数学物理方法第九章课件2

1、蒋耿明蒋耿明 工工 程程 数数 学学Engineering Mathematics复旦大学通信科学与工程系光华楼东主楼1108室 Tel.: 65100226 E-mail: 2022-2-2222200( , )( , )( , )0,0,0( , )( ),0 xxltu x tuatxu x tu x ttxxu x txxl 2022-2-23)()(),(tTxXtxu),(),(2txuatxuxxtXTaTX 2TaTXX2 TaTXX22022-2-240)()( xXxX0)()(2tTatT0)(0)0(lXX，0( , )( )( )(0)( )tu x txX x Tx

2、2022-2-25 0)(0)0(0)()(lXXxXxX，2( )( )0()(0)()TtaT tXx Tx2022-2-26 0)(0)0(0)()(lXXxXxX，211)()(0)(CxCxXCxXxX 211)(0)(0)0(CxXClXCX2022-2-270ypyqy二阶常系数微分方程二阶常系数微分方程：特征方程特征方程：20rprq根的三种情况根的三种情况：1212rrrrrri12121212(cossin)r xr xrxrxxyC eC eyC eC xeyeCxCx常系数微分方常系数微分方程的通解程的通解：2022-2-28 0)(0)0(0)()(lXXxXxX，2

3、12rrr，xxeCeCxX21)(00)()(0)()0(212121CCeCeClXCCXll2022-2-29 0)(0)0(0)()(lXXxXxX，irirr212，0sin)(00)0(122lClXCCX，xCxCxXsincos)(21 2022-2-21022)(,0sin0lnnllCnxCxCxXsincos)(21321cos)(1，nlxnCxXn2()0 1 23()c o snnnlnnxXxl， ，2022-2-2110)()(2tTatT2)(lnn0)()()(22tTlnatT2( )0,1, 2,3,antlnnTtA en，2()0narl2022-2

4、-212tlannnnneAxlntTxXtxu2cos)()(),(201(, )cosantlnnnux tAAxel2022-2-2130( , )( )tu x tx01(, 0)cos()nnnuxAAxxl02( )coslnnAdll 001( )lAdl 201(, )cosantlnnnux tAAxel2022-2-21422200(,),(1 0 ,4 0 )(,)(,)0 ,0 ,01, 2 02 1(,)() ,0,()0 ,xxltuxtuaaltxuxtuxttxxxuxtxtlx其 它01(, 0)cos()nnnuxAAxxl022 402120( )cos(

5、sinsin)404040lnnnnAdlln 00111( )(2120)4040lAdl 14010240cos)4020sin4021(sin2401),(ntnexnnnntxu2022-2-21522200( , )( , )( , )0,0,0( , )(),0 xxltu x tuatxu x tu x ttxu x txtl 2022-2-216)()(),(tTxXtxu),(),(2txuatxuxxtXTaTX 2TaTXX2 TaTXX22022-2-2170)()( xXxX0)()(2tTatT0)(0)0(lXX，0( , )( ),( )(0)( )tu x t

6、xX x Tx2022-2-218 0)(0)0(0)()(lXXxXxX，2( )( )0()(0)()TtaT tXx Tx2022-2-219 0)(0)0(0)()(lXXxXxX，211)()(0)(CxCxXCxXxX 0)(0)(0)0(12xXClXCX2022-2-220 0)(0)0(0)()(lXXxXxX，212rrr，xxeCeCxX21)(00)()(0)0(212121CCeCeClXCCXll2022-2-221 0)(0)0(0)()(lXXxXxX，irirr212，0cos)(0)0(21lClXCXxCxCxXsincos)(21 2022-2-2221

7、2220cos01()12()2nClnlnlxCxCxXsincos)(21，210)2/1(sin)(2nlxnCxXn2022-2-2230)()(2tTatT22(1 / 2)( )( )0nTtaT tl,3 ,2, 10)(2)2/1(，neAtTtlannn2022-2-224tlannnnneAlxntTxXtxu2)2/1()2/1(sin)()(),(0)2/1(2)2/1(sin),(ntlannelxnAtxu2022-2-2250( , )( )tu x tx0(1 / 2 )(, 0)sin()nnnxuxAxl02(1 / 2)( )sinlnnAdll 2022

8、-2-2262022-2-227延拓前 yf(x)延拓后 yF(x)2022-2-2282l 10)sincos()(nnnxlnDxlnCCxf lldflC)(210llndlnflCcos)(1llndlnflDsin)(12022-2-22900),(0, 00)()(xlxgxlxxgxG，002022-2-2302l lllndlnfldlnflD0sin)(2sin)(10sinsin0lxxlxnlxn 0)()0(lff1sin)(nnxlnDxf2022-2-23100),(0)()(xlxglxxgxG，002022-2-2322l 0scosco0lxxlxnlxn 0)()0(lffldflC00)(1lndlnflC0cos)(210cos)(nnxlnCCxf2022-2-23300002022-2-2342l 1sin)(mmxLmDxflLmdlmfldLmfLD2002sin)(1sin)(22sin)(2sin)(120llldlmfdlmfl, 5 , 3