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\'f7\'ed\'ee\'f1\'f2\'e8 [19]. \'ce\'f2\'ec\'e5\'f2\'e8\'ec, \'f7\'f2\'ee \'e3\'f0\'e0\'ed\'e8\'f7\'ed\'fb\'e5 
\par \'f3\'f1\'eb\'ee\'e2\'e8\'ff 1-\'e3\'ee \'f0\'ee\'e4\'e0 \'f1\'ee\'ee\'f2\'e2\'e5\'f2\'f1\'f2\'e2\'f3\'fe\'f2 \'f2\'e0\'ea \'ed\'e0\'e7\'fb\'e2\'e0\'e5\'ec\'ee\'e9 }{\cs304\b\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 \'ef\'e5\'f0\'e2
\'ee\'e9 \'ea\'f0\'e0\'e5\'e2\'ee\'e9 \'e7\'e0\'e4\'e0\'f7\'e5}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 .
\par *) \'d3\'f1\'f2\'e0\'ed\'ee\'e2\'e8\'ec \'ef\'e0\'f0\'e0\'ec\'e5\'f2\'f0\'fb \'ea\'ee\'ed\'ea\'f0\'e5\'f2\'ed\'ee\'e9 \'f0\'e5\'f8\'e0\'e5\'ec\'ee\'e9 \'e7\'e0\'e4\'e0\'f7\'e8. \'cf\'f3\'f1\'f2\'fc \'f2\'e0\'ea\'ee\'e2\'fb\'ec\'e8 \'e1\'f3\'e4\'f3\'f2:

\par }{\cs20\f2\insrsid8923009\charrsid1269225 L}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 :=1: }{\cs20\f2\insrsid8923009\charrsid1269225 a}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 :=1:}{
\b\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 
\par }{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 \'ca\'f0\'e0\'e5\'e2\'fb\'e5 \'f3\'f1\'eb\'ee\'e2\'e8\'ff \'ec\'ee\'e6\'ed\'ee \'e2\'fb\'e1\'e8\'f0\'e0\'f2\'fc \'e2 \'f0\'e5\'e6\'e8\'ec\'e5 \'f0\'e5\'e0\'eb\'fc\'ed\'ee\'e3\'ee \'e2\'f0
\'e5\'ec\'e5\'ed\'e8 \'e8 \'f0\'e0\'f1\'f1\'ec\'e0\'f2\'f0\'e8\'e2\'e0\'f2\'fc \'f0\'e5\'f8\'e5\'ed\'e8\'e5 
\par \'ef\'ee\'eb\'f3\'f7\'e5\'ed\'ed\'ee\'e9 \'f2\'e0\'ea\'e8\'ec \'ee\'e1\'f0\'e0\'e7\'ee\'ec \'e7\'e0\'e4\'e0\'f7\'e8. \'c8\'f2\'e0\'ea, \'f4\'ee\'f0\'ec\'f3\'eb\'e8\'f0\'f3\'e5\'ec \'ea\'ee\'ed\'ea\'f0\'e5\'f2\'ed\'f3\'fe \'e7\'e0\'e4\'e0\'f7\'f3.
\par \'d3\'ea\'e0\'e6\'e5\'ec \'f4\'f3\'ed\'ea\'f6\'e8\'e8, \'e7\'e0\'e4\'e0\'fe\'f9\'e8\'e5 \'ed\'e0\'f7\'e0\'eb\'fc\'ed\'fb\'e5 \'f3\'f1\'eb\'ee\'e2\'e8\'ff:
\par }{\cs20\f2\insrsid8923009\charrsid1269225 f}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 :=}{\cs20\f2\insrsid8923009\charrsid1269225 x}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 ->}{
\cs20\f2\insrsid8923009\charrsid1269225 x}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 *(}{\cs20\f2\insrsid8923009\charrsid1269225 L}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 -}{
\cs20\f2\insrsid8923009\charrsid1269225 x}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 ); }{\cs20\f2\insrsid8923009\charrsid1269225 F}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 :=}{
\cs20\f2\insrsid8923009\charrsid1269225 x}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 ->0; }{\b\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid1269225 
\par }{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 - \'f4\'f3\'ed\'ea\'f6\'e8\'e8 }{\cs310\i\insrsid8923009 phi}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs308\i\insrsid8923009 t}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ) \'e8  }{\cs311\i\insrsid8923009 psi}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs309\i\insrsid8923009 t}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ), \'e7\'e0\'e4\'e0\'fe\'f9\'e8\'e5 \'ef\'f0\'e0\'e2\'fb\'e5 \'f7\'e0\'f1\'f2\'e8 \'e3\'f0\'e0\'ed\'e8\'f7\'ed\'fb\'f5 \'f3\'f1\'eb\'ee\'e2\'e8\'e9 \'f0\'e5\'f8\'e5\'ed\'e8\'ff }{
\cs305\i\insrsid8923009 u}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs307\i\insrsid8923009 x}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs306\i\insrsid8923009 t}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ):
\par }{\cs20\f2\insrsid8923009\charrsid1269225 phi:=t->1-cos(t); psi:=t->0;  }{\b\insrsid8923009\charrsid1269225 
\par }{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 *) \'cf\'ee\'f1\'eb\'e5\'e4\'ed\'e5\'e5 \'ee\'f2\'f0\'e0\'e7\'e8\'ec \'e2 \'e2\'e8\'e4\'e5 \'f7\'e5\'f2\'fb\'f0\'e5\'f5 \'f0\'e0\'e2\'e5\'ed\'f1\'f2\'e2, \'ea\'ee\'f2\'ee\'f0\'fb\'e5 \'e7
\'e0\'ef\'e8\'f1\'e0\'ed\'fb \'ed\'e8\'e6\'e5. \'cd\'f3\'e6\'ed\'ee\'e5 \'e8\'e7 \'ed\'e8\'f5 
\par \'f1\'eb\'e5\'e4\'f3\'e5\'f2 \'ee\'f2\'ea\'f0\'fb\'f2\'fc, \'f1\'ed\'ff\'e2 \'e0\'ef\'ee\'f1\'f2\'f0\'ee\'f4\'fb.
\par }\pard \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0\pararsid1991549 {\cs20\f2\insrsid8923009\charrsid11479345 u}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 (0,}{\cs20\f2\insrsid8923009\charrsid11479345 t}{
\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 ):=}{\cs20\f2\insrsid8923009\charrsid11479345 phi}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 (}{\cs20\f2\insrsid8923009\charrsid11479345 t}{
\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 ); }{\cs20\f2\insrsid8923009\charrsid11479345 u}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 (}{\cs20\f2\insrsid8923009\charrsid11479345 L}{
\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 ,}{\cs20\f2\insrsid8923009\charrsid11479345 t}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 ):=}{\cs20\f2\insrsid8923009\charrsid11479345 psi}{
\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 (}{\cs20\f2\insrsid8923009\charrsid11479345 t}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid11479345 );}{
\cs20\b\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477                   }{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 1)
\par }\pard\plain \s366\qc \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0\pararsid1991549 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn7\insrsid9712127 {\pict{\*\picprop\shplid1026{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3687\pich496\picwgoal2090\pichgoal281\wmetafile8\bliptag-1689322489\blipupi-313{\*\blipuid 9b4efc0724c08500bc6e4ec98c91aec4}
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4e657720526f6d616e0058b1f37761b1f3772040f577300b66d9040000002d010100070000002105010074003f01ab031c000000fb025cfe0000000000009001
000000020700001253796d626f6c00009d0a0a14cc880a0058b1f37761b1f3772040f577300b66d9040000002d0102000800000021050300202d20203f01f607
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\par }{\dn7\insrsid9712127 {\pict{\*\picprop\shplid1027{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw2163\pich496\picwgoal1226\pichgoal281\wmetafile8\bliptag1962655051\blipupi-1948{\*\blipuid 74fbbd4b8aeaeece7b4c48b9808fc0d9}
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00000500000009020000ff001c000000fb025cfe0000000000009001000000000400001254696d6573204e657720526f6d616e0058b1f37761b1f3772040f577
c0096681040000002d0100000800000021050400203a3d203f01ea04070000002105010028003f013f01070000002105010029003f015c040700000021050100
75003f016a0007000000210501002c003f01d702070000002105010031003f0102021c000000fb025cfe0000000000009001010000000400001254696d657320
4e657720526f6d616e0058b1f37761b1f3772040f577c0096681040000002d010100070000002105010074003f01ab03040000002d010000070000002105010030003f012107030000000000}}{\insrsid8923009 
\par }\pard\plain \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0\pararsid1991549 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\cs20\f2\insrsid8923009\charrsid11479345 `D[1](u)(0,t):=phi(t); D[1](u)(L,t):=psi(t);`:   }{
\insrsid8923009\charrsid11479345 2)}{\b\insrsid8923009\charrsid11479345 
\par }{\cs20\f2\insrsid8923009\charrsid11479345 `D[1](u)(0,t):=phi(t); u(L,t):=psi(t);`:       }{\cs20\f2\insrsid11479345\charrsid11479345  }{\cs20\f2\insrsid8923009\charrsid11479345  }{\insrsid8923009\charrsid11479345 3)}{
\cs16\f2\cf6\insrsid8923009\charrsid11479345     }{\b\insrsid8923009\charrsid11479345 
\par }{\cs20\f2\insrsid8923009\charrsid11479345 `u(0,t):=phi(t); D[1](u)(L,t):=psi(t);`:}{\cs20\b\f2\insrsid8923009    }{\insrsid8923009                4)}{\cs16\b\f2\cf6\insrsid8923009  }{\insrsid8923009 
\par }\pard \ql \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 {\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 \'cf\'f0\'ee\'e2\'e5\'e4\'e5\'ec \'f1\'e5\'ec\'e0\'ed\'f2\'e8\'f7\'e5\'f1\'ea\'ee\'e5 \'ea\'ee\'ed\'e2
\'e5\'f0\'f2\'e8\'f0\'ee\'e2\'e0\'ed\'e8\'e5 \'ee\'ef\'e5\'f0\'e0\'f2\'ee\'f0\'e0 }{\cs312\i\insrsid8923009 D}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477  \'e2 }{\cs313\i\insrsid8923009 diff}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 :
\par }{\cs20\f2\insrsid8923009\charrsid11479345 uu(x,t): D[1](uu)(0,t): convert(%,diff);         }{\b\insrsid8923009\charrsid11479345 
\par }\pard\plain \s366\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn23\insrsid9712127 
{\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3577\pich1035\picwgoal2028\pichgoal587\wmetafile8\bliptag-979081918\blipupi-45{\*\blipuid c5a46542e31f6c4d8ff66555b8dbca27}
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\insrsid8923009 
\par }\pard\plain \ql \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 \'ce\'f2\'ec\'e5\'f2\'e8\'ec, \'f7\'f2
\'ee \'e2 \'f1\'f2\'f0\'f3\'ea\'f2\'f3\'f0\'e5 \'f0\'e5\'f8\'e5\'ed\'e8\'ff \'f4\'f3\'ed\'ea\'f6\'e8\'ff }{\cs323\i\insrsid8923009 z}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs322\i\insrsid8923009 x}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs324\i\insrsid8923009 t}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ) \'ef\'ee\'e4\'e1\'e8\'f0\'e0\'e5\'f2\'f1\'ff \'f2\'e0\'ea\'e8\'ec \'ee\'e1\'f0\'e0\'e7\'ee\'ec, 
\'f7\'f2\'ee\'e1\'fb \'e3\'f0\'e0-
\par \'ed\'e8\'f7\'ed\'fb\'e5 \'f3\'f1\'eb\'ee\'e2\'e8\'ff \'f0\'e5\'f8\'e5\'ed\'e8\'ff }{\cs325\i\insrsid8923009 u}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs326\i\insrsid8923009 x}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs327\i\insrsid8923009 t}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ) \'f1\'ee\'e2\'ef\'e0\'e4\'e0\'eb\'e8 \'f1\'ee \'e7\'ed\'e0\'f7\'e5\'ed\'e8\'ff\'ec\'e8 }{
\cs329\i\insrsid8923009 z}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs328\i\insrsid8923009 x}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs330\i\insrsid8923009 t}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ) \'e2 \'e0\'ed\'e0\'eb\'ee\'e3\'e8\'f7\'ed\'fb\'f5 \'f2\'ee\'f7\'ea\'e0\'f5, \'f2\'ee
\par \'e5\'f1\'f2\'fc \'e8\'f5 \'f0\'e0\'e7\'ed\'ee\'f1\'f2\'fc \'f0\'e0\'e2\'ed\'ff\'eb\'e0\'f1\'fc \'ed\'f3\'eb\'fe.
\par \'d1\'f4\'ee\'f0\'ec\'e8\'f0\'f3\'e5\'ec \'eb\'ee\'e3\'e8\'f7\'e5\'f1\'ea\'e8\'e9 \'e1\'eb\'ee\'ea \'e2\'fb\'e1\'ee\'f0\'e0 \'f2\'e8\'ef\'e0 \'e3\'f0\'e0\'ed\'e8\'f7\'ed\'fb\'f5 \'f3\'f1\'eb\'ee\'e2\'e8\'e9, \'ea\'ee\'f2\'ee\'f0\'fb\'e5 \'e1\'f3\'e4\'f3
\'f2 \'ee\'ef\'f0\'e5\'e4\'e5\'eb\'ff\'f2\'fc
\par (\'e7\'e0\'e4\'e0\'f7\'e0 \'d8\'f2\'f3\'f0\'ec\'e0-\'cb\'e8\'f3\'e2\'e8\'eb\'eb\'ff) \'f1\'ee\'e1\'f1\'f2\'e2\'e5\'ed\'ed\'fb\'e5 \'e7\'ed\'e0\'f7\'e5\'ed\'e8\'ff }{\cs314\i\insrsid8923009 b}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 
(}{\cs315\i\insrsid8923009 n}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ) \'e8 \'f1\'ee\'e1\'f1\'f2\'e2\'e5\'ed\'ed\'fb\'e5 \'f4\'f3\'ed\'ea\'f6\'e8\'e8 }{\cs316\i\insrsid8923009 Xn}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs317\i\insrsid8923009 x}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs318\i\insrsid8923009 n}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ), 

\par \'e0 \'f2\'e0\'ea\'e6\'e5 \'ef\'ee\'e4\'e1\'e8\'f0\'e0\'e5\'ec\'f3\'fe \'e2 \'f3\'ea\'e0\'e7\'e0\'ed\'ed\'ee\'ec \'e2\'fb\'f8\'e5 \'f1\'ec\'fb\'f1\'eb\'e5 \'ea \'e3\'f0\'e0\'ed\'e8\'f7\'ed\'fb\'ec \'f3\'f1\'eb\'ee\'e2\'e8\'ff\'ec  \'f4\'f3\'ed\'ea\'f6\'e8
\'fe }{\cs319\i\insrsid8923009 z}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs320\i\insrsid8923009 x}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs321\i\insrsid8923009 t}{
\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ):
\par }\pard \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0\pararsid1991549 {\cs20\f2\insrsid8923009\charrsid11479345 if u(0,t)=phi(t)and u(L,t)=psi(t) then}{\b\insrsid8923009\charrsid11479345 
\par }{\cs20\f2\insrsid8923009\charrsid11479345 b:=n->Pi*n/L: Xn:=(x,n)->sin(b(n)*x):}{\b\insrsid8923009\charrsid11479345 
\par }{\dn23\insrsid9712127 {\pict{\*\picprop\shplid1029{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw6519\pich1035\picwgoal3696\pichgoal587\wmetafile8\bliptag-1443763315\blipupi-618{\*\blipuid a9f1eb8ddd18fb4846a82d212585c2a8}
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\par }{\cs20\f2\insrsid8923009\charrsid11479345 elif D[1](u)(0,t)=phi(t) and D[1](u)(L,t)=psi(t) then}{\b\insrsid8923009\charrsid11479345 
\par }{\cs20\f2\insrsid8923009\charrsid11479345 b:=n->Pi*n/L: Xn:=(x,n)->cos(b(n)*x): }{\b\insrsid8923009\charrsid11479345 
\par }{\dn21\insrsid9712127 {\pict{\*\picprop\shplid1030{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw6980\pich1106\picwgoal3957\pichgoal627\wmetafile8\bliptag-278473975\blipupi-411{\*\blipuid ef66d309093640db281ab6a91a38d21b}
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\par }{\cs20\f2\insrsid8923009\charrsid11479345 elif D[1](u)(0,t)=phi(t) and u(L,t)=psi(t) then}{\b\insrsid8923009\charrsid11479345 
\par }{\cs20\f2\insrsid8923009\charrsid11479345 b:=n->Pi*(2*n-1)/2/L: Xn:=(x,n)->cos(b(n)*x):}{\b\insrsid8923009\charrsid11479345 
\par }{\dn7\insrsid9712127 {\pict{\*\picprop\shplid1031{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
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\par }{\cs20\f2\insrsid8923009\charrsid11479345 elif u(0,t)=phi(t) and D[1](u)(L,t)=psi(t) then}{\b\insrsid8923009\charrsid11479345 
\par }{\cs20\f2\insrsid8923009\charrsid11479345 b:=n->Pi*(2*n-1)/2/L: Xn:=(x,n)->sin(b(n)*x):}{\b\insrsid8923009\charrsid11479345 
\par }{\dn7\insrsid9712127 {\pict{\*\picprop\shplid1032{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
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\par }\pard\plain \s366\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn7\insrsid9712127 
{\pict{\*\picprop\shplid1046{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
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\'ee\'e5 \'f3\'f0\'e0\'e2\'ed\'e5\'ed\'e8\'e5, \'ef\'ee\'eb\'e0\'e3\'e0\'ff \'ed\'f3\'eb\'e5\'e2\'fb\'ec\'e8
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\'eb\'e8\'ec \'ed\'e0\'f7\'e0\'eb\'fc\'ed\'fb\'e5 \'f3\'f1\'eb\'ee\'e2\'e8\'ff \'e4\'eb\'ff 
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\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ):
\par }{\cs20\f2\insrsid8923009\charrsid8923009 f}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 1:=}{\cs20\f2\insrsid8923009\charrsid8923009 x}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 ->}{
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\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid10188371 ;}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009  }{\b\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 
\par }\pard\plain \s366\qc \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\dn7\insrsid9712127 
{\pict{\*\picprop\shplid1047{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
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F}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 1(}{\insrsid8923009 x}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 )=}{\insrsid8923009 F}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{
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\par }{\cs20\f2\insrsid8923009\charrsid8923009 F}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 1:=}{\cs20\f2\insrsid8923009\charrsid8923009 x}{\cs20\f2\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 ->}{
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\par }{\cs60\i\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 \'cf\'f0\'e8\'ec\'e5\'f7\'e0\'ed\'e8\'e5}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 . \'cf\'f0\'e8 \'fd\'f2\'ee\'ec \'ef\'ee\'eb\'f3\'f7\'e8\'eb\'e8 \'ed\'f3\'eb
\'e5\'e2\'fb\'e5 \'e3\'f0\'e0\'ed\'e8\'f7\'ed\'fb\'e5 \'f3\'f1\'eb\'ee\'e2\'e8\'ff \'e4\'eb\'ff }{\cs347\i\insrsid8923009 w}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs345\i\insrsid8923009 x}{
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\par \'e4\'eb\'ff \'e4\'e0\'eb\'fc\'ed\'e5\'e9\'f8\'e5\'e3\'ee \'ef\'ee\'f1\'f2\'f0\'ee\'e5\'ed\'e8\'ff \'e0\'eb\'e3\'ee\'f0\'e8\'f2\'ec\'e0.
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\'fe\'f9\'e5\'e9 \'ed\'e0 \'f1\'e2\'ee\'e9\'f1\'f2\'e2\'e0 \'ef\'e0\'f0\'e0\'ec\'e5\'f2\'f0\'ee\'e2, 
\par \'f3\'f7\'e0\'f1\'f2\'e2\'f3\'fe\'f9\'e8\'f5 \'e2 \'e2\'fb\'f7\'e8\'f1\'eb\'e5\'ed\'e8\'ff\'f5. \'c1\'f3\'e4\'e5\'ec \'e8\'f1\'ef\'ee\'eb\'fc\'e7\'ee\'e2\'e0\'f2\'fc \'fd\'f2\'f3 \'ee\'ef\'f6\'e8\'fe \'ef\'f0\'e8 \'ed\'e5\'ee\'e1\'f5\'ee\'e4\'e8\'ec\'ee
\'f1\'f2\'e8 \'e4\'eb\'ff 
\par \'f3\'ef\'f0\'ee\'f9\'e5\'ed\'e8\'ff \'e2\'fb\'f0\'e0\'e6\'e5\'ed\'e8\'e9. \'d3\'ea\'e0\'e6\'e5\'ec \'ed\'e0 \'f1\'e2\'ee\'e9\'f1\'f2\'e2\'ee \'ef\'e0\'f0\'e0\'ec\'e5\'f2\'f0\'e0 }{\cs64\i\insrsid8923009 n}{
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\par }{\cs20\f2\insrsid8923009\charrsid8923009 `assume(n,integer)`: N:=infinity: }{\b\insrsid8923009\charrsid8923009 
\par }\pard\plain \s365\ql \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 \f2\fs20\cf2\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\insrsid8923009 
\par }\pard\plain \ql \li0\ri0\sl360\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid10188371 \fs24\cf1\lang1033\langfe1049\cgrid\langnp1033\langfenp1049 {\cs69\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 2. \'c7\'e0\'ef\'e8\'f8\'e5\'ec 2-
\'fe \'ea\'ee\'ec\'ef\'ee\'ed\'e5\'ed\'f2\'f3 }{\cs120\i\insrsid8923009\charrsid8923009 w}{\cs227\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 (}{\cs118\i\insrsid8923009\charrsid8923009 x}{
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\cs61\i\insrsid8923009\charrsid8923009 u}{\cs70\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 (}{\cs62\i\insrsid8923009\charrsid8923009 x}{\cs71\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 ,}{
\cs63\i\insrsid8923009\charrsid8923009 t}{\cs72\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid8923009 )}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 . 
\par \'cd\'e0\'f7\'ed\'e5\'ec \'f1 \'e2\'fb\'f7\'e8\'f1\'eb\'e5\'ed\'e8\'ff \'ea\'ee\'fd\'f4\'f4\'e8\'f6\'e8\'e5\'ed\'f2\'ee\'e2 \'f0\'ff\'e4\'e0 \'d4\'f3\'f0\'fc\'e5:
\par - \'e7\'e0\'ef\'e8\'f8\'e5\'ec \'ea\'ee\'fd\'f4\'f4\'e8\'f6\'e8\'e5\'ed\'f2\'fb \'f0\'e0\'e7\'eb\'ee\'e6\'e5\'ed\'e8\'ff \'e2 \'f0\'ff\'e4 \'d4\'f3\'f0\'fc\'e5 \'ef\'ee \'f1\'ee\'e1\'f1\'f2\'e2\'e5\'ed\'ed\'fb\'ec \'e7\'ed\'e0\'f7\'e5\'ed\'e8\'ff\'ec }{
\cs352\i\insrsid8923009 Xn}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{\cs353\i\insrsid8923009 x}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 ,}{\cs354\i\insrsid8923009 n}{
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\par }{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 \'e8 \'ef\'ee\'f1\'f2\'f0\'ee\'e8\'ec \'ef\'ee\'e2\'e5\'f0\'f5\'ed\'ee\'f1\'f2\'fc }{\cs230\i\insrsid8923009 R}{\lang1049\langfe1049\langnp1049\insrsid8923009\charrsid9974477 (}{
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\par }{\insrsid8923009 \'f0\'e5\'f8\'e5\'ed\'e8\'ff.   
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