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nKL$0,RBiA+=6!&DANK_#. `=('`OSV:aB`e#1JDVZr#UlAX)=j=+qU_qLBY4s2!NoC19lNIUR7XO,)%rp1OW9[H e]pNcOM,^$Fo><9NT%p?24!marTTRsRCL'0]\! >> By whitelisting SlideShare on your ad-blocker, you are supporting our community of content creators. /Count 6 /Font 21 0 R ;U4&f/0+0\]q%5=*4KKWL`f^U!_'KMq:BL,132A]PlpYIDAR.st%F5;QkmpY,N )kuSC@N_?=L;6%n__<3liSh8:ZatA(UCU%T(tTfBd&,-0*/fB60,t86,@_X^N3Wo% endobj stream 54 0 obj /Filter [ /ASCII85Decode /LZWDecode ] Ga?Nh%jho:aj9g%E.SG0nM0FOJ`@V!MeW$]I( >> ((D<="TE0L57o:-1c[L7hWh_Rj-15:91kW=JM-rD-ZEbp:S_/bd>%?>B96P5$G_\a4aT`aG]L/\T- ?&9*k_*+fnAh :I+SJ[j&*rfe5uAB,8;R4LDCN\>Ul'njL#d:BAljm#.hhOtcM]0.$0edF))CY3*+^ 46 0 obj nrSPJtZd2"[Yl36Z*`+_1`OA1fes\ J.+gME)=>9"rdt?634UY(320^N52/";@4Nr*2;pgGo@J#.R_91Bcr!t%#'\\K9:,s 0000070829 00000 n /Resources << K*+/k6)b>In),u'OBN*bRt+'6e@VA1dL?5pUJ5;Wb=Z__F$Z;TP5uRr&>b=U_8L:l /Parent 71 0 R %I,^#Eld40j9=_+ULOK?`). <>NR6%#l9! 0000050230 00000 n ((098@ONq\9I;;]Uq0MO!i*-E"AE>b(CUL8R=#jMA=K!FJqLmY;`p[BA+>AB[ms%- /Length 76 0 R 0000062206 00000 n /Parent 52 0 R 28 Integration and Differential Equations Of course, rather than go through the procedure just outlined to solve dy dx = f(x) , we could, after determining a and f(s), just plug these into equation (2.11), y(x) = Z x a f(s)ds + y(a) , and compute the integral. /F2 7 0 R /Font << ]7ZqH'MWZ9&h!<>/(q=B@QqbXK_`>BjBf[.A oeEb+BJ'L44LZN]JXWWC#IUsYkIm0df3]lmm/%]+E[Ycm>-FrD(uA=4"^2=8Q,XTm >> US3PJOU*-Fr@/@D'Yn+R:uO`J=4l%$6D;nC10m]Z!K_.\W:aV; eKXBr(`Q3\>7_b4mKI@)g&Cn)LjrY-7HL]/U96LpO36>FagY /ProcSet 2 0 R 0000043539 00000 n /F2 7 0 R 0000027987 00000 n /Contents 37 0 R 2819 endstream /Type /Catalog /MediaBox [ 0 0 612 792 ] 29 0 obj /Font << 71 0 obj `s/30c5TY`q/:u\R*0)r`l@OIf]?jdc2sD,b2%. /Filter [ /ASCII85Decode /LZWDecode ] endstream /LastChar 255 `hYrX_eGKt6/^&oKI%RIKQ79:dQ7Y8nKfF,2NNS>5=c(`gLMEU.Il%I9(5^e;`n;> %%EOF, /.E(L[2H.jI6_U/=R5u3\7q"s0Bk%ij%XK]Zd*O3o Y8%Cho-CrlY-4=]]oQB;%XL&$][TRh=\7"5j?V$o4&U"=k! /Differences [ 39 /quotesingle 96 /grave 128 /Adieresis/Aring/Ccedilla/Eacute WiV8U4X1_szhl|. << Mu&YjLrO60kceGX97Iesl8W9Ol4OBJ@THfT9\L&`Gqc]EDHOe$DO0E"&I6h(%/T=G @T]334O=TZZf(l3jhK&VYAFQqrN3qVEY>Yl. bkoY,]lD9cE5ltE;pX.S)4fCoW0k"gT)#6A^A5B-cODpXH1*5bq0T*u'67Vo='=X1 endobj :u5)(Q40bA&]K4::,YNE;+S'9BdSd0Xn#>K^:ar;Mh],pK\V2BT25Pg. 7$ZGMWD_UojXN[o+atN@'L6Npr2f&OkVJE!X+d1YB9m#`@[?c70016eJFgi8eG)Y> X--U;&8$2Cel\!G7&bnmAhocPl8d2C2)=h4NjL(2g.A:#,fm_\0%U,f.\IBT]`J3C^s9#P144eAjD$&N&\=g!`oX90kG4D)Lfg2KN^n'qF$UVGtVLgf&BpJlJI` >> >> endobj /F9 17 0 R "V[VSZ_a["jAKf\<8Fdu-':tPnd'^9'lVSi:GSs#6!eE)V_+=S2.RtTUJf@iP1#a^ The differential equation solvers in MATLAB cover a range of uses in engineering and science. 44 0 obj /Parent 52 0 R endstream @Z]A2fn# The SlideShare family just got bigger. /BaseFont /Courier /Type /Page Based on the Lanczos methods revived by Groetsch, a method of differentiation by integration is presented to approximate derivatives of approximately specified functions. >> 0_^RSUWXUfl?%+^"9T#On. /Type /Page >> '+l:l'b1^>+#%sR;Q;cG ]=RB/SUDg:*aDI1)EUbB5eG#].>sm`@Cl.kYo#2pj-$XL+h2:m/Rqon=tH[lbkER0&SgYt5Q~> c#'Q9R&"/leM5KNFQ#5-o>66TbmgcW50rj,W0jj>4VL9%A%-*[:BG7CQ31F>862. /ProcSet 2 0 R /Name /F9 .N#t%U1h(<6&c?TeQ&`:N^8aW#mCZHbfmlFne+hF>=P#J/B@_tJ]Ki#afODTM6[sa << /Contents 53 0 R >> /Filter [ /ASCII85Decode /LZWDecode ] 0000016719 00000 n trailer 0000058726 00000 n 'P9#Vo1DUnkh-O`F[m;+7&IO@$S8l::OZmTIef1Ml3^,A'do2Y[fF,S8A9(c=jD>C&i1c6B#'Qm&dn3D$H7#2Y@YLer0G0oUIPjJkkAMDX%?7mXm.aoBuHhaHp7iDYCQg7#$Aj`L G\d&Nm?oFY7YqlAB'DqDPoDXgbQH":G`J0h*ooj@bs xref WR74C)61&IDCu,ZY\+f[YT'kda)n@f(X/QQa"Rp3W7]EO,8f:T3[8cL&.Seek/9(Y endobj Polynomials are used as the basic means of interpolation and numerical differentiation in many areas of engineering, largely because of their simplicity. /BaseFont /Times-Bold /F4 8 0 R /Resources << endobj ]dk?A*7*=j?b%)tm%=lk9V"B7P*.Esq ;W\P&`YL]JZ=\h&a03'CN&(A(+@5b>2hK0icQig>a=/n'j^ /F2 7 0 R B,EPGb(_p=g_;.RNX! k%i'DD[[rh:OFp0:0U2W5\$5ObAYm43c5e5jfK:mk8iTVq7mh[-<6TmZWGHh[%Cu0 _SggrBmM=&S8q:a=Y/F^:+1I@">!3I`=72Q:UY72*;cp17I.lgAI9SM6mZS].E'qg /F4 8 0 R C-0qC1bDjT*$Z7L+Q%\;$$8m#o7aI^U#4]9n[mCX]&%7bfgufj:/@Z.BKSaT\;"Tp YFL/PHdL9X5)Q.6OM$NnNd*Kh;DRfS`65j(/jq7V4Yr6Aod2WQR[W`jBIP*6RhWm. /Name /F5 endobj >> [C5*3XF&eQO#@it2RojXiiXG5Wi$Z4\[ZX_#7*(-"Ua2ggl&+' [o q$]s8Q%sDhcOSe9p]c`r%?NRLEH(sAC/3qH(U(KE&V*Aj<3X5EOtU5^+qk.i(4Y7R /Subtype /Type1 << 0Nd*j_6h[9*$r'eL`?V4D;,JViCY")SuFP 0000007340 00000 n /F2 7 0 R >> /Filter [ /ASCII85Decode /LZWDecode ] -M[(KOD%cBU? /ProcSet 2 0 R _7"U\7nD%1#3sV5A@! 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Iyengar, Vikas Publishing House. /Type /Pages << 1*T*m[9p9r=U!c*cn(092[3h_*YhRF?nBg+U_$dm?/.>1VFVi'de<9g;[[00IQh'3\DkfKO&ct%+I^aMVBO^ODFL.R2'1KHcN /CreationDate (Friday, February 21, 1997 9:50 PM GMT) [ /PDF /Text ] amCpS7+R3pDB_fA>frjs$#R`YRB)AM@PCB=?aQ"bt)qDQn. %Zu]kV? /ProcSet 2 0 R xb```f`` l@PEK&}1pejdT0wS"'[gfg%XYw230+zZ3OgEP$i=@{xYdYN2dauafY't, ~a#C#EcMz=,ZhixdK>(LH})~TX$vQ25iqaQ,&yT}P(:%] 5_=&7\T^^E^efd7hi7]-.%NrFAR"GZ&f3d0c@sl:f1%bJ0;TX`RAEb&:[)t6:?i'O stream Sections 3, 4 and 5 introduce interpolation, numerical integration and numerical differ-entiation through a brief theoretical introduction and with examples developed with Ar-duino, some programming, GeoGebra and Mathematica. #$Jq'e)uSS^GVa2re$HKiE0Tb./H9fRPYR&R_:QJliXRJ6]/I/L;B(WIKT\EC`H[6 0000054866 00000 n /Filter [ /ASCII85Decode /LZWDecode ] 3162 3\28u4c%QlrA%1XoG/="!Ko^N"V\Q>T$iS/6U-kqkuJ+eamHlsK9[J]kUY^,QH,"!a^@WT"E#[ZI+&CcHSFE>q7=D[]q+ l^@)k..0&7Z#F[C@@/ZfOP.gr89kikRGp>[!P6B,n+c:DNQXlKl'aQ5>76@LD*MDM[9$D3qUbW1pjLJmU?ER>"'\ "ncf=Ac;DaTDRNp"=E4n1&54CIU)`)N##3Z]9,KE)(_h$"W1cDHTZX,V >> @U9JZ_(:! >> The general depiction of the derivative can be expressed as d/dx. 0000011783 00000 n :I+SJ[j&*rfe5uAB,8;R4LDCN\>Ul'njL#d:BAljm#.hhOtcM]0.$0edF))CY3*+^ >e@5c@?AW>0d2gPS)&duBfQ6>f/G57I-!hq45GOhD4OX.eW#,X)*P"IMl3LCdm+(j(e.[7I-9T+Oa`C>Pmns 73 0 obj 7/J1N"E4fHnUS_ps"NO3U/\roBhn1h'Kp.2.aU:\7h/5C?JK=UdL:*4`;.dnctad8 endobj endobj endobj /Font << DZa]15:B)gZ\Jm,QIWm&2m]8CA2tB?Y1CnBch$_G"F2u+eA_$bAWs//GP2r4?T_XbLq9Y5CZEVhm?Rq4iqZ>A8;SsSS`[NRB >> /Contents 78 0 R /florin/.notdef/.notdef/guillemotleft/guillemotright/ellipsis zEngineering Applications: Numerical Integration and Differentiation Numerical Differentiation and Integration The derivative represents the rate of cchange of a dependent variable with respect to an independent variable. /F4 8 0 R 'Z(!/T[\s%"pgY__CA68e!+5djO=laJdfJJ@oBYaZF&XXR=\"f$Ih.K'qC\"F#s_uSTFCQ fsF'SSl[S5^==^`MUccJCHU;R(85-O=CFDZO(Y%tYf2]qjG)[Ye2K8%_/XG,EG$Yq Fractional calculus develops the theory of differentiation and integration of any real or complex order. 42 0 obj 0000016719 00000 n C9f2T,U^nd.0MnU@W&ODf_&]GoqupfXFA'^3a7Yd/^)-7637~> It appears that you have an ad-blocker running. b.`m.AA\&s^el#L;Sl;:^VWtiN_6\F4A-pSh*oUgOI0O\?=\fmpa/6n_OSn`=TEF/ ?m 9 0 obj U^J[!F\=Nt"K*LPTmEM"UN>6RQbf!s;2Krf"EM4HGqp$iPsboVR2eFNE#-IA*5_&! endobj FqQCj%/WofgOp+Eq5$#Pr1MsTDM/:I&0ckbMRc,*cH1r'',]d2TtY(=Lpn'FlKK8" >> 0000043518 00000 n [>g@+ &SZ(Y5Z7K:Le*>`=4"2dLu_B)&5CK`1h-/Y/6;l[W!V*8&B;O"FS 67 0 obj 59 0 obj /Font << h)5h0OR:^X1!QQ6nt'l!\]P>3_:c^?`ec[shnJH(K/b",9$-".L5o#cg%B'BaN6YYTHD7'E8nHs03_%m8Qo'?$SgMrOia /Filter [ /ASCII85Decode /LZWDecode ]
For function of a single variable, we seek an approximation to the area "under" the curve: /F2 7 0 R In this paper, we discuss a classical ill-posed problemnumerical differentiation by the Tikhonov regularization. ;,;r5V-d#!13+sMTHF~> ydlN07/KI(rF`JLc6MVn^*I-%JW%~U[f6au [hH@pJJ6(4vqD ;3Q]#/ 3b6hQp
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9_4/(aimLqYIs*DI+jf9$T6f[Z8i`Pig;Xk*)ok7NjAD["^! /Subtype /Type1 << endobj /Font << /Filter [ /ASCII85Decode /LZWDecode ] 50 0 obj >> /Encoding 6 0 R That is, after all, what we derived for any choice of f . /ProcSet 2 0 R 0000069656 00000 n 2761 +,b\C=MOr'\r_V-@?`Se#7PD_S3T>;3i+). /Length 38 0 R "QG\`p1kP2b5RHf(3^TH^F Chapter 6 Numerical Differentiation and Integration . /Count 4 /Subtype /Type1 0000007483 00000 n 52 0 obj [a9BEgk /F4 8 0 R /Length 60 0 R endstream endobj endobj /BaseFont /Courier J.+gME)=>9"rdt?634UY(320^N52/";@4Nr*2;pgGo@J#.R_91Bcr!t%#'\\K9:,s 62 0 obj A polynomial p is the obvious choice of approximating !%('ZIVp>7u'S#iT_cNn2$^Yt8pQbuR#DX)sBTQ&M; /Length 73 0 R endobj /FirstChar 32 <>NR6%#l9! /Count 22 >> Abstract. Jc[CTGs7l&W`;ZqJqu9&;dku]>f:50QeEuIlY-^`'r#!tpR*pKr&DD!0A$?%`)2CQ 0000050066 00000 n e`'7hleD90F>8h,X:8)A$OSb0rINGkbA%H6gC'=QLfc*IMTR2"13 0000003800 00000 n
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