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Section - IIToghrs ed nomals, Cudaluq Asynpioles, Singuld poinli, TFcing of (]W*. SEMESTER ICalculusSecfior -ILinit ed mnLinuitr, Types of disconrinniries Differentiability of nrdions. Sum6siledrifeEntiatioq Leibdtzk tbeorm, Panial differenliation, Eulers thcoren on hodogtueous Section - IIIRolle's $turem, Mean value $eoEns. Taylor's thmEn wifi Lasrmses ed Cauchy's fomsofrmlda. Taylor's seies, Mmlauin's sdies ofsiD r, cos r, e', log(l+'), (l+r)", Applistionsof ded !al!e theorens to nonoronic nrcdoN &d inequaliris. Mdina dd minina. RFERxNcEs:i E, AntoD, I. Bivers md S, Dr!'s, Cu lcuhs, Jobn Wiley dd Sons, Inc., 2002.2. G ,B. Thohtu dd R. L. 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indelendelce dddepmden of rectos, bdrs ed dimdron of a v4tor sFa. TDes of Bshices, RanI of anabi{, trvmdce of 6nk under elemdllrv tdsfomatios' Reducliot to nomal iomSoluiiod ofliner lonogenturs dd mn_honogeneous equtioDs with nuber of equations ddunlnoMs upto fou, Carley-Emilton rhoom, C!@cteristic roots dd veclors Section - IIDe Moiws theorm Oorh intecraL and ntional index) SolulioG of equations usnrsdgononeirt, Exposion for cos r md sin d in lems of powqs of sin t md cos r, Expmsionof cos'r md sin'xilt@s of cosine md sine ofnultilles afa Sumation of senes Relationbctu*n roob md coef6cients of ,'h degee equatiorL SolurioN of cubic dd biquadEticequarios, vhm sone conditiods on ioots of ihc equlion ee siren Stmnetric tuoclions of lherools for culic dd biqudralic equarions. Section - mIlteses moduto ,, ?edntalioN, Groups, Subgroups Lasrmse's Tlreoen' Eulers Tncoren'slmetry ercups of a Fgnenr of a line md reguld , gans for n - i, 4, 5 md 6 Nngs ddsubdngs in Lhe codexr of C[0,1] md Z, REFERXNCES:L John A, Be*hy ud WiltiamD.Rr^ir, Abstact Alsebld with a Canctete lhnadudion,PreDticeILl,19902. N - J, Gnbe.r, Moden Abs7a.t Algebru with Appttatio$' lohn Wrlev & Sons 1976 endstream endobj 29 0 obj 1283 endobj 30 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE2_TEXTON endstream endobj 31 0 obj << /Length 100 >> stream q 612.00 0 0 792.00 0.00 0.00 cm /Obj24 Do Q q 0.196 g 478.08 0 0 686.16 46.08 38.88 cm /Obj25 Do Q endstream endobj 32 0 obj << /Type /Page /MediaBox [ 0 0 612.00 792.00 ] /Parent 13 0 R /Resources << /Font << /F3 7 0 R >> /XObject << /Obj24 24 0 R /Obj25 25 0 R >> /Subtype 28 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 30 0 R 31 0 R 26 0 R ] >> endobj 33 0 obj << /Type /XObject /Subtype /Image /Width 850 /Height 1100 /BitsPerComponent 8 /ColorSpace /DeviceRGB /Filter /DCTDecode /Length 27268 >> stream JFIFdd (B+(%%(Q:=0B`Ued_U][jxjqs[]gɺǙ(#(N++Nn]n  }!1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyzw!1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyzLR! ?5hkD 1VI@%PI@%%!bP\P]``.@ K`(E.(PP(RP@ĥ1F(1@)1@( QQ1F(bb Q1F(E&(zYW 8bxdhR TQ@Q@-!]/?UDf`&(Q1I1I@&(&(&(qK1J0PK@REԀ(c-b Q@(Q^P1@()q@ģ(aE-b(Q@ 1@“b(4 3u3yBZzԱJ( (h!h|; hQEX I@%PI@LRb Q1F(qF(Q@ F(qE-REQ@ K@-PE Q@PE( (Rb PhbQ(b 1@ ((&(0g5- aVw^/?!hb9* %P E@>O35TwEX( (1F(\QZ( Z(Z( (Q@ EPE  (PE%-(( ;PK)7(` =hhJ(JJJU$sHg[~M͸CS+&J)PK@@- }tgjQ@ K@&( ()hPK@(Z()h (Q@ )h)h ) (B(;RPPE (t (i@I()(%PGIsJWIarazxTM PE--]/m#4()}i( ( (h )QH( ( 1@ZPERQ@PEPhaE?JP@(Q3IJ( ( (cI\U}B;c kQifH%x]TuPK@-! q TVPEPEQ@ Eb Z()EP@Q@ K@PI@-PERQEPEPE ZA@ IZ(<Iހ ( ( ()h4@ (3Efkzgb?p?=+baE (  q@KOvojQ@Q@Q@PES QH (h.( ( ( ( (B(  ( (J(<)h ( (((f`_*Ԙ3B@(Cпտ#Uk@ ( (PEHր(CJ(i(hP@͘zlR=FyFzQ :u9ME91?*"sǸ(yc` E1(aE (((4Q@Q@uъ(PA WWӾ6}+8 (CtMUk@ (i(PEPPJ( E-PK@Q@# ' e`A@׎;P1cO RK|(dzN aIQ;Z3@Rc]ZĎE? 5]KFFE>PEPEQ@%-4u((%Q@i(";ZFQ{!yj GCRW@-%]V4A?'GqB(\Q1F(bPъ1EP1@P@i@ Z)h ( ( (0:dsҀjiRqd@ hʗEb ◀@8P! 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Reclification of cuNcs, Volumcs &d areas otsurfaces oftuvolu1i.n.Section - II: Ordinary Djtferential EqualiorsInsr o er exacr dillerental eqlarions ncluding les for tndins inleeralDs tacrors, ftsr orderhigher deeree eqlalions solvable for x. ),, p, w.onskid dd irs FroFdies, Lincd homosdeousequelions wilh conslaDt coefiicients, Lnretu non troDoce.eous cqtrariols. Merhod otvariarion ofFdnerers, EDle.t equtions, Sinulraneous diffedrial eqMrioN, Toral dillerenriat squarions,ADpli.ali.ns ol ordinaly diffeEnrial equalio.s 10 MixruE lr.bl3ms. CroMh ard dccay,Popnl ion drnmics ed orrhogonal r'ajecLones.Section - III: Partial Differential trqratioDsorder ad deerce of paniaL difercnnal equarions, concelt of linc& m.l nontincd pnialdijferenrbl cqnalions, fomarion oI fisr order lanial dife.eniiat equjLioDs, I_inear parrialditrerentiat equations of firsr o er, LasrMge,s nrettrad, Chapilr meltro.l. Clasficaiion .fsecond o.der pafiial ditreFnlial equations jnto ellitric, laabotic ard hyperlolic thouehillutaLiors only, AFpiicanons lo TEfic Florn.IiITXRENCES:L lI, /\nt04 L Bivens and S, Davis, C,/c,t,s, Jobn Viley md Sons, tnc 2oo22 S, L, P.oss. DilJerential Equan,a, Jotxr Wjley ed Sons, ftud Edirion, 1994.3. 1, Snedd.n. 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Numerical AnalysisSolllion oflinetu eqnalions: Gau$id eli in.lion nrclu d ing !i!o1ing, I reaLive n erhods: canssJacobi and causs Siedel nelhods, Roots of No. Ihed equarions, Biseririon ne$od, NeMoD snEtlFd, Inte,?olationr lagtugian rnte.polalids pol)nonials, Newron incrrolalinB potFoniats,Divided ditrerence, Eftr malysh. RrFxRxNcxsl .2 M. lt Jain,2001. 2. Mathematics SlatisticsIleasues of skcMess dd kunosis biyaiate data, Scaner diacld, PilciFles ofteasL squaEsmd irs alplication in fit1jng of cu(es, CoEelalion, Rani coftlarion ed ljned Fgressior,Rmdon !di,ble, Conoept of nathernari cal exp ectations and ih sinple p&lenies, I4omenls Ddmone generating turctions, DiscEte ard conrinuous d$hiburions: Binonial, Poisson.eeonetric, unilotu ard nounal djstibutios md thei! sinple rrcperries. d d I. O, Nher.lrJ.,4 prr dI t.- iral 41o ),.s, < i\ | .d, o-,,\dd o, RIFXRTNCES:L V. K. Roht,si, ,,1, Ii,rndlrtioh to Prcbobilit! Thzary ond Mdthenatical Stdlnhcs., Iot\1wiley dd Sons,19?6. S. R, K lyengrr dd RConluatio., New Age K, Jain, NDerical Mdrods for Scientinc andInremarional lrblisher, 4rb Edition, New Dethi. Inr'aduction to 4hemancal starirnds, AmerindD, C. Eaes, Ihtra.lrction ta the Theary afS.attrliet, 2 n. V. Eogg dd A, T, Cmig,Publhhes Co. Pi. Lrd.,19703. A, M. Mood.nd F. 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