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ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 1 ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 2 ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 3 ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 4 ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 5 ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 6 ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ) Slide 7
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ΠΛΗ20 ΜΑΘΗΜΑ 1.5 (ΕΚΤΥΠΩΣΗ)

  1. 1. 20 1: 1.5: !"# ! " # $ ! % & " ' () $ () ! "# $ ! $ () * + , - . () , / ( ' % 0 $ ( * (1 ' . $" % " " & '" ( ) * ) * " " "& "+ , ' ) $ ' " " "&, . "'" "*& * ' $ $ *" & $ , . & '" - (-) %! "# $ ! (-) & '" (-) -. . , & * ( " " "# * & ' $) "+ , , / : ) " ( 1.5) % " " " " : 0 %+ "* ( ' ) ) 0 %+ ' " " "&, $ , "'"( &! "# $ ! 0 %+ ' " " "&, $ , "'"( ) " $ $ * ( 1.6) % " " " " : 0 %+ ' / 0 %+ ' " ' 1" $) $ , (, & "'"( ) , * + $"# «$% " » ( 1.6) " "# " " " " : 0 %+ ' " ' 1" $) $ , "'"( .
  2. 2. -. . , & 1. 1. " % "& "+ , ' ) # , %+ "* ( ' ) ) $ ) , ( ) * , / : ! "# $ ! "'" "*& " " "& "+ , ' ) 1. " &2, ' 1" $ $ & % " "& $ , "* $ ' 1" $% $ & " * 1, " , "$ ' 1" $% $ & " * 1, " , " : *$ $ 1 &2, " % " xi, (, ' $ &, /, i 1" " *$ $ " $ & ". 2. 1, * , " * % " , " ) " (, $ * 3 . 3. "' $ #, " " % " xk, " * * % " k " " , $ , " *,. n xxxxxxx ++++++++ ...1 65432 -. . , & 1. 1. " % "& "+ , ' ) '! "# $ ! ' * " " "& "+ , ' ) : 0 , 5 $%$$ " , 3 " $ 2 # " +% " . % " % " " ) /, 4 +% " , /, " " $%$$ , +% , $ % " , +% , ; : 4 " " ) * * & %$ * %+ ' ) • * " $%$$ " +% " & : • * " " +% " & : • * " # " +% " & : ) * & : " 2 "# " '& % " " x4 " * * . 42 1 xx ++ 3 xx + 2 1 xx ++ )1)()(1( 2342 xxxxxx +++++ -. . , & 1. 1. " % "& "+ , ' ) (! "# $ ! " "* % $ " " " "* % " , ' " 2 $1) $ . 2 & $ " " * * , ' ' % / ( $ ) "$ " " 1 " , # " . : 2342 )1)()(1( xxxxxx =+++++ ) " " % " x4 & 2, " & % " %+ ( 2 # ( * $ " % " & : (2 ,1 ,1 ) $ (0 ,3 ,1 ) 98765432 98776554332 2725232 2753 275533 234323 32423 222222 )1()1(2)1(2)1( )1)(22( )1)(( )1))(()()(1( xxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxxxx xxxxxxxx xxxxxxxxxx ++++++++= =+++++++++++= =+++++++++++= =+++++= =+++++++= =+++++++= -. . , & 1. 1. " % "& "+ , ' ) )! "# $ ! : * " "*&2 $ " $% "+ ( $ "* $ , $1) . .(.: • "* 3 $ , "' $ # % " " x3 " * * . & : 3, (" 3 # . * $ " # & : (2 ,1 ,0 ) $ (0 ,3 ,0 ) $* $ " # & : (2 ,1 ,0 ) $ (0 ,3 ,0 ) $ (0 ,1 ,2 ). • "* 8 $ , "' $ # % " " x8 " * * . & : 1, (" 1 # . * $ " # & : (4 ,3 ,1 ) • "* 10 $ , "' $ # % " " x10 " * * . & 0, ' ( # * "* 10 $ , . • $.".$. 5 4 ! " ' ( " " "# * $ % $ " $ " &2 $1) .
  3. 3. -. . , & 1. 2. " % "& "+ , " "&, # , %+ ' " " "&, $ , "'"( $ ) , ( ) * , / : *! "# $ ! "'" "*& " " "& "+ , " "&, 1. " &2, "'"( " "& $ , ' " , " "&, $ "'"( * 1, " , " :$ "'"( * 1, " , " : *$ $ 1 &2, " % " xi, (, ' $ &, (, i $ & "'"( . 2. 1, * , " * % " , " ) " (, $ * 3 . 3. "' $ #, " " % " xk, " * * % " k " " , $ , " ' ,. n xxxxxxx ++++++++ ...1 65432 -. . , & 1. 2. " % "& "+ , " "&, ! "# $ ! ' * " " "& "+ , ' " " "&, : 0(" 50 ' $ $ " +% " . % " % " " ) " " , 3 ' , ) " 1" '& " " # 3 +% " , " 2" '& % " +% , $ " 3" '& " ( " 4 +% " . : 4 " " ) * * & %$ * %+ ' " " "&, . • * 1 "'"( (1" '&) & : • * 2 "'"( (2" '&) & : • * 3 "'"( (3" '&) & : ) * & : " 2 "# " '& % " " x50 " * * . 32 1 xxx +++ 4953 ... xxxx ++++ 5054 ... xxx +++ )...)(...)(1( 5054495332 xxxxxxxxxx ++++++++++ . "'" "*& 1. /& , ! "# $ ! ' * : 0 , 50 ( " " & , 5 ), 60 ( " " & , 10 ) $ 80 ( " " & , 20 ). % " % " " "# /" 40 ( " " & ; . : & $ $ *" & $ , & "+ " " "# " " " "# /& , . 6 ' " " "&, " %+ " " " & * . ( " " & ; : " %+ " " " & /& , : 7 " x1 ( " " & , 5 ), x2 ( " " & , 10 ) $ x3 ( " " & , 20 ) " *" & " ( . • * x1 & • * x2 & • * x3 & ) * & : " 2 "# " & " " % " " * * 40321 =++ xxx 0, ≥∈ ii xZx 402 ...1 xxx ++++ 3402 )...1( xxx ++++ 40 x 402 ...1 xxx ++++ 402 ...1 xxx ++++ . "'" "*& 2. /& , ! "# $ ! ' * : " " " & * " %+ # , 2) /& , : . : 7 (, /& , + , % * 1, $ " $ " , " $ * 1, " " . 100020105 321 =++ xxx 0, ≥∈ ii xZx : /& , * 1 : % " : • " z1 & " / " " 5, ( : • " z2 & " / " " 10, ( : • " z3 & " / " " 20, ( : ) * & : " 2 "# " & " " % " " * * 100020105 321 =++ xxx 0, ≥∈ ii xZx 5 10 1000 1 ...x x x+ + + + 1000 x 10 20 1000 1 ...x x x+ + + + 10004020 ...1 xxx ++++ 5 10 1000 10 20 1000 20 40 1000 (1 ... )(1 ... )(1 ... )x x x x x x x x x+ + + + + + + + + + + + 1000321 =++ zzz
  4. 4. . "'" "*& 3. +" " 8 "# " %(" %! "# $ ! ' * : 0 , 50 ( " " & , 5 ), 60 ( " " & , 10 ) $ 80 . : " "( $1, " $ "* " $ " + ' 1" $ " 2 "# " %(". % $ ) " /& , " ' &( +" " 2 "# " %(" $ " " " "# * " %+ " "$# . $1, & *" ( " " & " "&2" " % $ *" + " "&2" " $% + " . ' * : 0 , 50 ( " " & , 5 ), 60 ( " " & , 10 ) $ 80 ( " " & , 20 ). % " % " " "# /" ( " " & /& 1000 ); : 4 " " ) * ' % & %+ "* % " " $ $1 2" +" " 2 "# " %(": " 2 "# " & " " % " " * * 1000 x )...1)(...1)(...1( 100040206002010250105 xxxxxxxxx ++++++++++++ . "'" "*& 4. /& , ) &! "# $ ! ' * : 100 , " ( ' $ $ " ) + & $" " $ %$ $ +" % " 4 % . ) * % * , &2" % " % , + ) " $ +" ' # & * # " & " " . : 7 $ ) , /& , * " " " , * , ' ( ' ) $ $ " " " % & , /# , + ) " ( " " "# . % 1 %2" ' & "'" "*& . % , + ) " $ +" ' # & * # " & " " "# , + ) " $ +" & $ $ % " & " ) " $ +" ) . : x1,x2,x3,x4 + ) " $ + & " 4 , " (# : % " " " "# & , : $ )1(1004321 =+++ xxxx 0, ≥∈ ii xZx )3(32 xx ≥ . "'" "*& 4. /& , ) ! "# $ ! (…. ( ….) & , (2) * 1 : % " $ & , (3) * 1 : % " $ ) (3) (1) $ (,: )3(122 xsx =+ )4(233 xsx =+ 02 ≥s 03 ≥s $ ) (3) (1) $ (,: " "& $ " (4) & " : 1002 100)( 4322 43222 =+++ ⇔=++++ xxsx xxxsx 10023 10022 100)(2 4233 43233 43233 =+++ ⇔=++++ ⇔=++++ xssx xxssx xxssx . "'" "*& 4. /& , ) '! "# $ ! " "& * 1 : % " : • " z1 & " / " " 3, ( : • " z2 & " / " " 2, ( : • " z3 & (, & " %, ( : 1004321 =+++ zzzz 9963 ...1 xxx ++++ 10042 ...1 xxx ++++ 1002 ...1 xxx ++++• " z3 & (, & " %, ( : • " z4 & (, & " %, ( : ) * & : " 2 "# " & " " " * * . ...1 xxx ++++ 1002 ...1 xxx ++++ ( ) ( ) ( )21002100429963 ...1...1...1 xxxxxxxxx ++++⋅++++⋅++++ 100 x
  5. 5. . "'" "*& 5. "* % 0 (! "# $ ! ' * : 0(" 6 & " + + &" -1, 7 & " -2, 11 & " -3. . : & ' $ $ & "* % . $ " 2" $ " $ & '#" " , $ " " *$ $ " " $ , . $ 1 & ' " , & %+ "* " " " & , ' "& * " % '#" " . ' * : 0(" 6 & " + + &" -1, 7 & " -2, 11 & " -3. $ * ) '#" 1" " 12 + + & $ " *% " 2 & % $ + + &". " " * + & $ ? : $ & /, *$ " ' % 12 + + &, * " 1" . " % " . " (" , % " .(. 3" " 1" 1" " " # 4 + + & -1, ) 3" 2 + + & -1 * $ " " & " " % " 2" 1" . • - + & -1 ( % 2 ) 4), : • - + & -2 ( % 2 ) 5), : • - + & -3 ( % 2 ) 9), : ) * & : " 2 "# " & " " % " " * * 432 xxx ++ 12 x )...)()(( 9325432432 xxxxxxxxxx ++++++++ 5432 xxxx +++ 932 ... xxx +++ . $ 9 $ % 1 ( ) ) * " " " " & " %+ "* k $ , % n (, & 3 . (-) " " % " " '& " " , ' ) "*) ; ( ) " & " *$ $ " ; )! "# $ ! . $ 9 $ % 2 ( ) ) * " " " " & " %+ "* k $ , % n 3 . (-) " " % " " '& " " , ' ) "*) ; ( ) " & " *$ $ " ; *! "# $ ! . $ 9 $ % 3 ( ) ) * " " " " & " %+ ' " n " "&, $ , m "'"( . (-) " " % " " '& " " , ' ) ' " ) ; ( ) " & " *$ $ " ; ! "# $ !
  6. 6. . $ , 1 . , "# (x) = (1 + x + x2 + x3 + …. )n. " % $ , " #" $ " %( ; 1. " xk A(x) & & " " % , ' " ) n &' , $ , k ' $ $ "'"( . ! "# $ ! 2. " xk A(x) & & " " % , ' " ) k &' , $ , n ' $ $ "'"( . 3. " xk A(x) & & " " % , ' ' $) +" " ) $" n " (" k ' $ . 4. " xk A(x) & & " " % , ' ' $) +" " ) $" n+k–1 " ( &2" % k " $ n – 1 ' $ . . $ 1 "* 1 $ , & * $ "' &/ " % " " " "&" '& " % " /" 15 $ & % 30 ,30- $ 30 /" " ( " '#" , " ( " & -, " ( " 4 $ " " # 10 % $ & . ! "# $ ! . $ 1 "* 2 0(" ' 4 $ , 2 ), 5 $ " 1 ) $ 7 $ , 0.50 ). ' ) * $ "' &/ " % " " " "&" " " "*&2 " % " "* 3 $ , ; %! "# $ ! . $ 1 "* 3 ' ) * $ "' &/ " % " " " "&" " " "*&2 " % " ' " 20 % " , +% , 3 ' % : 1. " 1" '& " ( " 4 +% " . 2. " 1" '& " " # 2 +% " . 3. '& " ( " 3 +% " 4. " 1" '& " ( " 2 $ " " # 5 +% " . &! "# $ !
  7. 7. . $ 1 "* 4 0 " " 50 $ $ . " * " & ' $ $ % + " 1 $ "# $ , 2 $ ) , 1 % " + " , 5 $ ) $ 2 % " + , 10 $ ) . * 3 * " ( " " & * " " "* % , ' 1" $) % , " " "&" " " & #( " %(" " . " '# " " "*& " ; ! "# $ ! . $ 1 "* 5 100 % / ' , $"# * 1 &" ( " , "# ' $ $ " ) %$ /" "" % * " ' $" % 3 ' " "" "# , , ,- $ . ) * $ '# " x " "& " '& " % , % , *& %, % A. ( " % " " , ) " /" $ "" %. B. " "" % " ( " % " + " "" % '! "# $ ! B. " "" % " ( " % " + " "" % - $ " "" % - " ( " % " + " "" % .

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