Newton's Method Help [1/1]
- To: mathgroup at smc.vnet.net
- Subject: [mg5073] Newton's Method Help [1/1]
- From: rligeski at webbernet.net
- Date: Fri, 25 Oct 1996 22:48:19 -0400
- Organization: WebNet
- Sender: owner-wri-mathgroup at wolfram.com
Here is the notebook that we used in school. I hope that someone will be able
to help.
Thanks Again,
Brian Ligeski
begin 664 newton.ma
M*"I>#0H-"CHZ6PEF<F]N=$5N9%9E<G-I;VX@/2`B36EC<F]S;V9T(%=I;F1O
M=W,@36%T:&5M871I8V$ at 3F]T96)O;VL at 1G)O;G0 at 16YD(%9E<G-I;VX@,BXR
M(CL-"@EM:6-R;W-O9G17:6YD;W=S4W1A;F1A<F1&;VYT16YC;V1I;F<[#0H)
M9F]N='-E="`]('1I=&QE+"`B07)I86PB+"`R-"P at 3#,L(&-E;G1E<BP@;F]H
M<V-R;VQL+"!B;VQD.PT*"69O;G1S970@/2!S=6)T:71L92P@(D%R:6%L(BP@
M,3 at L($PR+"!C96YT97(L(&YO:'-C<F]L;"P at 8F]L9#L-"@EF;VYT<V5T(#T@
M<W5B<W5B=&ET;&4L(")!<FEA;"(L(#$T+"!,,BP at 8V5N=&5R+"!N;VAS8W)O
M;&PL(&)O;&0[#0H)9F]N='-E="`]('-E8W1I;VXL(")!<FEA;"(L(#$R+"!,
M,BP@;F]H<V-R;VQL+"!B;VQD+"!2-C4U,S4L(&=R87E";W at [#0H)9F]N='-E
M="`]('-U8G-E8W1I;VXL(")4:6UE<R!.97<@4F]M86XB+"`Q,"P at 3#(L(&YO
M:'-C<F]L;"P at 8F]L9"P at 8FQA8VM";W at [#0H)9F]N='-E="`]('-U8G-U8G-E
M8W1I;VXL(")!<FEA;"(L(#$R+"!,,BP@;F]H<V-R;VQL+"!B;VQD+"!2-C4U
M,S4L($(V-34S-2P at =VAI=&5";W at [#0H)9F]N='-E="`]('1E>'0L(")4:6UE
M<R!.97<@4F]M86XB+"`Q,BP at 3#([#0H)9F]N='-E="`]('-M86QL=&5X="P@
M(E1I;65S($YE=R!2;VUA;B(L(#$P+"!,,CL-"@EF;VYT<V5T(#T@:6YP=70L
M(")#;W5R:65R($YE=R(L(#$R+"!,,BP@;F]W;W)D=W)A<"P at 8F]L9#L-"@EF
M;VYT<V5T(#T@;W5T<'5T+"`B0V]U<FEE<B!.97<B+"`Q,BP at 3#(L(&YO=V]R
M9'=R87`[#0H)9F]N='-E="`](&UE<W-A9V4L(")#;W5R:65R($YE=R(L(#$R
M+"!,,BP@;F]W;W)D=W)A<"P at 4C8U-3,U.PT*"69O;G1S970@/2!P<FEN="P@
M(D-O=7)I97(@3F5W(BP@,3(L($PR+"!N;W=O<F1W<F%P.PT*"69O;G1S970@
M/2!I;F9O+"`B0V]U<FEE<B!.97<B+"`Q,BP at 3#(L(&YO=V]R9'=R87`[#0H)
M9F]N='-E="`]('!O<W1S8W)I<'0L(")#;W5R:65R($YE=R(L(#$R+"!,,BP@
M;F]W;W)D=W)A<#L-"@EF;VYT<V5T(#T@;F%M92P@(D%R:6%L(BP@,3`L($PR
M+"!N;VAS8W)O;&PL(&ET86QI8RP at 0C8U-3,U.PT*"69O;G1S970@/2!H96%D
M97(L(")4:6UE<R!.97<@4F]M86XB+"`Y+"!,,BP@<FEG:'0[#0H)9F]N='-E
M="`](&9O;W1E<BP@(E1I;65S($YE=R!2;VUA;B(L(#DL($PR+"!C96YT97([
M#0H)9F]N='-E="`](&AE;'`L(")!<FEA;"(L(#$P+"!,,CL-"@EF;VYT<V5T
M(#T at 8VQI<&)O87)D+"`B07)I86PB+"`Q,BP at 3#([#0H)9F]N='-E="`](&-O
M;7!L971I;VYS+"`B07)I86PB+"`Q,BP at 3#([#0H)9F]N='-E="`](&=R87!H
M:6-S+"`B0V]U<FEE<B!.97<B+"`Q,"P at 3#`L(&YO=V]R9'=R87`L(&YO:'-C
M<F]L;#L-"@EF;VYT<V5T(#T@<W!E8VEA;#$L(")!<FEA;"(L(#$R+"!,,CL-
M"@EF;VYT<V5T(#T@<W!E8VEA;#(L(")!<FEA;"(L(#$R+"!,,BP at 8V5N=&5R
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M(#DL($PR+"!C96YT97([#0H)9F]N='-E="`](')E<V5R=F5D,2P@(D-O=7)I
M97(@3F5W(BP@,3`L($PP+"!N;W=O<F1W<F%P+"!N;VAS8W)O;&P[70T*.EMF
M;VYT(#T at =&ET;&4[(&EN86-T:79E.R!P<F5S97)V94%S<&5C=#L@<W1A<G1'
M<F]U<#L@;F]H<V-R;VQL.R!C96YT97([(&)A8VM#;VQO<E)E9"`](#8U-3,U
M.R!B86-K0V]L;W)'<F5E;B`](#8U-3,U.R!B86-K0V]L;W)";'5E(#T at -C4U
M,S4[(&9O;G1#;VQO<E)E9"`](#8U-3,U.R!F;VYT0V]L;W)'<F5E;B`](#`[
M(&9O;G1#;VQO<D)L=64@/2`V-34S-3L at 8F]L9#L@9F]N=$YA;64@/2`B07)I
M86PB.R!F;VYT4VEZ92`](#$T.R!=#0I.97=T;VXG<R!-971H;V0-"CI;9F]N
M="`]('1E>'0[(&EN86-T:79E.R!B86-K0V]L;W)2960@/2`V-34S-3L at 8F%C
M:T-O;&]R1W)E96X@/2`V-34S-3L at 8F%C:T-O;&]R0FQU92`](#8U-3,U.R!F
M;VYT0V]L;W)2960@/2`P.R!F;VYT0V]L;W)'<F5E;B`](#`[(&9O;G1#;VQO
M<D)L=64@/2`P.R!P;&%I;CL at 9F]N=$YA;64@/2`B5&EM97,@3F5W(%)O;6%N
M(CL at 9F]N=%-I>F4@/2`Q,#L at 70T**"HI"51H92!O<&5R871O<G,@3F5W=&]N
M(&%N9"!.97=T;VY486)L92!W97)E('=R:71T96X at #0IB>2!(87)T;75T($8N
M5RX at 2)IF="P at #0I$97!A<G1M96YT(&]F($-O;7!U=&5R(%-C:65N8V4L(`T*
M16%S=&5R;B!-:6-H:6=A;B!5;FEV97)S:71Y#0H-"E1W;R!I;7!L96UE;G1I
M;F<@;W!E<F%T;W)S+ at T*57!D871E9"!T;R!-871H96UA=&EC82!V97)S:6]N
M(#(N,"`Z.B` at 1&5C96UB97(@,3<L(#$Y.3(N#0HZ6V9O;G0@/2!I;G!U=#L@
M:6YI=&EA;&EZ871I;VX[('-T87)T1W)O=7`[(&YO=V]R9'=R87`[(%T-"BHI
M#0I.97=T;VY;9F-T7RQ[>%\L>#!??2QK7TEN=&5G97(L<F%N9V5?.D%U=&]M
M871I8UTZ/0T*36]D=6QE6WL)9BQX>"QD97)I=BQN97AT87!P<F]X+'!O:6YT
M<RQS;&]P97,L9F-T<RP-"@D)9"QL;W<L:&EG:"QS='EL97,L=FQI;F5S?2P-
M"@D)#0H)9 at D)"0D]($9U;F-T:6]N6W at L9F-T73L)"0D-"@ED97)I=EMX>%]=
M"0D]($1;9EMX>%TL>'A=.PT*"6YE>'1A<'!R;WA;>'A?70D]('AX+69;>'A=
M+V1E<FEV6WAX73L-"@EP;VEN=',)"0D]($YE<W1,:7-T6VYE>'1A<'!R;W at L
M3EMX,%TL:UT[#0H-"@ES;&]P97,]($UA<%M[9&5R:79;(UTL;F5X=&%P<')O
M>%LC77TF+'!O:6YT<UT[#0H)9F-T<R`@/2!*;VEN6WMF8W1]+`T*"0E-87!;
M<VQO<&5S6ULC+#%=72AX+7-L;W!E<UM;(RPR75TI)BQ286YG95MK75U=.PT*
M"0T*"60)/2`H36%X6W!O:6YT<UTM36EN6W!O:6YT<UTI(#`N,3L-"@EL;W<)
M/2!-:6Y;<&]I;G1S72`M(&0["6AI9V at ]($UA>%MP;VEN='-=("L at 9#L-"@E)
M9EM(96%D6W)A;F=E73T]3&ES="P-"@D);&]W"3T@<F%N9V5;6S$L,5U=.PEH
M:6=H/2!R86YG95M;,2PR75T at 73L-"@D-"@ES='EL97,]($IO:6Y;>WM21T)#
M;VQO<ELP+#`L,%TL5&AI8VMN97-S6S`N,#`T77U]+`T*"0E-87!;>U)'0D-O
M;&]R6R,O:RPP+"AK+2,I+VM=+%1H:6-K;F5S<ULP+C`P,5U])BP-"@D)"5)A
M;F=E6S`L:RTQ75U=.PT*"0T*"79L:6YE<ST at 36%P6WM4:&EC:VYE<W-;,"XP
M,#%=+`T*"0D)"5)'0D-O;&]R6R at C+3$I+VLL,"PH:RLQ+2,I+VM=+`T*"0D)
M"4QI;F5;>WMP;VEN='-;6R-=72PP?2P-"@D)"0D)>W!O:6YT<UM;(UU=+&9;
M<&]I;G1S6ULC75U=?7T at 77TF+`T*"0D)"5)A;F=E6S$L:RLQ75T[#0H-"@T*
M"4UA<%M0;&]T6U)E;&5A<V5;5&%K95MF8W1S+"-=72Q[>"QL;W<L:&EG:'TL
M#0H)"0E0<F]L;V<@("`M/E1A:V5;=FQI;F5S+"-=+`T*"0D)4&QO=%)A;F=E
M+3YR86YG92P-"@D)"4%X97-/<FEG:6XM/GLH;&]W*VAI9V at I+S(L,'TL#0H)
M"0E0;&]T4W1Y;&4M/E1A:V5;<W1Y;&5S+"-=+`T*"0D)4&QO=$QA8F5L+3Y4
M86ME6W!O:6YT<RPC72!=)BP-"@D)4F%N9V5;,BQK*S%=73L-"ET-"@D)"0T*
M*"H-"CI;9F]N="`](&UE<W-A9V4[(&EN86-T:79E.R!F;W)M871T960[(&]U
M='!U=#L at 96YD1W)O=7`[(&YO=V]R9'=R87`[(%T-"D=E;F5R86PZ.G-P96QL
M,3H at #0H@("!0;W-S:6)L92!S<&5L;&EN9R!E<G)O<CH@;F5W('-Y;6)O;"!N
M86UE(")F8W1S(@T*("`@("!I<R!S:6UI;&%R('1O(&5X:7-T:6YG('-Y;6)O
M;"`B9F-T(BX-"@T*#0H[6V]=#0I'96YE<F%L.CIS<&5L;#$Z(`T*("` at 4&]S
M<VEB;&4@<W!E;&QI;F<@97)R;W(Z(&YE=R!S>6UB;VP@;F%M92`B9F-T<R(-
M"B`@("`@:7,@<VEM:6QA<B!T;R!E>&ES=&EN9R!S>6UB;VP@(F9C="(N#0HZ
M6V9O;G0@/2!I;G!U=#L@:6YI=&EA;&EZ871I;VX[(&5N9$=R;W5P.R!N;W=O
M<F1W<F%P.R!=#0HJ*0T*3F5W=&]N5&%B;&5;9F-T7RQ[>%\L>#!??2QK7TEN
M=&5G97(L86-C=7)A8WE?.CA=.CT-"DUO9'5L95M["68L>'@L9&5R:78L;F5X
M=&%P<')O>'TL#0H)#0H)9B`]($9U;F-T:6]N6W at L9F-T73L)"0D-"@ED97)I
M=EMX>%]=(#T at 3EM$6V9;>'A=+'AX72QA8V-U<F%C>5T[#0H);F5X=&%P<')O
M>%MX>%]=(#T at 3EMX>"UF6WAX72]D97)I=EMX>%TL86-C=7)A8WE=.PT*"0T*
M"51A8FQE1F]R;5M.6TYE<W1,:7-T6VYE>'1A<'!R;W at L3EMX,%TL:UTL86-C
M=7)A8WE=70T*70T*"0T**"H-"CI;9F]N="`]('1E>'0[(&EN86-T:79E.R!=
M#0I';V%L<SH@($1E=F5L;W` at 86X@=6YD97)S=&%N9&EN9R!O9B!.97=T;VXG
M<R!M971H;V0 at 9F]R(&9I;F1I;F<@=&AE(')E86P@<F]O=',@;V8 at 97%U871I
M;VYS+"!A;F0@;&5A<FX at 86)O=70 at =&AE('!O=V5R(&%N9"!T:&4@<&ET9F%L
M;',@;V8 at =&AE(&UE=&AO9"X@(`T*.EMF;VYT(#T at =&5X=#L@:6YA8W1I=F4[
M(%T-"E=E(&EN=')O9'5C92!T:')E92!N97<@36%T:&5M871I8V$@(&]P97)A
M=&]R<RP at 3F5W=&]N6R!=+"!.97=T;VY486)L95L at 72!A;F0 at 1FEN9%)O;W1;
M(%TN("!!;&P at =&AR964 at =VEL;"!B92!U<V5D('1O(&9I;F0 at =&AE(')E86P@
M<F]O=',@;V8 at 9G5N8W1I;VYS+B` at 5&AE(&9I<G-T('1W;R!O<&5R871O<G,@
M=V5R92!W<FET=&5N(&9O<B!T:&ES('!A<G1I8W5L87(@;F]T96)O;VL at 86YD
M(&-A;B!B92!U<V5D(&]N;'D@:6X at =&AI<R!N;W1E8F]O:RX@(%1H97D@:&%V
M92!T;R!B92!I;FET:6%L:7IE9"!B969O<F4 at =&AE>2!C86X at 8F4@=7-E9"X@
M("A#;&EC:R`B>65S(B!W:&5N(&%S:V5D(&EF('EO=2!W86YT('1O(&EN:71I
M86QI>F4N*2` at 1FEN9%)O;W1;(%T@:7,@82!S=&%N9&%R9"!-871H96UA=&EC
M82`@;W!E<F%T;W(@86YD('=I;&P at 86QS;R!W;W)K(&]U='-I9&4@;V8 at =&AI
M<R!N;W1E8F]O:RX at #0H-"E-O;64 at 97AA;7!L97,@87)E(&1O;F4 at 8F5L;W<N
M("!296%D('1H92!E>&%M<&QE<R!C87)E9G5L;'D at =&\ at =6YD97)S=&%N9"!T
M:&4 at 8V]M;6%N9',L('1H96X@<&]S:71I;VX@>6]U<B!C=7)S;W(@86YY=VAE
M<F4@;VX at =&AE(&9I<G-T(&EN<'5T(&QI;F4 at *'1H92!B;VQD(&9A8V4@;&EN
M97,@87)E(&EN<'5T(&QI;F5S*2P at 8VQI8VL@=&AE(&UO=7-E+"!A;F0@<')E
M<W,@=&AE($5.5$52(&ME>2!O;B!T:&4 at 36%C:6YT;W-H("AN;W0 at =&AE(%)%
M5%523B!K97DI(&]R(%-(2494+U)%5%523B!I;B!7:6YD;W=S('1O(&5X96-U
M=&4 at =&AE(&-O;6UA;F0N("!3='5D>2!T:&4@<F5S=6QT(&%N9"P at 869T97(@
M>6]U('5N9&5R<W1A;F0 at =VAA="!H87!P96YE9"P@;6]V92!Y;W5R(&-U<G-O
M<B!T;R!T:&4@;F5X="!I;G!U="!L:6YE(&%N9"!E;G1E<B!I="X at 0V]N=&EN
M=64 at =6YT:6P@>6]U(')E86-H('1H92!E;F0@;V8 at =&AE(&YO=&5B;V]K+B`-
M"CI;9F]N="`]('-E8W1I;VX[(&EN86-T:79E.R!N;VAS8W)O;&P[(%T-"D5X
M86UP;&5S#0HZ6V9O;G0@/2!S=6)S=6)S96-T:6]N.R!I;F%C=&EV93L@;F]H
M<V-R;VQL.R!=#0I4:&4@;W!E<F%T;W)S($YE=W1O;B!A;F0 at 3F5W=&]N5&%B
M;&4-"CI;9F]N="`]('1E>'0[(&EN86-T:79E.R!=#0I.97=T;VY;9EMX72P@
M>W at L('@P?2P@;ET@('5S97,@>#` at 87,@86X@:6YI=&EA;"!E<W1I;6%T92!O
M9B!A(')O;W0L(&=R87!H<R!T:&4 at =&%N9V5N="!L:6YE('1O('1H92!F=6YC
M=&EO;B` at 9B!A="` at 9BAX,"DL(&%N9"!C;VUP=71E<R!T:&4@<&]I;G0@;V8@
M:6YT97)S96-T:6]N('@Q(&]F('1H870 at =&%N9V5N="!L:6YE('=I=&@@=&AE
M("!X+6%X:7,N($ET(&-O;G1I;G5E<R!W:71H('1H92!T86YG96YT(&QI;F4@
M870@(&8H>#$I+"!A;F0 at 8V]M<'5T97,@=&AE('!O:6YT(&]F(&EN=&5R<V5C
M=&EO;B!X,B!O9B!T:&ES('1A;F=E;G0@;&EN92!W:71H('1H92!X+6%X:7,N
M("!)="!C;VYT:6YU97,@=&AI<R!P<F]C97-S(&9O<B`@;B`@:71E<F%T:6]N
M<RX at 06)O=F4 at =&AE(&=R87!H(&ET(&QI<W1S('1H92!V86QU97,@;V8@('@P
M+"`-"G at Q+"`N+BX at +"!X;BP at =&AE(&EN=&5R<V5C=&EO;G,@;V8 at =&AE('1A
M;F=E;G0@;&EN97,@=VET:"!T:&4@>"UA>&ES+B!4:&4 at 9W)A<&@@;V8 at =&AE
M(&9U;F-T:6]N(&ES(&1O;F4@:6X at 8FQA8VLL('1H92!F:7)S="!T86YG96YT
M(&QI;F4@:7,@9&]N92!I;B!B;'5E+"!A;F0 at =&AE(&-O;&]R(&]F('1H92!T
M86YG96YT(&QI;F5S('1U<FYS(&UO<F4 at =&]W87)D<R!R960 at 87,@=V4@<G5N
M('1H<F]U9V@@=&AE(&ET97)A=&EO;G,N(`T*.EMF;VYT(#T at =&5X=#L@:6YA
M8W1I=F4[(%T-"D5804U03$4@,3H@(%=E('=A;G0 at =&\ at 9FEN9"!T:&4@<F5A
M;"!R;V]T<R!O9B!T:&4 at 9G5N8W1I;VX@(&8H>"D@/2!X7C,@+2`R('@N("!4
M;R!G970 at 86X@:61E82!W:&5R92!T:&4@;W1H97(@<F]O=',@87)E(&QO8V%T
M960L('=E('!L;W0 at =&AE(&9U;F-T:6]N+B` at 3V)V:6]U<VQY(&]N92!O9B!T
M:&4@<F]O=',@:7,@('@@/2`P+B`@(`T*.EMF;VYT(#T@:6YP=70[(&YO=V]R
M9'=R87`[(%T-"E!L;W1;>%XS+3(@>"Q[>"PM,RPS?2Q0;&]T4F%N9V4M/GLM
M,34L,35]70T*.EMF;VYT(#T at =&5X=#L@:6YA8W1I=F4[(%T-"DET(&QO;VMS
M(&QI:V4 at =&AE<F4 at 87)E('1W;R!M;W)E(')E86P@<F]O=',L(&]N92!A="!A
M<'!R;WAI;6%T96QY("`M(#$N-2P@('1H92!O=&AE<B!A="!A<'!R;WAI;6%T
M96QY("`Q+C4N("!4;R!A<'!R;WAI;6%T92!T:&4@<&]S:71I=F4@<F]O="P@
M=V4 at =7-E($YE=W1O;EL at 72!W:71H(&%N(&EN:71I86P at 97-T:6UA=&4@;V8@
M('@P(#T@,B!A;F0@;VYE(&ET97)A=&EO;BX-"CI;9F]N="`](&EN<'5T.R!N
M;W=O<F1W<F%P.R!=#0I.97=T;VY;>%XS("T@,B!X+'MX+#)]+#%=#0HZ6V9O
M;G0@/2!T97AT.R!I;F%C=&EV93L at 70T*5&%K:6YG("!N(#T@,B!W:6QL(&=I
M=F4 at =7,@='=O(&ET97)A=&EO;G,L(&]N92!A9G1E<B!T:&4@;W1H97(N#0HZ
M6V9O;G0@/2!I;G!U=#L@;F]W;W)D=W)A<#L at 70T*3F5W=&]N6WA>,R`M(#(@
M>"Q[>"PR?2PR70T*.EMF;VYT(#T at =&5X=#L@:6YA8W1I=F4[(%T-"D]N92!M
M;W)E('1I;64 at =VET:"!T:')E92!I=&5R871I;VYS+"!O;F4 at 869T97(@=&AE
M(&]T:&5R+ at T*.EMF;VYT(#T@:6YP=70[(&YO=V]R9'=R87`[(%T-"DYE=W1O
M;EMX7C,@+2`R('@L>W at L,GTL,UT-"CI;9F]N="`]('1E>'0[(&EN86-T:79E
M.R!=#0I)9B!W92!D;R!M;W)E(&ET97)A=&EO;G,L(&ET('=I;&P at 8F4@9&EF
M9FEC=6QT('1O(&ME97` at =')A8VL@;V8 at =&AE('9A<FEO=7,@=&%N9V5N=',N
M(%=E('-W:71C:"!T;R!.97=T;VY486)L95L at 72X-"CI;9F]N="`]('1E>'0[
M(&EN86-T:79E.R!=#0I.97=T;VY486)L95MF6WA=+"![>"P@>#!]+"!N72!C
M;VUP=71E<R!T:&4@<&]I;G1S('@P+"!X,2P@>#(L("XN+B!X;BP at =&AE('-U
M8V-E<W-I=F4@<&]I;G1S(&]F(&EN=&5R<V5C=&EO;B!O9B!T:&4 at =&%N9V5N
M="!L:6YE<R!W:71H('1H92!X+6%X:7,N($ET(&QI<W1S('1H97-E('!O:6YT
M<R!I;B!A('1A8FQE+ at T*.EMF;VYT(#T@:6YP=70[(&YO=V]R9'=R87`[(%T-
M"DYE=W1O;E1A8FQE6WA>,R`M(#(@>"Q[>"PR?2PX70T*.EMF;VYT(#T at =&5X
M=#L@:6YA8W1I=F4[(%T-"DYO=&4@:&]W('%U:6-K;'D at =V4@<F5A8V@@=&AE
M(')O;W0N("!4:&4@;&%S="!F;W5R(&%P<')O>&EM871I;VYS(&%R92!I9&5N
M=&EC86PN#0HZ6V9O;G0@/2!T97AT.R!I;F%C=&EV93L at 70T*268@=V4 at =V%N
M="!H:6=H97(@86-C=7)A8WD at =V4@8V%N('-P96-I9GD at =&AA="!W92!W86YT
M(#$R('-I9VYI9FEC86YT(&1I9VET<RP@;W(@(#$U('-I9VYI9FEC86YT(&1I
M9VET<RP@;W(@:6X at 9V5N97)A;"`@:R`@<VEG;FEF:6-A;G0 at 9&EG:71S+ at T*
M.EMF;VYT(#T@:6YP=70[(&YO=V]R9'=R87`[(%T-"DYE=W1O;E1A8FQE6WA>
M,R`M(#(@>"Q[>"PR?2PX+#$R70T*.EMF;VYT(#T at =&5X=#L@:6YA8W1I=F4[
M(%T-"@T*15A!35!,12`R.B` at 5V4@=V%N="!T;R!F:6YD('1H92!R96%L(')O
M;W1S(&]F("`@>%XT("T@,R!X7C,@*R`S('@@*R`Q+ at T*.EMF;VYT(#T@:6YP
M=70[(&YO=V]R9'=R87`[(%T-"E!L;W1;>%XT("T@,R!X7C,@*R`S('@@*R`Q
M+'MX+"TR+#-]70T*.EMF;VYT(#T at =&5X=#L@:6YA8W1I=F4[(%T-"DET(&QO
M;VMS(&%S(&EF("!X,"`](#$N,"`@;6EG:'0 at 8F4@82!G;V]D(&EN:71I86P@
M97-T:6UA=&4 at =&\ at 87!P<F]X:6UA=&4 at =&AE(')O;W0 at 8F5T=V5E;B`Q(&%N
M9"`R+ at T*.EMF;VYT(#T@:6YP=70[(&YO=V]R9'=R87`[(%T-"DYE=W1O;EMX
M7C0 at +2`S('A>,R`K(#,@>"`K(#$L>W at L,7TL,5T-"CI;9F]N="`](&EN<'5T
M.R!N;W=O<F1W<F%P.R!=#0I.97=T;VY;>%XT("T@,R!X7C,@*R`S('@@*R`Q
M+'MX+#%]+#)=#0HZ6V9O;G0@/2!T97AT.R!I;F%C=&EV93L at 70T*5&AE(&EN
M:71I86P at 97-T:6UA=&4@>#`@/2`Q+C` at 9&]E<R!N;W0@;&5A9"!T;R!A('-O
M;'5T:6]N('-I;F-E($YE=W1O;B=S(&UE=&AO9"!B;W5N8V5S(&)A8VL at 86YD
M(&9O<G1H(&)E='=E96X at =&AE(&EN=&5R8V5P=',@(#$@(&%N9"`@,BX@("!,
M970G<R!S964 at =VAA="!.97=T;VY486)L95L at 72!D;V5S('=I=&@@=&AI<RX-
M"CI;9F]N="`](&EN<'5T.R!N;W=O<F1W<F%P.R!=#0I.97=T;VY486)L95MX
M7C0 at +2`S('A>,R`K(#,@>"`K(#$L>W at L,7TL-ET-"CI;9F]N="`]('1E>'0[
M(&EN86-T:79E.R!=#0I#;&5A<FQY+"!T:&4@:6YT97)C97!T<R!A<F4 at 8F]U
M;F-I;F<@8F%C:R!A;F0 at 9F]R=&@@8F5T=V5E;B`Q("!A;F0@(#(N(`T*.EMF
M;VYT(#T at =&5X=#L@:6YA8W1I=F4[(%T-"E1O(&=E="!T:&4@<F]O="!W92!H
M879E('1O(&-H86YG92!O=7(@:6YI=&EA;"!E<W1I;6%T92X at 3&5T)W,@=')Y
M("!X,"`](#$N,BX at #0HZ6V9O;G0@/2!I;G!U=#L@;F]W;W)D=W)A<#L at 70T*
M3F5W=&]N6WA>-"`M(#,@>%XS("L@,R!X("L@,2Q[>"PQ+C)]+#)=#0HZ6V9O
M;G0@/2!I;G!U=#L@;F]W;W)D=W)A<#L at 70T*3F5W=&]N5&%B;&5;>%XT("T@
M,R!X7C,@*R`S('@@*R`Q+'MX+#$N,GTL-ET-"CI;9F]N="`]('-U8G-U8G-E
M8W1I;VX[(&EN86-T:79E.R!N;VAS8W)O;&P[(%T-"E1H92!O<&5R871O<B!&
M:6YD4F]O=`T*.EMF;VYT(#T at =&5X=#L@:6YA8W1I=F4[(%T-"D9I;F12;V]T
M6R!F6WA=+"![>"P@>#!]72`@<V5A<F-H97,@9F]R(&$@;G5M97)I8V%L('-O
M;'5T:6]N('1O('1H92!E<75A=&EO;B` at 9BAX*2`](#`@('-T87)T:6YG('=I
M=&@@('1H92!I;FET:6%L(&5S=&EM871E("!X(#T@>#`N("!)="!A<'!L:65S
M($YE=W1O;B=S(&UE=&AO9"!A;F0@<F5T=7)N<R!O;FQY('1H92!R97-U;'0@
M=VET:"!N;R!I;G1E<FUE9&EA=&4@<W1E<',N#0HZ6V9O;G0@/2!I;G!U=#L@
M;F]W;W)D=W)A<#L at 70T*1FEN9%)O;W1;>%XS("T@,B!X+'MX+#)]70T*.EMF
M;VYT(#T@:6YP=70[(&YO=V]R9'=R87`[(%T-"D9I;F12;V]T6U-I;EMX72Q[
M>"PR?5T-"CI;9F]N="`](&EN<'5T.R!N;W=O<F1W<F%P.R!=#0I&:6YD4F]O
M=%M,;V=;>%TL>W at L,GU=#0HZ6V9O;G0@/2!I;G!U=#L@;F]W;W)D=W)A<#L@
M70T*1FEN9%)O;W1;+30@>%XS("L at -2!X+'MX+#$O,GU=#0HZ6V9O;G0@/2!T
M97AT.R!I;F%C=&EV93L at 70T*5&AE(')E9"!E<G)O<B!M97-S86=E(&UE86YS
M('1H870 at 1FEN9%)O;W1;(%T at =V%S(&YO="!A8FQE('1O(&9I;F0 at 82!R;V]T
M(&%F=&5R(#$U('-T97!S+"!A;F0 at =&AA="` at =&AE(&%N<W=E<B`@>"`M/B`M
M(#`N-2!W87,@=&AE(&QA<W0 at 87!P<F]X:6UA=&EO;B!T:&%T('=A<R!C;VUP
M=71E9"X@(%1H:7,@9&]E<R!N;W0@;65A;B!T:&%T('1H92!R;V]T(&ES("`M
M(#`N-2P@:70@;65A;G,@97AA8W1L>2!W:&%T('1H92!E<G)O<B!M97-S86=E
M('-A>7,Z($$@<F]O="!C;W5L9"!N;W0 at 8F4@9F]U;F0[(&%N9"P@("T@,"XU
M('=A<R!T:&4@;&%S="!V86QU92!T:&%T('=A<R!C;VUP=71E9"X at #0HZ6V9O
M;G0@/2!S96-T:6]N.R!I;F%C=&EV93L@;F]H<V-R;VQL.R!=#0I%>&5R8VES
M97,-"CI;9F]N="`]('1E>'0[(&EN86-T:79E.R!=#0I$;R!T:&4 at 97AE<F-I
I<V5S('-T87)T:6YG(&]N('1H92!F;VQL;W=I;F<@<&%G92X at #0I>*BEE
`
end
begin 664 newton.mb
M-!0*`!T```#0! at ``%0`````````H`.P";0$`````````````\#\```````#P
M/P```````/`_````````\#\````````20```````@"9````!````````````
M````0'U```````",GT`H`````0`L```````` at #!````7`/X"?P%`,0$`&```
M````____`!$``P`!````````````=&ET;&4`````````````````````````
M````````````07)I86P`````````````````````````````````````````
M``````````$`$ at ``````____`!$``@`!````````````<W5B=&ET;&4`````
M````````````````````````````07)I86P`````````````````````````
M``````````````````````````$`# at ``````____`!$``@`!````````````
M<W5B<W5B=&ET;&4`````````````````````````````07)I86P`````````
M``````````````````````````````````````````$`#`#_````____`!``
M` at `!``````````4`<V5C=&EO;@``````````````````````````````````
M07)I86P```````````````````````````````````````````````````$`
M"@``````____`!``` at `!``````````8`<W5B<V5C=&EO;@``````````````
M````````````````5&EM97,@3F5W(%)O;6%N````````````````````````
M``````````````$`#`#_`/\`____`!``` at `!``````````0`<W5B<W5B<V5C
M=&EO;@``````````````````````````07)I86P`````````````````````
M````````````````````````````````#```````____`!``` at `!``$`````
M````=&5X=```````````````````````````````````````5&EM97,@3F5W
M(%)O;6%N````````````````````````````````````````"@``````____
M`!``` at `!``$`````````<VUA;&QT97AT````````````````````````````
M````5&EM97,@3F5W(%)O;6%N````````````````````````````````````
M``$`#```````____````` at ````$`````````:6YP=70`````````````````
M````````````````````0V]U<FEE<B!.97<`````````````````````````
M````````````````````#```````____````` at ````$`````````;W5T<'5T
M````````````````````````````````````0V]U<FEE<B!.97<`````````
M````````````````````````````````````#`#_````____````` at ````$`
M````````;65S<V%G90``````````````````````````````````0V]U<FEE
M<B!.97<`````````````````````````````````````````````#```````
M____````` at ````$`````````<')I;G0`````````````````````````````
M````````0V]U<FEE<B!.97<`````````````````````````````````````
M````````#```````____````` at ````$`````````:6YF;P``````````````
M````````````````````````0V]U<FEE<B!.97<`````````````````````
M````````````````````````#```````____````` at ````$`````````<&]S
M='-C<FEP=```````````````````````````````0V]U<FEE<B!.97<`````
M``````````````````````````````````````(`"@```/\`____`!``` at `!
M````````````;F%M90``````````````````````````````````````07)I
M86P`````````````````````````````````````````````````````"0``
M````____`!(`` at `!``$`````````:&5A9&5R````````````````````````
M````````````5&EM97,@3F5W(%)O;6%N````````````````````````````
M````````````"0``````____`!$`` at `!``$`````````9F]O=&5R````````
M````````````````````````````5&EM97,@3F5W(%)O;6%N````````````
M````````````````````````````"@``````____`!``` at `!``$`````````
M:&5L<```````````````````````````````````````07)I86P`````````
M````````````````````````````````````````````#```````____`!``
M` at `!``$`````````8VQI<&)O87)D````````````````````````````````
M07)I86P`````````````````````````````````````````````````````
M#```````____`!``` at `!``$`````````8V]M<&QE=&EO;G,`````````````
M````````````````07)I86P`````````````````````````````````````
M````````````````"@``````____````````````````````9W)A<&AI8W,`
M````````````````````````````````0V]U<FEE<B!.97<`````````````
M````````````````````````````````#```````____`!``` at `!``$`````
M````<W!E8VEA;#$`````````````````````````````````07)I86P`````
M````````````````````````````````````````````````#```````____
M`!$`` at `!``$`````````<W!E8VEA;#(`````````````````````````````
M````07)I86P`````````````````````````````````````````````````
M````#```````____`!(`` at `!``$`````````<W!E8VEA;#,`````````````
M````````````````````07)I86P`````````````````````````````````
M````````````````````#```````____`!``` at `!``$`````````<W!E8VEA
M;#0`````````````````````````````````07)I86P`````````````````
M````````````````````````````````````#```````____`!``` at `!``$`
M````````<W!E8VEA;#4`````````````````````````````````07)I86P`
M````````````````````````````````````````````````````"0``````
M____`!(`` at `!``$`````````;&5F=&AE861E<@``````````````````````
M````````5&EM97,@3F5W(%)O;6%N````````````````````````````````
M````````"0``````____`!$`` at `!``$`````````;&5F=&9O;W1E<@``````
M````````````````````````5&EM97,@3F5W(%)O;6%N````````````````
M````````````````````````"@``````____````````````````````<F5S
M97)V960Q````````````````````````````````0V]U<FEE<B!.97<`````
M``````````````````````````````````````$`!08 at ````````````````
M````$D```.C____G00`````` at #!``(`!````````````````````;B33!P``
M$0```/__________`````````0`.`/\`_P#___\`$0````$```````````!T
M:71L90```````````````````````````````````%=!<FEA;```````````
M``````````````````````````R?"`8`$<L``%```0`%! at ``````````````
M`````(`Y0```Z/___^=!``````"P4T`&@`````````````````````!>)+((
M``#I````__________\```````````H``````/___P`0`````0`!````````
M`'1E>'0`````````````````````````````````````5U1I;65S($YE=R!2
M;VUA;@``````````````````````#)\(! at `1RP$`4``!`!$"````````````
M````````,%M```#H____YT$``````(R`0` at ``0``````````````````````
MV at D``#8$``#__________P````````$`90`````````````````````6A$``
M`$#____G00``````0$1`"@````$```````````````````!<# at ``<@```- at .
M``!R`````````````0`1` at ```````````````````'Z%0```Z/___^=!````
M``#P8D`(`````0```````````````````(</```.`0``__________\`````
M```!``4"````````````````````7HI```#H____YT$``````(`\0`8`````
M````````````````````M1```)H```#__________P````````$`!0(`````
M``````````````!FBT```.C____G00``````8&5`! at ``````````````````
M``````!K$0``K@,``/__________`````````0`%` at ``````````````````
M`'&00```Z/___^=!``````"`+$`#`````````````````````````$,5```*
M````__________\````````!``4"````````````````````O)!```#H____
MYT$``````(`L0`4`````````````````````````?14``"8```#_________
M_P````````$`!08````````````````````'D4```.C____G00`````` at %Q`
M! at ````````````````````````"_%0``G@(``/__________`````````0`%
M! at ```````````````````.&20```Z/___^=!``````"`/$`&````````````
M`````````````'D8``#"````__________\````````!``$"````````````
M````````99-```#H____YT$````````K0` at `````````````````````````
M6AD``"P```#__________P````````$`!0(```````````````````"MDT``
M`.C____G00``````8$5`! at ````````````````````````"B&0``V````/__
M________`````````0`!` at ```````````````````&J40```Z/___^=!````
M````*T`(`````````````````````````)D:```;````__________\`````
M```!``4"````````````````````LI1```#H____YT$``````(`L0`8`````
M````````````````````T!H``$$```#__________P````````$``0(`````
M``````````````#]E$```.C____G00```````"M`"```````````````````
M```````P&P``&P```/__________`````````0`%` at ``````````````````
M`$650```Z/___^=!``````"`+$`&`````````````````````````&<;```[
M````__________\````````!``$"````````````````````D)5```#H____
MYT$````````K0` at `````````````````````````P1L``!L```#_________
M_P````````$`!0(```````````````````#8E4```.C____G00`````` at #Q`
M! at ````````````````````````#X&P``=````/__________`````````0`%
M` at ```````````````````%R60```Z/___^=!``````"`/$`&````````````
M`````````````(@<``"U````__________\````````!``$"````````````
M````````X)9```#H____YT$````````K0` at `````````````````````````
M7!T``"````#__________P````````$`!0(````````````````````HET``
M`.C____G00``````@"Q`! at ````````````````````````"8'0``4 at ```/__
M________`````````0`%` at ```````````````````'.70```Z/___^=!````
M``"`/$`&``````````````````````````8>``"0````__________\`````
M```!``$"````````````````````]Y=```#H____YT$````````K0` at `````
M````````````````````M1X``",```#__________P````````$`!08`````
M```````````````_F$```.C____G00`````` at #Q`!@``````````````````
M``````#T'@``2 at ```/__________`````````0`!` at ``````````````````
M`,.80```Z/___^=!````````*T`(`````````````````````````%T?```F
M````__________\````````!``4"````````````````````"YE```#H____
MYT$``````(`L0`8`````````````````````````GQ\``&4```#_________
M_P````````$``0(```````````````````!6F4```.C____G00```````"M`
M"``````````````````````````C(```)P```/__________`````````0`!
M` at ```````````````````)Z90```Z/___^=!````````*T`(````````````
M`````````````&D at ```G````__________\````````!``4"````````````
M````````YIE```#H____YT$``````(`\0`8`````````````````````````
MK"```+L```#__________P````````$``0(```````````````````!JFD``
M`.C____G00```````"M`"`````````````````````````"&(0``+````/__
M________`````````0`%` at ```````````````````+*:0```Z/___^=!````
M``"`+$`&`````````````````````````,XA``!)````__________\`````
M```!``4"````````````````````_9I```#H____YT$``````(`L0`8`````
M````````````````````,R(``$\```#__________P````````$``0(`````
M``````````````!(FT```.C____G00```````"M`"```````````````````
M``````"A(@``*0```/__________`````````0`!` at ``````````````````
M`)";0```Z/___^=!````````*T`(`````````````````````````.DB```N
M````__________\````````!``4"````````````````````V)M```#H____
MYT$``````(`L0`4`````````````````````````1R,``!<```#_________
M_P````````$`!0(````````````````````CG$```.C____G00``````8$5`
M! at ````````````````````````!Z(P``V0```/__________`````````0`!
M` at ```````````````````."<0```Z/___^=!````````*T`(````````````
M`````````````'(D```;````__________\````````!``$"````````````
M````````*)U```#H____YT$````````K0` at `````````````````````````
MK"0``! at ```#__________P````````$``0(```````````````````!PG4``
M`.C____G00```````"M`"`````````````````````````#C)```&````/__
M________`````````0`!` at ```````````````````+B=0```Z/___^=!````
M````*T`(`````````````````````````!HE``` at ````__________\`````
M```!``4"`````````````````````)Y```#H____YT$``````(!,0`8`````
M````````````````````5B4``%(!``#__________P````````$`!0(`````
M``````````````#VGD```.C____G00``````@"Q``P``````````````````
M``````#2)@``"P```/__________`````````0`%` at ``````````````````
M`$&?0```Z/___^=!``````"`+$`&`````````````````````````/DF```S
1````__________\```````"`
`
end