常微分方程教案(王高雄)第三章.pdf

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1、目录第三章一阶微分方程的解的存在定理.........................................................................................I内容提要及其它.......................................................................................................................13.1解的存在唯一性定理与逐步逼近法........................

2、........................................................33.1.1存在唯一性定理.....................................................................................................33.1.1.1特殊情况...............................................................................................

3、.......31、等价积分方程.............................................................................................42、逐步逼近法.................................................................................................43、引理..........................................................

4、...................................................43.1.1.2一般情况......................................................................................................83.1.2近似计算和误差估计.............................................................................................93.2

5、解的延拓..........................................................................................................................113.2.1局部的利普希茨条件...........................................................................................113.2.2解的延拓.................................

6、..............................................................................113.2.3饱和解...................................................................................................................123.2.4解的延拓定理.............................................................

7、..........................................133.2.5解延拓定理的应用...............................................................................................133.3解对初值的连续性和可微性定理..................................................................................153.3.1引言...............

8、.............................................................