《含参变量广义积分》PPT课件.ppt

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1、本节研究形如的含参变量广义积分的连续性、可微性与可积性，以及与之相关的特殊函数。下面主要对无穷限积分讨论，无界函数的情况可类似处理。11－3含参变量的广义积分含参量广义积分与函数项级数在所研究问题与论证方法上极为相似，学习时应注意比较。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NE

2、T3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.定义：设无穷积分Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.关于不一定收敛的充分条件：命题设含参变量的无穷积分在上点点收敛，若存在常数，不论多大，总存在及，使则无穷积分在上不一致收敛.命题的极限形式：在不一致收敛.Evaluationonly.Created

3、withAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.一致收敛的柯西收敛准则:定理1：利用柯西收敛准则证明下列M判别法:Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.例1积分在内一致收敛.解因为而积分收敛，所以在内一致收敛.Evaluationonly.Created

4、withAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.例2考虑积分证明证存在.又这时Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0

5、.Copyright2004-2011AsposePtyLtd.定理2（狄利克雷判别法）Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.定理3（阿贝耳判别法）Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.一致收敛积分具

6、有如下性质：定理4：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.定理5：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.3.一、考虑含参数无穷限积分特点:1)积分区间为无穷，是一个无穷积分；称此类积分为无穷瑕积分.将

7、它分为两项：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.同收敛.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.称为函数，记作Evaluationonly.CreatedwithAspose.Slidesfor.NE

8、T3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePt