{VERSION 7 1 "Linux" "7.1" } {USTYLETAB {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "MS Serif" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1 " -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 12 40 120 40 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "MS Serif" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Norm al" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "MS Serif" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Orde red List 4" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Wa rning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "He ading 1" -1 3 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 2" -1 204 1 {CSTYLE "" -1 -1 "Times " 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 } {CSTYLE "Equation Label" -1 200 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Page Number" -1 33 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 202 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "MS Serif" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{PSTYLE "" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 12 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 203 23 "Modern alkalmazott anal" }{TEXT 203 8 "\303\255" }{TEXT 203 3 "zis" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 18 "J\303\241rai Antal" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 68 "Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\2 41lnak" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 3 "" 0 "" {TEXT 205 7 "Bevezet" }{TEXT 205 8 "\303\251" }{TEXT 205 1 "s" }}}{EXCHG {PARA 3 "" 0 "" {TEXT 201 0 "" }}}{EXCHG {PARA 3 " " 0 "" {TEXT 205 4 "I. M" }{TEXT 205 8 "\303\251" }{TEXT 205 2 "rt" } {TEXT 205 8 "\303\251" }{TEXT 205 2 "k " }{TEXT 205 8 "\303\251" } {TEXT 205 8 "s integr" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "1. M" }{TEXT 205 8 "\303\251" }{TEXT 205 2 "rt" } {TEXT 205 8 "\303\251" }{TEXT 205 4 "kelm" }{TEXT 205 11 "\303\251let" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 9 "2. Integr" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {PARA 3 "" 0 "" {TEXT 205 12 "II. Funkcion" }{TEXT 205 8 "\303\241" } {TEXT 205 5 "lanal" }{TEXT 205 8 "\303\255" }{TEXT 205 3 "zis" }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 17 "3. Metrikus terek" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 15 "3.114. Banach-f" }{TEXT 206 8 "\303\251" }{TEXT 206 11 "le fix pontt" }{TEXT 206 8 "\303\251" }{TEXT 206 4 "tel." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 15 "3.115. Megjegyz" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "s." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 15 "3.116. Feladat." } }{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "T:=x->(cos(x/2)-abs(x-0.5))/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 " f*6#I\"xG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&#\"\"\"\"\"#F,-I$cosGF%6# ,$*&F+F,F$F,F,F,F,*&F+F,-I$absG%*protectedG6#,&F$F,$\"\"&!\"\"F;F,F;F% F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "0.6;T(%);T(%);T(%) ;T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%) ;T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"\"'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+YCowU!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fNYCX!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+wT$[j%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Gjv$o%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+BQR0Z! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+kW&\\r%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+pq<>Z!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+%pT5s% !#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5]'=s%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+F&GAs%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+G!*QA Z!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+#*)fCs%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+!=\"\\AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+% *\\]AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+$46Ds%!#5" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+'y8Ds%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +v\\^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++b^AZ!#5" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+Kd^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ Me^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ze^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++f^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3f ^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+7f^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+9f^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+:f^A Z!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+9f^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+:f^AZ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+9f^AZ! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+:f^AZ!#5" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 15 "3.117. Feladat ." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 15 "3.118. Feladat." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "Feladat." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solve([x1^2+x2^2=1,2* x1+x2=1],[x1,x2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$/I#x1G6\"\"\"! /I#x2GF&\"\"\"7$/F%#\"\"%\"\"&/F)#!\"$F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "T1:=x->[(1-x[2])/2,sqrt(1-x[1]^2)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arrowGF%F%7$,&#\"\"\"\" \"#F,*&F+F,&F$6#F-F,!\"\"-I%sqrtGF%6#,&F,F,*$)&F$6#F,F-F,F1F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "x:=[-0.9,0.9];T1(%);T1(%);T1 (%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$!\"*!\"\"$\"\"*F%" }}{PARA 11 "" 1 "" {XPPMATH 20 " 7$$\"*++++&!#5$\"+W*)*)eVF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+G0b ?G!#5$\"+y@\\()**F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"(6RD'!#5$\"+ 9A)Rf*F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"*$*)3I?!#5$\"+W!)****** F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"$y*!#5$\"+d\"Rz***F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$$\"(A/.\"!#5$\"\"\"\"\"!" }}{PARA 11 " " 1 "" {XPPMATH 20 "7$$\"\"!F$$\"+Z********!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"#E!#5$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7 $$\"\"!F$$\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"\"!F$$\"\"\"F $" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"\"!F$$\"\"\"F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "T2:=x->[(1-x[2])/2,-sqrt(1-x[1]^2)] ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arro wGF%F%7$,&#\"\"\"\"\"#F,*&F+F,&F$6#F-F,!\"\",$-I%sqrtG6$%*protectedGI( _syslibGF%6#,&F,F,*$)&F$6#F,F-F,F1F1F%F%F%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 303 "x:=[0.9,0.9];T2(%);T2(%);T2(%);(%);T2(%);T2(%);T2( %);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T 2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%) ;T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2( %);(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"\"*!\"\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"*++ ++&!#5$!+W*)*)eVF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+s%\\%zr!#5$! +y@\\()**F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+*3YP***!#5$!+r))*4' pF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+*3YP***!#5$!+r))*4'pF%" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+O%*\\![)!#5$!+ip3ON!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+[V!o<&!#5$!+xI;*H&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+Q:e\\w!#5$!+s0ub&)F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+'GqyF*!#5$!+=)*zSkF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+ 4**R?#)!#5$!+6@5JPF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+c5blo!#5$! +;wH%p&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+3)[r%y!#5$!+BxxqsF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+i))QN')!#5$!+M)o&)>'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+!)!#5$!+;qnhF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+F9$)f!)!#5$! +$R,w,'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+'p+)3!)!#5$!+\")[Q>fF %" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+SCpfz!#5$!+vxC))fF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+))Q7%*z!#5$!+`1P`gF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+E`oE!)!#5$!+Lo#y+'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+;M\"R+)!#5$!+SPDkfF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+ qo7#)z!#5$!+k&yZ*fF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+#G*Q(*z!#5 $!+'=dP-'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+$fy=,)!#5$!+!QzM+'F %" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+!pR<+)!#5$!+F\"HT)fF%" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+kX1#*z!#5$!+7(zw*fF%" }}{PARA 11 " " 1 "" {XPPMATH 20 "7$$\"+c)R))*z!#5$!+Igc5gF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+:IG0!)!#5$!+Zla,gF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+uKx+!)!#5$!+7&\\H*fF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+c ZZ'*z!#5$!+I)o*)*fF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+:W[**z!#5$ !+^up/gF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+E([B+)!#5$!+&Q(o+gF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+#pV.+)!#5$!+)3no*fF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+WNV)*z!#5$!+< " 0 "" {MPLTEXT 1 0 42 "with(LinearAlgebra); with(VectorCal culus);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7brI#&xG6\"I$AddGF$I(AdjointG F$I3BackwardSubstituteGF$I+BandMatrixGF$I&BasisGF$I-BezoutMatrixGF$I/B idiagonalFormGF$I-BilinearFormGF$I5CharacteristicMatrixGF$I9Characteri sticPolynomialGF$I'ColumnGF$I0ColumnDimensionGF$I0ColumnOperationGF$I, ColumnSpaceGF$I0CompanionMatrixGF$I0ConditionNumberGF$I/ConstantMatrix GF$I/ConstantVectorGF$I%CopyGF$I2CreatePermutationGF$I-CrossProductGF$ I-DeleteColumnGF$I*DeleteRowGF$I,DeterminantGF$I)DiagonalGF$I/Diagonal MatrixGF$I*DimensionGF$I+DimensionsGF$I+DotProductGF$I6EigenConditionN umbersGF$I,EigenvaluesGF$I-EigenvectorsGF$I&EqualGF$I2ForwardSubstitut eGF$I.FrobeniusFormGF$I4GaussianEliminationGF$I2GenerateEquationsGF$I/ GenerateMatrixGF$I2GetResultDataTypeGF$I/GetResultShapeGF$I5GivensRota tionMatrixGF$I,GramSchmidtGF$I-HankelMatrixGF$I,HermiteFormGF$I3Hermit ianTransposeGF$I/HessenbergFormGF$I.HilbertMatrixGF$I2HouseholderMatri xGF$I/IdentityMatrixGF$I2IntersectionBasisGF$I+IsDefiniteGF$I-IsOrthog onalGF$I*IsSimilarGF$I*IsUnitaryGF$I2JordanBlockMatrixGF$I+JordanFormG F$I(LA_MainGF$I0LUDecompositionGF$I-LeastSquaresGF$I,LinearSolveGF$I$M apGF$I%Map2GF$I*MatrixAddGF$I2MatrixExponentialGF$I/MatrixFunctionGF$I .MatrixInverseGF$I5MatrixMatrixMultiplyGF$I+MatrixNormGF$I,MatrixPower GF$I5MatrixScalarMultiplyGF$I5MatrixVectorMultiplyGF$I2MinimalPolynomi alGF$I&MinorGF$I(ModularGF$I)MultiplyGF$I,NoUserValueGF$I%NormGF$I*Nor malizeGF$I*NullSpaceGF$I3OuterProductMatrixGF$I*PermanentGF$I&PivotGF$ I*PopovFormGF$I0QRDecompositionGF$I-RandomMatrixGF$I-RandomVectorGF$I% RankGF$I6RationalCanonicalFormGF$I6ReducedRowEchelonFormGF$I$RowGF$I-R owDimensionGF$I-RowOperationGF$I)RowSpaceGF$I-ScalarMatrixGF$I/ScalarM ultiplyGF$I-ScalarVectorGF$I*SchurFormGF$I/SingularValuesGF$I*SmithFor mGF$I*SubMatrixGF$I*SubVectorGF$I)SumBasisGF$I0SylvesterMatrixGF$I/Toe plitzMatrixGF$I&TraceGF$I*TransposeGF$I0TridiagonalFormGF$I+UnitVector GF$I2VandermondeMatrixGF$I*VectorAddGF$I,VectorAngleGF$I5VectorMatrixM ultiplyGF$I+VectorNormGF$I5VectorScalarMultiplyGF$I+ZeroMatrixGF$I+Zer oVectorGF$I$ZipGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7YI#&xG6\"I\"*G%*p rotectedGI\"+GF&I\"-GF$I\".GF$I$<,>GF$I$<|gr>GF$I/AddCoordinatesGF$I*A rcLengthGF$I,BasisFormatGF$I)BinormalGF$I*CrossProdGF$I-CrossProductGF $I%CurlGF$I*CurvatureGF$I\"DGF$I$DelGF$I0DirectionalDiffGF$I+Divergenc eGF$I(DotProdGF$I+DotProductGF$I%FluxGF$I8GetCoordinateParametersGF$I/ GetCoordinatesGF$I)GradientGF$I(HessianGF$I)JacobianGF$I*LaplacianGF$I (LineIntGF$I+MapToBasisGF$I&NablaGF$I%NormGF$I*NormalizeGF$I(PathIntGF $I0PrincipalNormalGF$I2RadiusOfCurvatureGF$I0ScalarPotentialGF$I8SetCo ordinateParametersGF$I/SetCoordinatesGF$I+SurfaceIntGF$I)TNBFrameGF$I( TangentGF$I,TangentLineGF$I-TangentPlaneGF$I.TangentVectorGF$I(Torsion GF$I'VectorGF$I,VectorFieldGF$I0VectorPotentialGF$I*WronskianGF$I%diff GF&I'evalVFGF$I$intGF$I&limitGF$I'seriesGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "x:='x';T1:=<(1-y)/2,sqrt(1-x^2)>;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"xG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG 6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*_>'G9" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Jacobian(T1,[x,y]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6&-I%mrowGF$6#-I'mtableGF$6$-I$mtrGF$6$-I$mtdGF$6#-I#m nGF$6$Q\"0F'/%,mathvariantGQ'normalF'-F56#-F,6$-I#moGF$60Q*&uminus0;F' F;/%&fenceGQ&falseF'/%*separatorGFH/%)stretchyGFH/%*symmetricGFH/%(lar geopGFH/%.movablelimitsGFH/%'accentGFH/%%formGQ'prefixF'/%'lspaceGQ$0e mF'/%'rspaceGQ2verythinmathspaceF'/%(minsizeGQ\"1F'/%(maxsizeGQ)infini tyF'-I&mfracGF$6(-F86$FjnF;-F86$Q\"2F'F;/%.linethicknessGQ\"1F'/%+deno malignGQ'centerF'/%)numalignGF[p/%)bevelledGFH-F26$-F56#-F,6$FB-F_o6(- F,6#-I#miGF$6%Q\"xF'/%'italicGQ%trueF'/F " 0 "" {MPLTEXT 1 0 19 "a:=subs(x=0,y=1,%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,Typesetting GI(_syslibGF'6%-I#miGF$6%Q\"aF'/%'italicGQ%trueF'/%,mathvariantGQ'ital icF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)s tretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/ %%formGQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsizeGQ\" 1F'/%(maxsizeGQ)infinityF'-I(mfencedGF$6&-F#6#-I'mtableGF$6$-I$mtrGF$6 $-I$mtdGF$6#-I#mnGF$6$Q\"0F'F9-F^o6#-F#6$-F660Q*&uminus0;F'F9F;F>F@FBF DFFFH/FKQ'prefixF'/FNQ$0emF'/FQQ2verythinmathspaceF'FRFU-I&mfracGF$6(- Fao6$FTF9-Fao6$Q\"2F'F9/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF' /%)numalignGF^q/%)bevelledGF=-F[o6$F]oF]o/%%openGQ\"[F'/%&closeGQ\"]F' /I+msemanticsGF$Q'MatrixF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "MatrixNorm(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "#\"\"\"\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "T2:=<(1-y)/2,-sqrt(1-x^2)>;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6 \"6#I'columnGF(6#/I$%idGF(\"*SDKV\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Jacobian(T2,[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " -I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6&-I%mrowGF$6# -I'mtableGF$6$-I$mtrGF$6$-I$mtdGF$6#-I#mnGF$6$Q\"0F'/%,mathvariantGQ'n ormalF'-F56#-F,6$-I#moGF$60Q*&uminus0;F'F;/%&fenceGQ&falseF'/%*separat orGFH/%)stretchyGFH/%*symmetricGFH/%(largeopGFH/%.movablelimitsGFH/%'a ccentGFH/%%formGQ'prefixF'/%'lspaceGQ$0emF'/%'rspaceGQ2verythinmathspa ceF'/%(minsizeGQ\"1F'/%(maxsizeGQ)infinityF'-I&mfracGF$6(-F86$FjnF;-F8 6$Q\"2F'F;/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGF [p/%)bevelledGFH-F26$-F56#-F_o6(-F,6#-I#miGF$6%Q\"xF'/%'italicGQ%trueF '/F " 0 "" {MPLTEXT 1 0 24 "a:=subs(x=4/5,y=-3/5,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mro wG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q\"aF'/%'it alicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%& fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopG F=/%.movablelimitsGF=/%'accentGF=/%%formGQ&infixF'/%'lspaceGQ/thickmat hspaceF'/%'rspaceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ)infinityF'-I(mfenced GF$6&-F#6#-I'mtableGF$6$-I$mtrGF$6$-I$mtdGF$6#-I#mnGF$6$Q\"0F'F9-F^o6# -F#6$-F660Q*&uminus0;F'F9F;F>F@FBFDFFFH/FKQ'prefixF'/FNQ$0emF'/FQQ2ver ythinmathspaceF'FRFU-I&mfracGF$6(-Fao6$FTF9-Fao6$Q\"2F'F9/%.linethickn essGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGF^q/%)bevelledGF=-F[o6$- F^o6#-F#6%-Fbp6(-Fao6$Q\"4F'F9-Fao6$Q#45F'F9FipF\\qF_qFaq-F660Q1&Invis ibleTimes;F'F9F;F>F@FBFDFFFHFJF]p/FQF^pFRFU-F#6%-I&msqrtGF$6#-Fao6$Q\" 9F'F9Far-Fhr6#-Fao6$Q#25F'F9F]o/%%openGQ\"[F'/%&closeGQ\"]F'/I+msemant icsGF$Q'MatrixF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "MatrixN orm(a); evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(#\"\"%\"#X\"\" \")\"\"*#F'\"\"#F')\"#DF*F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+LLL L8!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Eigenvalues(a); e valf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6 \"I,TypesettingGI(_syslibGF'6&-I%mrowGF$6#-I'mtableGF$6$-I$mtrGF$6#-I$ mtdGF$6#-F,6%-F,6%-I&mfracGF$6(-I#mnGF$6$Q\"1F'/%,mathvariantGQ'normal F'-F?6$Q\"3F'FB/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numal ignGFM/%)bevelledGQ&falseF'-I#moGF$60Q1⁢F'FB/%&fenceGFR /%*separatorGFR/%)stretchyGFR/%*symmetricGFR/%(largeopGFR/%.movablelim itsGFR/%'accentGFR/%%formGQ&infixF'/%'lspaceGQ$0emF'/%'rspaceGFdo/%(mi nsizeGFA/%(maxsizeGQ)infinityF'-F,6#-F?6$Q\"IF'FBFS-I&msqrtGF$6#-F?6$Q \"6F'FB-F26#-F56#-F,6$-FT60Q*&uminus0;F'FBFWFYFenFgnFinF[oF]o/F`oQ'pre fixF'Fbo/FfoQ2verythinmathspaceF'FgoFioF7/%%openGQ\"[F'/%&closeGQ\"]F' /I+msemanticsGF$Q*ColVectorF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfen cedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6&-I%mrowGF$6#-I'mtab leGF$6$-I$mtrGF$6#-I$mtdGF$6#-F,6%-I#mnGF$6$Q-0.8164965809F'/%,mathvar iantGQ'normalF'-I#moGF$60Q1⁢F'F=/%&fenceGQ&falseF'/%*se paratorGFF/%)stretchyGFF/%*symmetricGFF/%(largeopGFF/%.movablelimitsGF F/%'accentGFF/%%formGQ&infixF'/%'lspaceGQ$0emF'/%'rspaceGFX/%(minsizeG Q\"1F'/%(maxsizeGQ)infinityF'-F:6$Q\"IF'F=-F26#-F56#-F,6$-FA60Q*&uminu s0;F'F=FDFGFIFKFMFOFQ/FTQ'prefixF'FV/FZQ2verythinmathspaceF'FenFhnF7/% %openGQ\"[F'/%&closeGQ\"]F'/I+msemanticsGF$Q*ColVectorF'" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 15 "3.119. Feladat." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 37 "3.120. Feladat: a fixpont folytonos f" }{TEXT 206 8 "\303\274" }{TEXT 206 2 "gg" }{TEXT 206 8 "\303\251" }{TEXT 206 10 "se a param" }{TEXT 206 8 "\303\251" }{TEXT 206 6 "terekt" }{TEXT 206 8 " \305\221" }{TEXT 206 2 "l." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 17 "- >3.121. Feladat." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 17 "Fixpont tul ajdons" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "g." }}}{SECT 1 {PARA 4 " " 0 "" {TEXT 206 10 "Retraktum." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 1 "T" }{TEXT 206 8 "\303\251" }{TEXT 206 4 "tel." }}}{SECT 1 {PARA 4 " " 0 "" {TEXT 206 8 "\303\226" }{TEXT 206 5 "sszeh" }{TEXT 206 8 "\303 \272" }{TEXT 206 4 "zhat" }{TEXT 206 8 "\303\263" }{TEXT 206 1 "s" } {TEXT 206 8 "\303\241" }{TEXT 206 2 "g." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 1 "T" }{TEXT 206 8 "\303\251" }{TEXT 206 4 "tel." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 1 "T" }{TEXT 206 8 "\303\251" }{TEXT 206 4 "tel." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 1 "T" }{TEXT 206 8 "\303\2 51" }{TEXT 206 4 "tel." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 8 "Megjeg yz" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "s." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 25 "*3.122. Egyenletek megold" }{TEXT 206 8 "\303\241" } {TEXT 206 3 "sa " }{TEXT 206 8 "\303\251" }{TEXT 206 10 "s fixpontt" } {TEXT 206 8 "\303\251" }{TEXT 206 6 "telek." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "v:='v'; f:=Vector (2,[v[1]^2+v[2]^2-1,2*v[1]+v[2]-1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " I\"vG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_ syslibG6\"6#I'columnGF(6#/I$%idGF(\"*cWRU\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "J:=Jacobian(f,[v[1],v[2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I #miGF$6%Q\"JF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$60Q#: =F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symm etricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%%formGQ&infixF'/ %'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ)i nfinityF'-I(mfencedGF$6&-F#6#-I'mtableGF$6$-I$mtrGF$6$-I$mtdGF$6#-F#6% -I#mnGF$6$Q\"2F'F9-F660Q1⁢F'F9F;F>F@FBFDFFFHFJ/FNQ$0emF '/FQFjoFRFU-I%msubGF$6%-F,6%Q\"vF'F/F2-F#6#-Fco6$FTF9/%/subscriptshift GQ\"0F'-F^o6#-F#6%FboFfo-F]p6%F_p-F#6#FboFfp-F[o6$-F^oF`q-F^oFcp/%%ope nGQ\"[F'/%&closeGQ\"]F'/I+msemanticsGF$Q'MatrixF'" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 23 "Jinv:=MatrixInverse(J);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I #miGF$6%Q%JinvF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$60Q #:=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*sy mmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%%formGQ&infixF '/%'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ )infinityF'-I(mfencedGF$6&-F#6#-I'mtableGF$6$-I$mtrGF$6$-I$mtdGF$6#-I& mfracGF$6(-F#6#-I#mnGF$6$FTF9-F#6%-Ffo6$Q\"2F'F9-F660Q1&InvisibleTimes ;F'F9F;F>F@FBFDFFFHFJ/FNQ$0emF'/FQFapFRFU-FY6#-F#6%-I%msubGF$6%-F,6%Q \"vF'F/F2Fco/%/subscriptshiftGQ\"0F'-F660Q(−F'F9F;F>F@FBFDFFFHFJ /FNQ0mediummathspaceF'/FQFdqFRFU-F#6%FjoF]p-Fhp6%Fjp-F#6#FjoF]q/%.line thicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFar/%)bevelledGF=- F^o6#-F#6$-F660Q*&uminus0;F'F9F;F>F@FBFDFFFH/FKQ'prefixF'F`p/FQQ2veryt hinmathspaceF'FRFU-Fao6(-F#6#Fhq-F#FdpF\\rF_rFbrFdr-F[o6$-F^o6#-F#6$Fj r-Fao6(FeoFesF\\rF_rFbrFdr-F^o6#-Fao6(-F#6#FgpFesF\\rF_rFbrFdr/%%openG Q\"[F'/%&closeGQ\"]F'/I+msemanticsGF$Q'MatrixF'" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 58 "Jinv0:=subs(v[1]=-2.,v[2]=2.,Jinv); v:=Vector( 2,[-2.,2.]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG 6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q&Jinv0F'/%'italicGQ%trueF'/% ,mathvariantGQ'italicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF' /%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelim itsGF=/%'accentGF=/%%formGQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rspa ceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ)infinityF'-I(mfencedGF$6&-F#6#-I'mt ableGF$6$-I$mtrGF$6$-I$mtdGF$6#-I#mnGF$6$Q7&uminus0;0.08333333335F'F9- F^o6#-Fao6$Q-0.3333333333F'F9-F[o6$-F^o6#-Fao6$Q-0.1666666667F'F9-F^o6 #-Fao6$Q-0.3333333334F'F9/%%openGQ\"[F'/%&closeGQ\"]F'/I+msemanticsGF$ Q'MatrixF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI (_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*Gw\"R9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jin v0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f; v:=v-Jinv0.f;v:=v-Jinv0.f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'Vector G6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*C$*eW\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\"6# I'columnGF(6#/I$%idGF(\"*;`yW\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'V ectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*?t&\\9" }} {PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\"6# I'columnGF(6#/I$%idGF(\"*!)3=U\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I' VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*wRPU\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\"6 #I'columnGF(6#/I$%idGF(\"*7,`U\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I' VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*Kw\\V\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\" 6#I'columnGF(6#/I$%idGF(\"*CVyU\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I 'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*7-uW\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\" 6#I'columnGF(6#/I$%idGF(\"*+kcW\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I 'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*3D'[9" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "v:=Vector(2,[-0.9,0.9]);\n " }{MPLTEXT 1 0 84 "v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;v: =v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-& I'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*kOFV\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6 \"6#I'columnGF(6#/I$%idGF(\"*ClAV\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "- &I'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*_yHX\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6 \"6#I'columnGF(6#/I$%idGF(\"*cZdV\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "- &I'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*k&Qc9" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6 \"6#I'columnGF(6#/I$%idGF(\"*_(3e9" }}{PARA 11 "" 1 "" {XPPMATH 20 "-& I'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$%idGF(\"*W%zf9" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\" 6#I'columnGF(6#/I$%idGF(\"*G![h9" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 34 "3.123. Aitken \316\224^2-m\303\263" }{TEXT 206 7 "dszere." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "Aitken:=proc(x1,x2,x3) x1-(x2-x1)^2/((x3-x2)-(x2-x1)) end;" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6%I#x1G6\"I#x2GF%I#x3GF%F%F%F%-_I/Vect orCalculusG6$%*protectedGI(_syslibGF%I\"+GF,6$F$-_F*I\"-GF%6#-_F*I\"*G F,6$*$)-F)6$F&-F16#F$\"\"#\"\"\"*$-F)6$-F)6$F'-F16#F&-F16#F:!\"\"F%F%F %" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 16 "*3.124. Feladat." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fsolve(x=cos(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+K8&3R(!#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 224 "x:=1.5;cos(%);cos(%);c os(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);c os(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);c os(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+n,stq!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+s;*\\(**!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+B*\\SU&!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+!4(pk&)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ " 0 "" {MPLTEXT 1 0 130 "x:=0.;cos(%);cos(%);Aitken(%%%,%%,%);cos(%);cos( %);Aitken(%%%,%%,%);cos(%);cos(%);Aitken(%%%,%%,%);cos(%);cos(%);Aitke n(%%%,%%,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fI -.a!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+uNt]o!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+QjsVx!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;()f [r!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+i:g'Q(!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+hLr$R(!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+KJ# *)Q(!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+j5&3R(!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+8:&3R(!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5 7&3R(!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+K8&3R(!#5" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 16 "*3.125. Feladat." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "x:=1.;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/ %;2/%;2/%;2/%;2/%;2/%;2/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++?! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5 !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++?!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++ ?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++++ +5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++ ++?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++?!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "x:=1.;2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2 /%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%); 2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#\"\" !" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+LLLL8! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mmm;9!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+2Zw69 !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mmm;9!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"+'o:UT\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+R9 @99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+'o:UT\"!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +jN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+jN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+jN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 16 "*3.126. Feladat." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT 206 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 7 "4. N orm" }{TEXT 205 8 "\303\241" }{TEXT 205 8 "lt terek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 7 "5. Line" }{TEXT 205 8 "\303\241" }{TEXT 205 8 " ris oper" }{TEXT 205 8 "\303\241" }{TEXT 205 5 "torok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 16 "6. Hilbert-terek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 9 "7. Spektr" }{TEXT 205 8 "\303\241" }{TEXT 205 4 "lel m" }{TEXT 205 8 "\303\251" }{TEXT 205 3 "let" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 15 "8. Kompakt oper" }{TEXT 205 8 "\303\241" }{TEXT 205 5 "torok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 13 "9. Differenci" } {TEXT 205 8 "\303\241" }{TEXT 205 3 "lsz" }{TEXT 205 8 "\303\241" } {TEXT 205 1 "m" }{TEXT 205 8 "\303\255" }{TEXT 205 1 "t" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{PARA 3 "" 0 "" {TEXT 205 15 "III. Vektoranal" }{TEXT 205 8 "\303\255" } {TEXT 205 3 "zis" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 3 " " 0 "" {TEXT 205 16 "10. A differenci" }{TEXT 205 8 "\303\241" }{TEXT 205 18 "lgeometria alapjai" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 20 "1 1. Stieltjes-integr" }{TEXT 205 8 "\303\241" }{TEXT 205 2 "l " }{TEXT 205 8 "\303\251" }{TEXT 205 3 "s g" }{TEXT 205 8 "\303\266" }{TEXT 205 16 "rbe menti integr" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 205 14 "12. Differenci" }{TEXT 205 8 "\3 03\241" }{TEXT 205 5 "lform" }{TEXT 205 8 "\303\241" }{TEXT 205 8 "k i ntegr" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241 " }{TEXT 205 2 "sa" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{PARA 3 "" 0 " " {TEXT 205 12 "IV. Komplex " }{TEXT 205 25 "f\303\274ggv\303\251nytan " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 15 "13. Analitikus " }{TEXT 205 24 "f\303\274ggv\303\251nyek" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 205 13 "14. Holomorf " }{TEXT 205 24 "f \303\274ggv\303\251nyek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 13 "15. \+ Meromorf " }{TEXT 205 24 "f\303\274ggv\303\251nyek" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{PARA 3 "" 0 "" {TEXT 205 14 "V. Fourier-elm" }{TEXT 205 8 "\303\251" }{TEXT 205 3 "let" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 28 "16. Klasszikus Fourier-sorok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 11 "17. Ortogon" }{TEXT 205 8 "\3 03\241" }{TEXT 205 13 "lis polinomok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 22 "18. Fourier-transzform" }{TEXT 205 8 "\303\241" }{TEXT 205 2 "ci" }{TEXT 205 8 "\303\263" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {PARA 3 "" 0 "" {TEXT 205 8 "VI. Vari" }{TEXT 205 18 "\303\241ci\303\2 63" }{TEXT 205 2 "sz" }{TEXT 205 17 "\303\241m\303\255" }{TEXT 205 1 " t" }{TEXT 205 9 "\303\241s" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 32 "19. Az Euler-Lagrange-egyenletek" }}} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{PARA 3 "" 0 "" {TEXT 205 6 "VII. K" }{TEXT 205 8 "\303\266" }{TEXT 205 1 "z" }{TEXT 205 8 "\303\266" } {TEXT 205 2 "ns" }{TEXT 205 8 "\303\251" }{TEXT 205 14 "ges differenci " }{TEXT 205 19 "\303\241legyenletek" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 16 "20. Alapfogalmak" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 16 "21. Elemi megold" }{TEXT 205 8 "\303\241 " }{TEXT 205 4 "si m" }{TEXT 205 8 "\303\263" }{TEXT 205 7 "dszerek" } }}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "22. " }{TEXT 205 8 "\303\201" } {TEXT 205 4 "ltal" }{TEXT 205 8 "\303\241" }{TEXT 205 9 "nos eredm" } {TEXT 205 8 "\303\251" }{TEXT 205 4 "nyek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 8 "23. Line" }{TEXT 205 8 "\303\241" }{TEXT 205 14 "ris egye nletek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 12 "24. Stabilit" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {PARA 3 "" 0 "" {TEXT 205 11 "VIII. Parci" }{TEXT 205 8 "\303\241" } {TEXT 205 14 "lis differenci" }{TEXT 205 8 "\303\241" }{TEXT 205 11 "l egyenletek" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 16 "25. Alapfogalmak" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 12 "26. Disztrib" }{TEXT 205 8 "\303\272" }{TEXT 205 2 "ci" }{TEXT 205 8 "\303\263" }{TEXT 205 1 "k" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 20 "27. Cauchy-feladatok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 9 " 28. Perem" }{TEXT 205 8 "\303\251" }{TEXT 205 2 "rt" }{TEXT 205 8 "\30 3\251" }{TEXT 205 7 "k probl" }{TEXT 205 8 "\303\251" }{TEXT 205 1 "m" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "k" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 20 "29. Vegyes feladatok" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 201 0 "" }}}{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 }