8zLAJZ55CsV+4THfoWJPHCBI+sa7CR8WHPz2QjY6eyVAAFJul1/S7JAMjo=[/tex]由[tex=5.357x1.429]4ViYsTmmvQy98fGdXIMWlzPOkr7jk4vv1lVy5G8K9/HMRkcP3NwO6vy7Qy6cTzdZ[/tex]推出[tex=2.357x1.0]RCOW/FnyUbo224TzMWpaSw==[/tex].由此得[tex=9.071x2.786]C3JGE2Lq4cEMOC5INYmluQvFHGAO68LRcEDGZVECQmiiQ7nBHF3Kr3ij74Cb7omddsjE7bzoJj6jN9Eip8VEpA==[/tex]因而有[tex=8.214x2.714]NktIrlSNpWpkwYnUNKj0rGTggHqpmlN6yd2IszBU/kyQyn/+D9oaVDy0mbqUfxzr[/tex]

举一反三

内容

0
求把上半平面 [tex=4.286x1.357]Hxr+WAd0pdX8wRxoSXYGR6MH5wUJTcuJa9P72mFCl6M=[/tex] 映射成单位圆[tex=3.143x1.357]Sui1bthb4ZFDHMAA/H0Myw==[/tex] 的分式线性映射 [tex=3.286x1.357]ySGySJBkLne3ga0KuR9uXg==[/tex], 并满足条件: [tex=8.214x1.429]zeL/sBcHx3LbyEw9cDbfrcXsgdPC+2SlHEc8N+brA/vRj1ZXMccbfdx1EtOTyIqK[/tex].
1
求将[tex=2.857x1.357]W2UvKR01GUJgbq0KdXYJYQ==[/tex]映射为[tex=3.143x1.357]Sui1bthb4ZFDHMAA/H0Myw==[/tex]的分式线性映射[tex=3.286x1.357]ySGySJBkLne3ga0KuR9uXg==[/tex],并满足条件:[tex=8.643x2.786]3uDDpJmj7lHTl9fkBeERIBKEIvnteFRrDW856ibKAl2POBLftQpuwQgAADc3N4ts[/tex].
2
求分式线性映射[tex=3.286x1.357]ySGySJBkLne3ga0KuR9uXg==[/tex] 它把[tex=2.857x1.357]W2UvKR01GUJgbq0KdXYJYQ==[/tex]映为 [tex=3.143x1.357]Sui1bthb4ZFDHMAA/H0Myw==[/tex]使得 [tex=10.0x1.429]bId6r0OnrpOn5gdqSDgEczAF57yjzOmzQnDWWwYp4UA=[/tex][br][/br]
3
求分式线性映射[tex=3.286x1.357]AQhvwmYnVhXPQa9e6WrGoA==[/tex],使上半平面映射为单位圆内部并满足条件[tex=7.0x1.357]C4AaF2CqxrpfMNLJcYYLVyDXZNo+dxMTE51KZ19h38A=[/tex].
4
求分式线性映射[tex=3.286x1.357]AQhvwmYnVhXPQa9e6WrGoA==[/tex],使上半平面映射为单位圆内部并满足条件[tex=8.143x1.429]UiUEh71niTJbnyfqEPJs177z+2ICPlZ4cwrXxnysM6r0KrdfyHWja8vsX+1B5CNd[/tex].