数学物理方法部分作业答案_姚端正_梁家宝_编著.pdf

Please visit for more information 大学数学吧 百度 6 2 1 1 21 2 tantan ttt x dxxttt x dxx ttt xxttt TTBudxCu dxdxu T uuBudxCu dxdxu uuTBC uuu dx a ubucuu 2 2 2 x dxxtt x dxx tt xxtt EuEuFdxdxu uuEF u dx a ufu 3 3 t x dxxt t x dxx t t xxt kuAdxkuAdxHeAdxc Adx u uukH eu cdxc Duheu 6 6 21 2 22 2 2 tantan 1 2 1 2 tt x dxxtt l x xtt T xdxT xdxu T xdx uT x udxu T xx dxlx lxuu x Please visit for more information 大学数学吧 百度 7 7 2 21 2 2 tantan tt x dxxtt l x xtt T xdxT xdxudx u T xdx uT x udxudxu T xgdxg lx g lx uuu x 9 9 xt xt xxtxxttt xxtxxttt dI V xdxV xLdx VLI dt dVICV I xdxI xCdx dt VLILILCV ICVCVCLI 7 1 1 u x t 1 2 1 2 1 0 1 u x t 1 2 0 0 1 2 1 2 2 sinx 2 u x t 1 2 sin sin 1 2 2 1 2 3 3 3 3 u x t 1 2 3 3 1 2 1 2 3 3 1 2 2 2 4 1 u x t 1 2 cos x at 1 2 1 cosxcosat 1 2 Please visit for more information 大学数学吧 百度 3 3 11 22 11 22 x at x at u x txatxat a xatxatxa a txat xt d a 4 4 2 1 0 1 0 sin 111 cos cos sin 22 11 cos cos cos cos 22 cos ttxx x t x at x at Va V V xAcoskxa CL I V xAkkx CCL V x tAk xatAk xatAkkx aCL Ak xatAk xatAk xatAk xat Ak xat 2 1 0 cos 1 0 sin 111 cos cos sin 22 11 cos cos cos cos 22 cos ttxx x t x at x at Ia I C I xAkxa LCL V I xkAkx LL CC I x tAk xatAk xatAkkx LLaL CCCC Ak xatAk xatAk xatAk xat LLLL C Ak xat L Please visit for more information 大学数学吧 百度 5 5 2 23 2 22 x x xxx xx ttxx tt tt vvv uu xxx vvv u xxx va v v u x v x t 6 6 22 2 22 2 22 22 2 22 2 1 11 let 1 11 1 1 1 tt tt x x x tt x tt xx xuxu xhxaht v u hx v vhx u u vhxv hx u hx vhxvvxx xhahhx hx vhxvvx xhahhx vhx ha 22 2 tt ttxx hx v h va v Please visit for more information 大学数学吧 百度 7 7 12 230 30 3 3 then 0 xxxyyy uuu u xyxy xy xy xyxy xy xy xyxy uuff 8 8 12 230 30 3 3 then 0 xxxyyy uuu u xyxy xy xy xyxy xy xy xyxy uuff Please visit for more information 大学数学吧 百度 10 10 0 0 12 12 12 12 1 2 1 0 0 0 0 important 11 2 11 2 0 1 2 t x x x x u x tf xatfxat u xf xfxx u xafxafxx utf atfat f xxd a fxxd a when xat f xatx 0 0 0 0 2 12 1 21 1 11 2 0 11 2 11 2 x at x x at x x at x at x x atd a fxatxatd a u x tf xatfxat when xat f xatxatd a fxatf atxatxd a u 00 1111 22 x atat x xx x txatdatxd aa Please visit for more information 大学数学吧 百度 13 13 See See 7 2 1 1 0 2 0 2 0 223 0 23 1 2 11 22 1 2 2 111 223 26 tx a t x a t x a t t x a t t t u x tad d a ad a xtxa tad xtxata xtat 0 0 0 2 0 2 1 8 2 1 8 2 1 16 2 1 8 2 4 yxy xy y xy xy y y u x yd d d yd y y 2 2 0 0 00 1 sinsin 2 1 2 1 2 2 111 I tx a t II x a t t tt tt t uxatxat ue d d a ax te d a xte dxe d xt exte xextx Please visit for more information 大学数学吧 百度 8 1 1 1 2 2 0 0 0 0 0 minus cossin 0 0 sin0 sin 0 txx nn n l nn uDu utu l t let uXT TX XTDX T DTX XX XX l X xAxBx XA n X lBlnN l n XxBx l n TDT l T tC e 2 2 2 1 11 0 0 11 sin 0 0 sin 2 sin 2 sinsin Dt n Dt l nn n n nn nn l n n Dt l l n nn n ux tE ex l u x tux t n u xxuxEx l n Exxdx ll nn u x tux tu x txxdx ex lll Please visit for more information 大学数学吧 百度 2 2 0 0 0 0 0 minus cossin 0 0 sin0 cos 0 txx xx xx x x nn n uDu utu l t let uXT TX XTDX T DTX XX XXl X xAxBx XB n XlAlnN l n XxAx l n TDT l T t 2 2 0 00 0 00 00 0 cos 0 0 cos 12 cos 12 cos n Dt l n n Dt l nn n n nn nn ll n ll n n C e n ux tE ex l u x tux t n u xxuxEx l n Ex dx Exxdx lll n u x tux tx dxxxdx e lll 2 1 cos n Dt l n n x l Please visit for more information 大学数学吧 百度 2 0 0 0 0 0 minus cossin 0 0 1 2 cos0 1 2 sin txx x x x nn uDu utu l t let uXT TX XTDX T DTX XX XXl X xAxBx XA n XlBlnN l n XxBx l 2 2 2 1 2 1 2 1 11 1 2 0 1 2 sin 1 2 0 0 sin 2 n Dt l nn n Dt l nn n n nn nn n n TDT l T tC e n ux tE ex l u x tux t n u xxuxEx l Ex l 2 0 1 2 0 11 1 2 sin 11 222 sinsin l n Dt l l n nn n xdx l nn u x tux txxdx ex lll Please visit for more information 大学数学吧 百度 2 2 2 2 2 2 2 0 2 0 0 0 0 0 2 0 minus cossin 0 0 sin20 2 sin 2 0 2 ttxx t nn ua u utut u x let uXT TX XTa X T a TX XX XX X AxBx XA n X lBnN n XxBx n a TT 1 1 212 001 cossin 22 0 0 0 sincos 22 0 sin 2 2 sinsin 2 sin 2222 22 sincoscosco 222 nnn n nn n n n n n n an a T tCtDt TD nn a uExt u x tux t n u xxEx nnn Exxdxhxxdxhxxdx nnn xxxdxxx nn 122 011 s 2 22 cossin 22 22222 cossin2coscossin 22222 22222 cossin2coscos2coss 222 n n xdx nn xxx nn nnnnn Ehxxxhxhxxx nnnnn nnn hhnhn nnnnn 22 22 1 2 incossin 22 8 sin 2 8 sinsincos 222 n nn n n hn n hnnn a u x txt n Please visit for more information 大学数学吧 百度 3 3 2 2 2 2 0 0 0 minus cossin 0 0 sin0 sin 0 0 0 cossin 0 0 0 nn nnn n let uXT TX XTa X T a TX XX XX XAxBx XA XBnnN XxBnx TnaT T T tCnatDnat TD T t 1 1 1 cos sincos 0 3sinsin 3 0 1 3sin cos n nn n n n n n Cnat uEnxnat u x tu u xxEnx EEn u x txat Please visit for more information 大学数学吧 百度 2 2 2 2 0 0 0 minus cossin 0 0 1 cos0 2 1 sin 2 1 0 2 0 0 x x nn n let uXT TX XTa X T a TX XX XX XAxBx XA XBnnN XxBnx TnaT T T 0 3 0 3 0 11 cossin 22 0 0 0 1 sin 2 11 sinsin 22 1 0 sin 2 2123 1 sin 2 1 2 nn n nn nn n n n n n n tCnatDnat TC T tDnat uEnxnat u x tu u xxEnx Exnxdx n 2 22 2 22 0 2 1 2 23 1 211 sinsin 22 11 22 n n n u x tnxnat nn Please visit for more information 大学数学吧 百度 0 0 2 2 4 0 0 1 0 4 4 0 0 1 0 minus cossin 0 0 1 sin0 sin 40 txx nn n let uvN vv v xN vtvt let vXT TX XTX T TX XX XX XAxBx XA XBnnN XxBn x TnT T tC 2 2 2 4 4 1 0 1 1 0 0 0 4 0 1 0 sin 0 sin 2 2sin cos1 2 cos1 sin nt n nt nn n n n n n nt n e uEn xe v x tu v xNEn x N ENn xdxn n N v x tnn xe n u x tv x tN Please visit for more information 大学数学吧 百度 2 2 0 0 1 0 minus cossin 0 0 1 sin0 sin 0 1 0 0 0 sh 1 sinsh 1 nn nn nn nn let uXY YX XYX Y YX XX XX XAxBx XA XBnnN XxBn x YnY YY YyDny uEn xny u 1 1 1 33 0 3 3 0 1 sinsh 2 1 1 4 1 1 1 1 sh 2 1 sin2 4 1 1 sh 4 1 1 s n n n n nn nn n n n n x tux t u xx xEn xn Enx xn xdx nn nn E nn u x t n 1 sinsh 1 hn n xny n Please visit for more information 大学数学吧 百度 4 4 2 2 2 2 2 Assume we obtain cossin 000 0 0 si n nn tttxx nnnn uauc u uXT XTaXTc X T TaTX c TX XAxBx XA n X n XB lln l n c TaTTT x ee l l Please visit for more information 大学数学吧 百度 5 5 Please visit for more information 大学数学吧 百度 2 2 2 2 0 0 0 0 0 0 0 0 minus cossin 0 0 1 cos0 2 ttxx x t x ua u utu l t u x Q ux ES let uXT TX XTa X T a TX XX XX l XAxBx XA X lBlnnN l 2 1 sin 2 1 0 2 11 cossin 22 0 0 1 cos 2 11 sincos 22 11 sincos 22 nn nnn nn nn nn n XxBnx l a TnT l aa TCntDnt ll TD a TCnt l a uEnxnt ll u x tEnxn l 0 0 0 0 2 2 11 0 cos 22 1 sin 1212122 cos 1122 22 12 1 2 2 n xn n l n l n n n a t l Q uxnEnx ESll nx lQQQ nEnxdx llESllESlES nn ll Ql E ES n uu x t 2 0 2 111 sincos 22 1 2 n n Qla nxnt ESll n Please visit for more information 大学数学吧 百度 6 6 2 2 2 2 0 0 0 0 0 0 0 0 minus cossin 0 0 1 cos0 2 ttxx x t x n ua u utu l t u x ux let uXT TX XTa X T a TX XX XX l XAxBx XA X lBlnnN l X 1 sin 2 n xBnx l Please visit for more information 大学数学吧 百度 2 0 1 0 2 11 cossin 22 0 0 1 cos 2 11 sincos 22 11 sincos 22 1 0 nnn nn nn nn n n x a TnT l aa TCntDnt ll TD a TCnt l a uEnxnt ll a u x tEnxnt ll uxn 0 0 0 2 2 2 2 1 cos 22 1 sin 1212122 cos 1122 22 1 2 1 2 11 2 sin 2 1 2 n n l n l n n n n Enx ll nx l nEnxdx lllll nn ll El n uu x tln n 0 1 cos 2 n a xnt ll Please visit for more information 大学数学吧 百度 7 7 2 2 2 2 2 22222 0 0 1 0 sin 0 0 1 0 sin 0 0 1 0 sin 0 nn mm pp let uXYZT XYZTaX YZTXY ZTXYZ T TXYZ a TXYZ XXXXXAn xn YYYYYBm ym ZZZZZCp zp TanmpT 222222 222 222 222 1 cossin 0 0 0 cos sinsinsincos sinsinsincos 0 si nmpnmpnmp nmp nmpnmp nnmp nmp nmp TtDnmpatEnmpat TE TtDnmpat ux y z tFn xm yp znmpat u x y z tFn xm yp znmpat u x y z 1 111 nsinsinsinsinsin 1 0 111 sinsinsincos 3 nmp n nmp xyzFn xm yp z FFnmp u x y z txyzat Please visit for more information 大学数学吧 百度 8 8 0 0 0 0 0 0 0 0 0 0 0 let 0 0 0 minus cossin 0 0 co txxtxx xx uDuvDv utuvt let uvu v l tu l t v xuu x v XT TX XTDX T DTX XX XX l X xAxBx XA X lB 2 2 2 2 1 2 1 2 1 2 1 s0 2 1 sin 2 1 0 2 1 sin 2 1 sin 2 nn a nDt l nn a nDt l nn n n lnnN l XBnx l a TnDT l T tC e vEnxe l v x tEnxe l 2 2 0 0 0 0 0 0 1 2 0 0 0 1 0 sin 2 221 sin 12 2 21 sin 12 2 a Dt l n n n l n a nDt l n v xuEnx l u Eunxdx ll nl u v x tnxe l nl u x tv x tu Please visit for more information 大学数学吧 百度 9 9 4 2 2 4 4444 4 4 2 2 0 0 0 0 0 0 cossinsinhcosh sin0 sin 0 nn n let uXT TX XTa XT a TX XX XX X lXl XAxBxCxDx n X lBlnN l n XxBx l n TaT l T t 22 22 22 1 0 1 cossin cossinsin cossinsin 2 0 sin sin nn nnn nn n l nn n t nn EatFat ll nnn uEatFatx lll nnn u x tEatFatx lll nn u xxEx Exxdx lll u 22 0 1 22 0 2 0 1 2 0 sin sin 2 sin 2 sincossinsin l nn n l l n nnnn xxFax Faxxdx lllll n xxdx nnnn ll u x txxdxatatx lllll n a l Please visit for more information 大学数学吧 百度 11 11 22 2 2 2 22 222 22 22 2 2 2 22 cossin 0 0 2 0 2 8 sin 2 1 0sinsin 2 1 0 1 n n n E t i nn E t i nn n n i tx XT i XTX T TX iE TX EE XAxaBxa XaA En X aanE a TC e n D exa a n xDxaxa aaa DD a x te a 2 sin E t i xa a 8 2 3 3 1 Please visit for more information 大学数学吧 百度 2 2 2 2 1 2 11 2 0 0 0 sin 0 sin sinsin si ttxx nn ntxx n nn nn nn ua u let uXT TX XTa X T a TX XX n XXxBxnN l X l n u x tTxua uAx l nn an TxTxAx lll n a TT l 1 2 0 2 2 2 n 22 sin1 2 1 cossin 2 1 0 0 0 0 2 1 cos1 2 1 n l n nn n nnn n nn nn n n n n xAx l n anAl TTAxxdx llln Al n an a n TCtDt ll n a l Al n TC n a l n a TD l Al n a n Tt l n a l Al n u x t 2 1 cos1sin n n n an tx ll n a l 2 Please visit for more information 大学数学吧 百度 2 2 2 2 2 0 0 0 0 sin 0 0 1 0 2 1 sin 2 1 sinsin 2 1 sin 2 txx nn ntxx n n n ua u let uXT TX XTa X T a TX XX XBx XX l X lnnN l XBnx l uTnxua uAt l Tnx l 2 0 2 0 2 0 11 sinsin 22 11 sinsin 22 122 sin sin 12 2 Asume cossin n n nn n l nn nnn a TnnxAt ll a TTnnxAt ll aAt TTnAtdx ll n TXtYt 2 2 4 2 2 12 sin sincoscossin 12 2 2 1 2 1 1 0 2 2 12 2 12 1 2 nnnn n nn nn n aAt XtYtnXtYt l n A n X a a YnX n l l aA A nYX l n n Y 2 2 4 2 2 1 2 44 22 1 2 2 1 2 221 112 22 cos 11 22 a nt l nn a n l a n l AAa n l nn T tD et aa nn ll 2 44 22 1 2 4 2 sin 22 11 22 0 0 11 22 221 112 22 1 cos 1 2 nn a nt l n t AA nn TDD aa nn ll AA n nn T tet a n l 2 2 4 2 21 2 4 2 4 2 sin 1 2 211 1cossin 12 1 2 2 21 1 1 2 2 a nt l a l t a n l Aa etnt l a n n l A u x t a n n l 2 21 2 0 11 1cossinsin 22 a nt l n a etntnx ll Please visit for more information 大学数学吧 百度 8 5 1 1 2 22 2 2 2 2 2 0 0 0 cossin 1 0 cossin cossin nnn nn nnn nn nnnn n n nn n let uR ddRR d dd d n AnBnd RCDddRn R d u RAnBnCD whena uAnBn u a 0 1 0 0 1 coscossin 0 cos cossin coscossin 0 cos n nn n n n nn n n nn n n AAnBna AaA B A u a whena uAnBn u aAAnBna A A B a Aa u Please visit for more information 大学数学吧 百度 2 2 2 0 0 0 0 cos cos0 cos cos cos 2 cos 2 nn n nn n n n n n n n n B n B n B RC n uC n u aC af n C afd u 0 coscos n n n ann fd 3 3 2 2 0 2 0 2 0 2 22 0 cossin cossin 0 n n n nn n n nn n n let uv v v aa RC vAnBn v aaAnBna AaB va ua Please visit for more information 大学数学吧 百度 4 4 0 0 0 10 1 01 12 011 21 0 cossin lim coscossin 0 cos cos0 cos nn nnnn n n nn r n nn u rAnBnC rD r uE rAnBnr AEAB u rErDr u aEaDaDa u rEra r 5 5 0 111 0 1 11 1 1 1 22 11 11 1 12 2 1 1 2 21 21 2 1 2 2 cossin cossin sin 0 sin sinsin sin 0 nn nnnn n nn nnnn n n u rAnBnC rD r u rAnBnC rD r A u rC rDrthis r C u rC rDr rr rr u rC rDr D rr 2 1 2 121 11 21 2 222222 122112 sinsin rrrr u rrrrr r rrrrrr Please visit for more information 大学数学吧 百度 6 6 0 0 22 12 00