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}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "int(( 3*x^3-x+14)/(x^2+4*x-4),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&#\"\" $\"\"#\"\"\")I\"xG6\"F&F'F'*&\"#7F'F)F'!\"\"*&#\"#fF&F'-I#lnG6$%*prote ctedGI(_syslibGF*6#,(*$F(F'F'*&\"\"%F'F)F'F'F:F-F'F'*(\"#QF')F&#F'F&F' -I(arctanhGF36#,$*(#F'\"\")F',&*&F&F'F)F'F'F:F'F'F=F'F'F'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "int(x*exp(x^3),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(#\"\"\"\"\"$F%)!\"\"F$F%,&**)I\"xG6\"\"\"# F%)F(#F.F&F%-I&GAMMAG6$%*protectedGI(_syslibGF-6#F0F%),$*$)F,F&F%F(F0F (F%**F+F%F/F%F7F(-F26$F0F8F%F(F%F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "diff_eqn:=diff(y(x),x$2)+t*diff(y(x),x)-2*t^2*y(x)=0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "/,(-I%diffG%*protectedG6$-F%6$-I\"yG 6\"6#I\"xGF,F.F.\"\"\"*&I\"tGF,F/F(F/F/*(\"\"#F/)F1F3F/F*F/!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "init_conds:=y(0)=t,D(y)( 0)=2*t^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-I\"yG6\"6#\"\"!I\"tGF&/ --I\"DG6$%*protectedGI(_syslibGF&6#F%F',$*&\"\"#\"\"\")F)F4F5F5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "dsolve(\{diff_eqn,init_conds \},y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I\"yG6\"6#I\"xGF%,&*(#\" \"%\"\"$\"\"\"I\"tGF%F--I$expG6$%*protectedGI(_syslibGF%6#*&F.F-F'F-F- F-*(#F-F,F-F.F--F06#,$*(\"\"#F-F.F-F'F-!\"\"F-F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Cheby:=proc(n,x) local T,k;\n" }{MPLTEXT 1 0 21 " T[0]:=1; T[1]:=x;\n" }{MPLTEXT 1 0 24 " for k from 2 to n do\n" }{MPLTEXT 1 0 38 " T[k]:=expand(2*x*T[k-1]-T[k-2]);\n" }{MPLTEXT 1 0 14 " od; T[n];\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"nG6\"I\"xGF%6$I\"TGF%I\"kGF%F%F%C&>&F(6#\"\"!\"\" \">&F(6#F/F&?(F)\"\"#F/F$I%trueG%*protectedG>&F(6#F)-I'expandGF66#,&*( F4F/F&F/&F(6#,&F)F/F/!\"\"F/F/&F(6#,&F)F/F4FBFB&F(6#F$F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Cheby(7,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"#k\"\"\")I\"xG6\"\"\"(F%F%*&\"$7\"F%)F'\"\"&F%! \"\"*&\"#cF%)F'\"\"$F%F%*&F)F%F'F%F." }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 15 "Ex1. 3. Feladat." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "int(x/(1+exp(x)),x);\n" }{MPLTEXT 1 0 18 "int(exp( x^2),x);\n" }{MPLTEXT 1 0 31 "int(sqrt((x^2-1)*(x^2-4)),x);\n" } {MPLTEXT 1 0 27 "int(sqrt((x-1)*(x-4)),x);\n" }{MPLTEXT 1 0 27 "int(sq rt((1+x)/(1-x)),x);\n" }{MPLTEXT 1 0 24 "int(log(x^2-5*x+4),x);\n" } {MPLTEXT 1 0 22 "int(log(x)/(1+x),x);\n" }{MPLTEXT 1 0 16 "int(1/log(x ),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&#\"\"\"\"\"#F%)I\"xG6\"F&F% F%*&F(F%-I#lnG6$%*protectedGI(_syslibGF)6#,&F%F%-I$expGF-6#F(F%F%!\"\" -I(polylogGF-6$F&,$F2F5F5" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(,$*&#\" \"\"\"\"#F'^#F'F'F'F')I#PiG%*protectedGF&F'-I$erfG6$F,I(_syslibG6\"6#* &F)F'I\"xGF1F'F'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*(#\"\"\"\"\" $F%I\"xG6\"F%),(\"\"%F%*$)F'F+F%F%*&\"\"&F%)F'\"\"#F%!\"\"#F%F1F%F%*,# F+F&F%),&F%F%*$F0F%F2F3F%),&F+F%F8F2F3F%F)F2-I*EllipticFG6$%*protected GI(_syslibGF(6$F'F3F%F%*,#\"#5F&F%F6F%F9F%F)F2,&F;F%-I*EllipticEGF=F@F 2F%F2" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(#\"\"\"\"\"%F%,&*&\"\"#F%I \"xG6\"F%F%\"\"&!\"\"F%),(F&F%*$)F*F)F%F%*&F,F%F*F%F-#F%F)F%F%*&#\"\"* \"\")F%-I#lnG6$%*protectedGI(_syslibGF+6#,(#F,F)F-F*F%*$F.F%F%F%F-" }} {PARA 11 "" 1 "" {XPPMATH 20 "**),$*&,&I\"xG6\"\"\"\"F)F)F),&F'F)F)!\" \"F+F+#F)\"\"#F)F*F)),$*&F*F)F&F)F+F,F+,&*$),&F)F)*$)F'F-F)F+F,F)F)-I' arcsinG6$%*protectedGI(_syslibGF(6#F'F+F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&I\"xG6\"\"\"\"-I#lnG6$%*protectedGI(_syslibGF%6#,(\" \"%F&*$)F$\"\"#F&F&*&\"\"&F&F$F&!\"\"F&F&*&F1F&F$F&F4-F(6#,&F$F&F&F4F4 *&F.F&-F(6#,&F$F&F.F4F&F4" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&-I&dilogG 6$%*protectedGI(_syslibG6\"6#,&I\"xGF(\"\"\"F,F,F,*&-I#lnGF%6#F+F,-F/F )F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 ",$-I#EiG6$%*protectedGI(_syslib G6\"6$\"\"\",$-I#lnGF%6#I\"xGF(!\"\"F0" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%# %?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 18 "2. Algebrai alapok" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 205 7 "3. Norm" }{TEXT 205 8 "\303\241" }{TEXT 205 6 "l form" }{TEXT 205 8 "\303\241" }{TEXT 205 12 "k, reprez ent" }{TEXT 205 18 "\303\241ci\303\263" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 13 "4. Aritmetika" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "5 . K" }{TEXT 205 8 "\303\255" }{TEXT 205 9 "nai marad" }{TEXT 205 8 "\3 03\251" }{TEXT 205 3 "kol" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }} }{SECT 1 {PARA 3 "" 0 "" {TEXT 205 14 "6. Newton-iter" }{TEXT 205 8 " \303\241" }{TEXT 205 2 "ci" }{TEXT 205 8 "\303\263" }{TEXT 205 16 ", H ensel-felemel" }{TEXT 205 8 "\303\251" }{TEXT 205 1 "s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 15 "7. Legnagyobb k" }{TEXT 205 8 "\303\266" }{TEXT 205 1 "z" }{TEXT 205 8 "\303\266" }{TEXT 205 6 "s oszt" }{TEXT 205 8 "\303\263" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 11 "8. Faktoriz " }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" } {TEXT 205 1 "s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 21 "9. Egyenletre ndszerek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 6 "10. Gr" }{TEXT 205 27 "\303\266bner-b\303\241zisok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 10 "11. Racion" }{TEXT 205 8 "\303\241" }{TEXT 205 5 "lis t" }{TEXT 205 8 "\303\266" }{TEXT 205 3 "rtf" }{TEXT 205 8 "\303\274" }{TEXT 205 3 "ggv" }{TEXT 205 8 "\303\251" }{TEXT 205 11 "nyek integr" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" }{TEXT 205 2 "sa" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 23 "12. A Risch-algoritmus ." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }