Engineering Mathematics Textbook, Fifth Edition

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IllliiD Ordinary Diffe rential Equations u Introduction to Differenlial Equations 1.1 .nd Terminology 1.2 lnitial-V.lu" Problems 1.J Oifferential Equ'!lQn, .. Mall1.mati..1Model, cr.apter 1 in Aeview fJ First-Order Differential Equations ,., " ,".• " " " ,".• Solution Curves WfthOutl Selmi." 2.1.1 Di'ection Fields ", Autonomou, Fim·Order De, Separ.ble Equations lin.ar Equation. Equ.tions Solohen. by Sub,Mutions ANumeriolr Method linnr Models Nonlinear Models Modeling with Systems of Firnl-Order DE. Chlpra, 2 in R.,iew 1 2 3 " " " 12 33 33 .," ;0 50 ." n OJ " " ., D Highel·Order DifferenliBI Equnlions ,. ,.,. U Thuof"/ 01 Linear Equations 3.1.1 Initial·Value sod Boundary-Velue Problem. l.1.2 Homog&oeou$ Equations J.l.3 Nonhomegeneous Equations " " ,".• ", Reduction of Order Homogeneous Line., Equations with Constant Coefficiems Undetermined Coefficients Variation of Pllameters Cauchy-Euler Equatio". Nonl; ..., Eqn.bOns 'OS lioear Models; Initial-Value Problems 3.1.1 SprinQIMass Systems: FlU U,damped Motion Spring/M... Systems: F,u Oampild Motio" ].I.] SpringIMa« Svstoms: Ori'lin Moti." 3.' U " " 3.\0 J.ll 3.12 '" l.U ..,,,'" Gr.an's Functions '" Serion e'Cn;l "".Ioguo Un.., Modol" Boundary-Valu" P,ebl.m. J.10.1 Initial-Volue Problems 3.10.2 Bounda/y.valul Problems Nonlin.., Models Solving Systems of Lin•• , Eou.tion, Chapler 3 in Re";.w n The L8pl8U Tr8nslorm U " " U ." '" ,.'" ,. '" ... e..t_ 103 Definition of the lopface Trln,!orm Tho fn"""e T'onsform and T"n,!orms o! Derivatives W h",."o Tran'form' on Transform' of Derivat",e, Trln,l.tio" Theorems Transl.tion on the s·uis Translation on t·olis Additionol Propertie, 404.1 Dor",ouoe, of Transforms 404.2 Transform' of fntegr.ls U3 Transform of. Poriodi' Function no Dirac Defta Function SY'lems of Une., Differenti.1 Equ.tion• Chapler 4 in Re";.w '" '" ti,. '" ", ", 'OS ,",.. 2",. ",'" "" "'m m m m no n, '"'OS ., iii Series Solutions of 5.' 5.2 5.3 Equ8tions Solulion; about O'din',,! Point; 5.1.1 Reviewof Power Serie, 5,1.2 Powe,S.,iesSolution. Solulion; about Point. FunClions 5.11 Bessel Fe"Olion, 5.32 Legendre Fun.oa". Chaple,S in Review 254 ,55 ,55 257 'Ill( ,73 213 ,it lBS [lI Numerical Solutions 01 Ordinary Omerentiat Equalions 2118 " " ,".• " II'!lD EuIG' Methods and E,ror Ana,""si1 Runge-Kutta Methods Multislep Methods Higher-O,de' Equalion; and Syslems SGcond-O'der Bounda"!-Value Problems CIllp1G,6 in Review Vectors, Matrices, and Vector Calculus o Vectors Veclors in 2·Space " Vouors in 3·Space " .".. " " " 001 P,odue! Cro•• Product Unos and in 3-Space Vecl0,Spa(as Gram-Schmidt Orthogonafi••tion Pro •••• Chlpte,7 in Review 309 '" '"'" m m ". 'w '" m e-, I. III Matrices '55 U "'Wi. Algobra " "•., Systems 0' lin"or Algeb,"ic EQuations Rank of, Mauix Detorminant, ,.,,, . ., 1.11 P,opel1ies of Oeterrninont$ Inverse 01 a Mot,i• 8.6.1 Finding the Inverse 8.6.2 Using the Inversu to Solve Sy$lams Aula The Eigenvalue Problem Pow... of M.!rices Orthogonal Matrioes Approximation 01 Eigenvalues 1,12 Oilgonalil"lioo 8.13 1.14 8.15 LU·faolo,i,.tion Cryptography .., ..." 1.10 1.16 An Error-Correcting Cod" ",.u,od of Le.,\ SQuares B.n Oi,,,et. Compartmental "'odels Cl'Japter 8 in Review III Vectar Cillculus U V.ctor Function. " Moti.n on I Curve Curvature and Components of Accelaration Pani.1 Derivatives Directional Deri.alive Tangent Planas Ind NOlTIlallines .," ".., . "••• Curllnd Oi•• rg"n, • Lin. Integral. Independanc. of the P.ln Double ,. '"' '"' '",OJ '" "" '" '" '" m .,•• •• .. '50 "' .".. ., ,.'" .. '""" •• '" mJ&J m 9.11 9.12 Doublo Integra's in Polar Coordinales G,een's Theorem 9.13 9.14 Su'faco Inleg,als Stoke.'Thoorom m 9.15 9.16 Triple Inleg,.ls Oive,ge"eoTheo,em m 9.11 Change 01 Variables in Multiple Integ,.'s CIlaple, S in A.view Systems of Differential Equations I]] Svstems 01 lineal Differential Equalions 10.1 10.2 Theoryolline.,Sy".ms Homogeneous lin.., Syslems '0.2.1 m"'inet Re" Eigenvalue. 10.3 10.4 10.5 '0.2.2 Ropealed Eigenvalue. '0.2.3 Campi." Eigenvalues Solutioe by Oi.gonalillnon No"homogeneous linea' Svslems '0,4,1 UndelOlmieodCeofficients '0.42 Venetia"afPeromole,. '0.4,3 Clagonali,ation Matrilc Exponential Chaple, 'Oin RevlelV iII Svslems 01 Nonlinear DiNerenlial Equalions "' ,. '",;> m S75 516 m '" 50< 51> m m '" m ••••"" ... 612 11.1 Auton.mou,Svstem, 013 11.2 11.3 11.4 11.5 Slal>ilil"j of Line., 5v'tems li"earim;o" and Local 5tabilil"j Autonomo", Sv'tem, as M'lnematical Model' Periodic Solution •. Cveles. and Global Stabilil"j SIS S16 S3S 0(2 Chapl"" in Raview OSO MISSING MISSING 1]1 Integ,elion in the Complex Plene t8.1 11.2 113 11.4 Contou,lmeg"ls Caucnv-Gours.tTheorem Independenn or the Path c.ucnV·slotlgral Fennul.. Ch.pte,IB in Aeyiew lID Series and Residues 19.t '" '" '" '" 19.6 Sequen..s and Series Tavlor Series Llu,ent Seriu le,os and Peles Re,iduo, and Residu. Theorem Eyaluauon of Reallnlegrals Chapter 19 in A.yiew ffil Conformal Mappings m., Comple, Functions a. Mappings m, Conro,mal Mapping. m, linea' F,.ctional Trln,fo,metionl m.• s cflw. 'I-Christortel T,. nsfo 'm atie nI m, Poissen Imegnl ,ormulu m. Application. Dlaplor 20 in Anyiew ,,.. ,. '" '" .."', on ". ,. 88' .,,.'" .., on App..dixl Oe'''a".e and Inlng,al formula. APP·2 App.ldixtl Gamma Function APP·4 App..di,11I Tlble 01 Llpllc" T,ansforms Confe,mal Mappings APP-ll APp·9 App..dixlY lodex ,., Crodil$ C, Answors to Soloctod Odd·Numberod P,oblems ... 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E0<9Q E/EQ A;AA8 A 8@A Tjc{ct@"C"0 <?Q 8A 517 D*AQ<'QG&Q1?$Q%&5FQ-9$E0<9Q#NQE/&Q*A5QDDI7>P A<AA!8A 8@ A Q V^x h~u~hlfJn^`Jfs^Nxò~x * ; A <Q #&.19Q L&Q $ %Q A<'Q&$E1<9Q =!:F Q L?0F&Q !8A 8A 19Q E&ADQ <'QF/&Q I91EQ DF&>Q -9$E1<9Q #NQ J1?FI&Q <'QQ !8A 8A Q 8 38A 8A "A 38A 8A " A NQ 509&?0ENQ9%Q = A<'Q&$E0<9Q = : F/&Q>4$&QF?9D*?7Q<'F/0DQ5DFQ&M>?&DD1<9Q0DQ =!8A 82>A Q 8 e }] e }] e} e] e] & > 09$&Q = /DQF/&Q 09%&E&?719E&Q *AQ *(* DQ * L&Q>>4NQ=>1F5DQ?I4&Q =8 8>A <LQL/&9Q 8A -+/ =!8 8>A ]R e3+rp ]R e] e] e3+ * 1FQD&&7DQ>5HD1#5&QE<Q$<9$5I%&Q+<7Q 9 F/EQ ; 8?A Q /&Q 4DFQ ?&DH5FQ &7>/D0O&DQF/&Q '$FQ E/FQ 8A0DQ 9<EQ E/&Q HDH4Q EN>&Q <'Q(I9$E0<9Q E/EQ L&Q /J&Q #&&9Q $<9D1%&@9.Q D19$&QL&Q&M>&$FQ+<7Q/&<?&7Q = 4 :E/EQ A;(8?A *DQ @#C UkdIm\_Idq\Mv_m|w 6?< 3H;>83 " Et7pbbLiGLiX?|tPiXl D>['a@C @C =C #.NW$;'%OaPDa J @! C a @! C N @! C a a @! C a 6'aP\Da8B9O9> [>W'aEGD$?'ANa%DX>&aN'G['aNa AD&'?Na2Ga&'N%G9$8B5aO6'aADTDBaD(aaANNaDBa aNEG8B5aAD[8B5a:BaaA'&9WAa:Ba\79%6a&AE8B5a8Na B'5?958$>' a Oa=C #.O6'aANNa 9Na 58['Baa N6"a $?D\ a BaEHOa a P6'a ANNa 8Na G'?'N'&a3DAaG'NOa a XB8Pa $'?D\a P6'a 'FX9?9$G8XAa EDN9O9DB a # EGPa$a P6'aANNa 8NaPaG'NPa8BaO6'a'FW8@8$IWAaEDN9P8DB a B=9FC6=< J GDAa ' P6'aE>%'aUBN2JaD(aP6'a&8,'G'BO9?a'FXO9DBa9Na "# ;'; C ;C '; C , DGa '; C , C ;C a ;C ! ;C ! N:B5aP6'a:B['GN'a2GAaD(aO6'aN'%DB&aOGBN?O8DBaO6'DG'Aa\'a0B&a # @= C %DNQaaN:B=C 9%=C #. :B%'aN8BQa #/ N:Ba= C O6'a2G'5D:B5aND>WP9DBa%Ba$'a\IOP'BaNa @=C # # #4MwfWgKksao\ kKa{ScK!# # # %DNQa a # =C # #/ =C #. %DNQ a N:BQa Ba # # \'a N''a3DAaO6'a5GE6aD(a * P6PaO6'aANNa 9Na ']79$8P8B5aN9AE>'a 6GADB9%aAD` P8DBaXBT>a8Oa9NaNPGX%<aOa=C "# #.6'a8B1X'B%'aD(aO6'aXB8Pa8AEW?N'a9NaODa:B%G'N'aP6'aAE?8PY&'a D(a[8$GP8DBaODa 2G = # #/ # O69Na %N'aS'aOGBN2GAaD(aS'a'FXP9DBa9Na N8AE?â '; C # @= C B&aNDa , <C C ;C ! aN:B=C #/9%=C #/ # # =C # #. # # # #4KkwhWgOkKaK {WoafScK!## # =C # #/ aN8Ba= C 6'a 5GE6a D(a + 9Ba # # N6D\Na Na \'a \DW?&a ']E'%Oa 3DAa P6'a 8B9O9?a %DB&8P9DBNa P6Pa P6'a ANNa']79$8PNa BDa ADO9DBaWBT>a 8Oa 8NaNUY%<aPa=C #. 1 C(a=C = C \'G'aa4B%TDBa:BaO6'aXNW>aN'BN'a P6'BaEGDE'GRâ 11 C DBaE5'a %& \DX>&a8AE?â =C = C+=C a GO6'Ga O6Ba =C = C+=C a 9B%'a P6'a :G%a &'?Oa *XB%O8DBa &8&a BDOa $'6['a?8<'aBaDG&8B#a4B%O9DBa'['BaO6DX56a9ONaXN'GNaEGD&X%'&a%DM'%PaG'NW?PNa8Oa\NaA'Oa 9B9P8?>â \9P6a 5G'Pa N%DKa $â AP6'AP9%8BN a D\'['Ga 8Ba P6'a Na :G%Na %DBOGD['GN9?a (XB%P8DBa\NaEXPaDBaaG95DLXNa(DDTB5a$âO6'aG'B%6aAO6'AP8%8BaWG'BPa%6\GO_a8Ba79Na $DD<a$0-7:1,C+,;C1;=:1*>=175; CB&aO79Na8BaV#>'&aODaBa'BP8G'>âB'\a$GB%6aD(aAO6'AP9%Na <BD\BaNa O6'a ^VrzrZT_~z_N_rn~ DGa [VnVzJe`VTZnR_rn~ # O79Na P6'DGâ #9Na BDPaBa %%'EP'&a&'0B9O9DBaD(a=C = CBDGa&D'Na DB'a NE'<aD(aa(XB%P8DBa\6DN'a[?W'Na!a'9O6'Ga DGa a>O6DX56a\'aN6?>aBDPaEXGNX'aS8NaODE9%aBâ(XGP6'Ga NW.%'a9PaPDaNâO6OaO6'a:G%a&'?Pa (XB%P8DBa9Na$'NPa%6G%P'I_'&a$â8PNa'-'%PaDBaDP6'Ga*YB%O9DBN a()8Naa%DBP8BXDWNa4B%P9DBaO6'Ba .= =C = C+=C .= C , %Ba$'a P<'BaNa S'a +,/51=185C D(a=C = C 68NaG'NX?Pa8Na=D\BaNaO6'a ~`Z n[vzrvVz N8B%'a =C = C6NaO6'a','%OaD(aN8(P8B5aS'aZ?X')= CDWPaD(aS'aN'PaD(a[>X'NaD()aDBaa DO'aO6Oa EGDE'GPâ 1 A C \9O6)Qa ! B&a ' \9S)Qa , C !a%DBN8NO'BOa\9O6a - 1A C Ba P6'a #,4):2;C 8Ba '%O9DBaa\'a 9B&9%O'&a SOa O6'a OG BN+Ga (XB%P8DBa D(a a 5'B'G>a >8B'Ga CO6 DG&'Ga &9,'G'BP9?a 'FXP9DBa \8O6a %DBNOBPa %D'/%9'BPNa 8Na &; C 3"; C \6'G'a"; C ) C )6(; C )BC 6'a U BN+Ga (XB%O8DBa8NaS'a E?%'a OG BN2GAaD(a4B%O9DBa ?= C $) 150@2A( D]U:IudIQUDxIm}Yqyj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pRÙp?EUY[p>f8NSK>pe>pYRKc>p\D>pNR=>Kp Oip O p 2p JLgLpp J2p J2p 2p [D8\p=>Y<UF:>Yp\D>pNR[ERQpR?p[eRpN8YY>YpOp8Q=pOpEQp[D>p<R`SM>=pYSWQCN8YYpYhY[>NpYDReQpEQp 'FCaU>p pR?p,><\FRQp p ?%280*@ @6,@ *'=/64@ @*>/;/=*)@ /Y>p[D>p)8SK8<>p_8QYAXp[RpYRKc>p ipp gp !gp !gpp p !gp Ya;H><[p\Rpgpp Op p8Q=Op pg&pp p pgp pgp p p @ p.DFYpFYpYhY[>NppeF\DpJp $ pJp !p $!@ .D>p\U9YAUNpR?p>8<Dp>T`8\FRQpEYp Z3Zp Zgp gI+pp 3Zp !3Zpp Z3Zp eD>U>p3Yp njg]lp9= 3 Zp -2p !3Zp gpp !3Zp p p nkg ]mp.D>pSU><>=FQCpYhY\>NpEYp^>pY8N>p8Yp !3GZpp Zpp !3Zp p ,RMcEQCp pAUp3Zp8Q=p `YFQCp S8V\F8KpB8<[ERQYp RQp\D>pU>YaM[phE>K=Yp 3ppZp Zp Zpp Zpp p $"p "p p p p Z p p Z p p 9=p\D>U>AU>p gp]pp 6$7n 4 5p5n p p p Z p p Z p p "dp "0p p %]p p op@ YPpop@ *]pp YPp #p ,a:Y\F[b[FQCp[D>p>fSU>YYERQpAUp3ZpFQ\Rp[D>p@UY\p>Ta8[ERQpR?p pCFc>Yp`Yp Zpp $p Zpp Zpp p "p p Z p p "p p Z p p 9=p 'EQ8KKhp\D>pYRKa[FRQp[Rp\D>pCEc>QpYhY\>NppFYp g]p g]p 0p p p p opp %]p YPp *]p YPpop # 1 0p p YPpopp *]p # p YPp p op %]p 1 .D>pYRK`[ERQp!pEYp\D>pY8N>p8Yp!pR?p,><\FRQp p @ !@@ ".+@&91&(+@#:&5<-7:3@ @ ' %#$' +¨!.¨wQ¨=LE^wt¨'¨ PL¨@¨Z@Ë Lt¨]¨"¨¨@tF¨](¨û¨ZL¨tLw}hËwt@û£ evX¨@v¨^vFEw~ ¨@¨^w~ ¨@vF¨@Ë@z@E^w~¨Zwv¨du¨" P + L}L¨XwLLF¨C¨\L¨Lq¨wR¨ S}w}FL}¨FdQQL}Lu@j¨P@wu¨ + G]"¨ 8Hc¨< ¨ ](¨1¨ 4¨ ' *]P ¨ ¨ <3Ï¨ ' 0P _"¨1¨ ¨ + "P + %!+"&#+ "P + '!+$()+ ?L¨wjL¨Zf¨Lq¨CÏP9@zj@ELÄU¨û¨\LüL¨L@qzkL¨ + ;P6+)GB1)%7P+GM>C4P =wjL¨[L¨Lq¨^t¨'tFL}¨\LËwtF^^wt¨4¨ 'PZLË Lv¨]$¨ 'P](¨ + ev^pj¨*+ -¨$P8¨ #¨[ ¨<¨ PP3¨ #+¨Q ¨ #!P ?L¨q¨wjL¨ G]"¨ ¨ HcÖP1¨ -¨ CgN¨w¨]$¨¨1¨ ¨](¨1¨ ¨ 2zzjdtX¨[L¨9@zj@ELÄU}q¨w¨L@E\¨L|@^wt¨wQ¨[L¨Lq¨@tF¨^qzj^WtX¨X^L¨ [L}L"¨1¨¢]"¡¨'P:1¨¥ ](¡¨=wjetX¨JPLqÜ¨"ÄF(BF FLEwqzwevX¨ [L¨}Lj¨^tw¨z@}^@j¨V@Ewu¨X^L¨ 7`¨1¨ -¨ + #' ¨ - ' ' (¨ 1¨ ¨ ! ¨ ¨ ' ' l ¨1¨ (¨ ¨¨! 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Engineering Mathematics Textbook, Fifth Edition

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Engineering Mathematics Textbook, Fifth Edition

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