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staadard mov .- l)
a
_l
o
P,{FER
I i!r-[-l' ]
CS
I
CO _ ORDIF{,TTE GEOMETRY AND
- LlRDir\.'\TE
GEOPIETRY (:0
CALCTIIIIS
h"tsrks)
:rnts- Ccnics defined b-v Fccus
- Cirecfi-' prope{ty,
rrl properiies .- Geneial eiii;ati.in of thre second degree and tire
l) a pair of lines. 2) a circl'o' 3) a parabcla 3) afl ellipse 4) att
of, conips - Polar co ordinates - Raduciioa oi'stai-,card ibr,ns (. oartesien onil') Trrrcing
to these currJ'es'
and
ncnnals
tion oi'a iine ' crcle and conics - Equations of tang"'nts
staadard
it mov
that
that
ocnditicrr
h-.vperboia .
Iis
-T'erl Rook: The F,lements oiCo
-
orriinate Get'rmetrv -- S'f '- illne-v
and graphing, comPosite functions,
-
two sided limits a',ive exanaplps
limit at infinr{l and intlnite timits
crf an intetrr4! - cronthr-rity test, c'ontinuit-r: of s
R*novalrlr iliscctrtirruiiy atl'J';cniiluous e-xisttsicrt
continuous functions on a irourrdcd ul<lsed
Difrbrcntiabilii-"- at pofu , non rliffcrcntiatrl c tirnctions. cxamplcs
and poifits of inflexion New-ton,s rnetirod fi:ir approxiiiiaiing soiutions ct'equations - cuncaviiv
-i1ryezoidat ana Simpson's rule
nrles of apprcximating <ieftnite intogl'als Properties of
Siatemeai of iscoiid frndam;ntai thecienl ll$r,ral iofarithm and its derivatives,
naturaliirgiiiitiuns,ihegraphofy=irr,t.Exponcrrlialiuiiuiiirt,'.thegrapirofY=,'atiditspropefries
gaph. Hiperbolic flistctions'
the ftxction y = .' , definition and gach . l-he f,rnction ], = iog *x aitd its
'.fert: (-laicuius aaci Anaiytical Geometry -- Thomas
ancl
Fhney
soctions: i.5,1.9,i.i0, apperrclix 3.1.ii= 2.g,3.2,1.9, +.i,6.4, 6.5, 6.6,6.i,6.8,
lNiT iii
f.i,
9.2" 9.3
&9'4
/r !r r---1.^\
( I JiVrt,ll\$_l
CALCTT.TiS
Theolem r.,oroilii'q-, - l,l,:t Inteimediate fotms an<i L - Hospitrls
ai:proximation errors
r.uie Ext.lndrng rhe irtean Vaiue The,-.rern to Ta,r, tdr's Ii onnula. Esdrnat[rg
Text: Caicuir:s and ,':n::i-:'ticai Gtcrnetry - Thornas and F-ianey
Rclis,s iheorem^ l,Iean
-,''a!.ue
Seciioris: -i.;,3.fi..1.9. -f
i0
Arff.i",rti^tic,tl
dorivatirrc of a prorlti't,
Sric.i;essir.,r
-
r-!
"'
r-lerir,atiles -- staEd:rrd
Tcrt Caliuius - l.Ieni.:ai;chiignili Pilla;
ciupl-er
-1
forrls, Leilrnii'n ili:':rent for the nth
-- tl-r -
,tcference hooks:
of Feai A'irail'sis
Ri;irrrctr R- Goiriberg irieiiioCs
Llaicuh:s
Shenthi l.,laral,'anan' l)iiitreatiai
(ieon''etry'
1.
,1
i,l,,t',1.o*.Li€om
3.
4.
S.S.
F-{FER
pillai'
Sastn,
Aliai-v-iical
Engg.ft,'l:rrhemstics
DIFflERENTL\L .Lr'"I} INTEGB-Ar' CALCfi-LtjS
iI
U|'{IT:I
(iS\'tarks)
.in.liidpolar)-Contre.radius.]iidcif{]loofciii-v.aiur$.Erolutesoiii.v.
s anci curr''o sketching
S. E,"Jachandia Rao irnd C'?' Slir'aiha
-i'2.1, 7'2'2' 7:-\'l' 12'i'
?.1..i. 7.tr.4, "1.t.6.
-
12.8,
i3,i,
1-3'2. i-3'-1, 1J'+,
-LII.{ITII
i-l'5, i3'5" 13'1' 13'8' 14'f i4'2' 1+'3'
i2'2'
L2':1' 12'4'
1l'5'
12'5', l2'?',
14'4'
(ls]vftrlke.)
F-eciu'-'tio
s-I'ieid';a
T
illai
tlto culires,'1';'olume of soiids' Lc'gi*r
.Apiliication af interE'aiiorr - Ateir bctwceir
arca in l-rala. co-oidinatcs af surfacc r:'f rcvolution' l" l"ogil- ancl sur-f-acc
Terl: Caioulus ani i{rr;ii-vtic GeorrieiiY - Tltunus aftd FkmJy
'.i'f a
piairi cutte' A''ea
Sec.ficirs: 5.2. 5.'1. 5'6' 5.7; itJ'4'
Cra-'-iti
l,{o:nent of lnEltia cf stLnii.aid bodies, Cenira of
Text: Dynamics and Statics - Llhannapailarn
Xffir":l
"t
S.,i}r,T*]',,'r*u"
..er-ies,
Tavlor's atcl
Taylor's Tlieorer,. {--.rrici,.r"s i-o*rr of Re*rairrdtr"
Niaclaurirt's series'
?.- sections.3'1'1, '11'2' 3i'3' 3i '4'
Text: Ci,lcutus - h{anica.vachagint.Pillai - Chapts
on
g,ri)onrrilri'ar,rl
iogaritnmic lieries and apprci;iirrlaiiGiis baseti
sem;nations b:rsed cn Binciniai,
Bincmia! apci Lcgarithmic series.
Te:rt : Aigebr;':- l.daniclr:aeirag+m Piiiai
Lri\itrT
IY
Calculus
(20\,1ar'ir,s)
of tw'o -"'ariah!cs.
Ftrnctions
of Two or morc v'aliabics,
I-,imits and continriif.v' Partial
I5'1' 15'2' 15"3' I5'4'
cticirs, Euler's'Iheorem' Difrerei'iials' J;:cobians'
lrir.ney
-
sectiens:
ints, Lagrange- s i\4erhod
.2.3,5.2.4,5.-a, 5.-3.1. 5'4. -<.4'i. -5'4'2
lirluiti
Terf:
_to. o
ais
and,a.iiaii-iic Grnirrei-r.7
-
Tii+iaix lnd Fu-ure-r'- s*ctions:16'f i6'2' L{r'3' 16'5' i'5'6'
PAI,ER.IIi ALGEBR,T.
I-'|NIT
I
i:i-A.TRICES tun L)'f HEOF-Y OF EQUATIL-Ii\.
S
(2
5\darl'-s
)
a Matri.t. Elerirentary, 'I'ransiirnnaiions. Reiiuctirirr ur Nt:nnal .and F.chcli:ti Forms,
f-i:ns!si,en+1., ;n[ sq!i'.ii+r1, of s.-,.{tetEr of lirrear: Eqr:aiion-s- Clia:-:ir.'ieristii-' eqi"l;,1i!61 cf a \'Itttrix, Eigen
Tho*rerri, i.iature r;f ru+is oi cii;,gonal. Iiefirriiian. Skow \rrlues ilii,.1Eig.;ii -,'.;,iois. Ca-i ie-v Iiani< <li
"'iarriiiton
Hciiniiien ;iitcl r:i:' iarl, ]', l;'ilrir:"r.
Silrtcic;,it ,:,f f grC;lxontai Thei-r;effi oi Algcbla, I)eductioit tiiai eve4,' poli'nonuoi of dcge e n has
1 aur{ ci*.,, fl rr,rcie. ileiirrior: i;el.xeen zcics an,i coslf-tcients of a polYncmial equa.tion, studl' ct'
s.,,gun.:tii: f.ilc::or: i:rs:ri I zeic ci ai:ci1 nomiaL, Transfcrmaticn l'f eq'+aticns, I{eciprccsi equetions,
Iierrr,a-I,-:ts rtlie ol sig:i!. .\t.ilrneli tti Stur:u's theor-ern.
-t-t:\iiT LI
?'i-IEOliI UF lJ.r\IBl,.]itS,Ll-tB n;EQtIALiTl0S:
(20i\{arks)
Dii.isii:llili'lircor1,'rifurtegari, ilir,isicn aigcriti'rn, G.C.D, E*clirJ'"q algorirlim, Pri:nes and their
Oisirilrutict. Iiirrelanientai iireerrem,-rf Ariihmeric. leive of Eraicrstirrnese, The,:4'(-)r- (:L)ngue{!ce. Basic
ln'oprri1, ,;i' c+rtgt";;;rce. i-i4rar !lr-!lgiitErrr;c,- Fetttut's titt+rern. l,ittle th*+i.;itr. v\tii-ro!t's tllr:o1'e!tr],
Euier's gerreralisation oiFctrrtiat's Tircrlrern- F.uier's,f i.-I'nction, anrl Euier's iheotetir.
Te-s.t: Eiemenr.:u],, itumlrcr-Theory:Darriei itd r-lurtcrn
-
secf.:2.1, 2.2, 2.'-3.
1.
1.,
-i.2, 4.2, 4.4, 5.3, 5-4,
rNM'\TTAT
.i1lr,! rr,' {l,l TTfD(T
! t !,.r}
1)
-iror
positi;e nurnbers,
n enrl n heino of tir,r qerrre sirm
acerrrciiug as l iies i:;:fi1iss1 0 aocl 1 ur n is greater ti:an
Pi+blei:rs t.;si:'J ,:;, ili+ ri.!:l't,r ii:eor*ni.
t.
ii ICTCE SF:\CES (15i.itlr,l.s)
lii
i,rcior lpi{(cs - jir'rrriiion. Brucs. Diincnsiun, Suiis
iii.t-iT
anci di'ect suttis, Tiie space of mailices. Linear
rj(iliriioi!, lv{iiltiplieatii-',i +f ciairi.ces, I.i:rEai Maoningi - \{aliprngi. I-in-cai iBapptngs, The ld+rrra! and
lmrqe ct a L;n*;,;: l,,Ia?:,. (,-,uiiiposition i,ind i-ftiage oi'a Liiie:rr l,tap. Geomeirio appiiuations. Linear rfl&ps
with a liriee.r maD, Basis,
,,*rl i.,[airioes The:ineal .mp a:jsi)uiate.l with a matrix. N{atrix associate<l
C
n,i"i*:.^-..
;!VJ
lvli(!I
^6.i
drltl
i;r^+,.
lulvrll
.4.=,..:iirua.
'i'r'r.r. i i.^11 .ii6-j-1.t
-' ..*..' I r*c Tf trin ,idfliSC t - WeSley
',
P.e!?rcnccs:
Line:.ry AlEelrra : Sc.i.::um Series
L.'in r,ir ^i.lE;rhrir : Httffrnau .{nd i.,un
i.,iarriccs : li,liriiuri seriss
\{aiiis The,:.:t-r: .D. R,.:qhatz R.ao '
Iiigii,:r lilgeiira: i)en'i,u.l anii Cliild
Tireoq,, of Equation s : Blahnranar li
z-c
Y!'rv.l
tr
Theory of F,opaiion: P.K.Chatterji
PAPER
UNIT
I
SET TIIEORY {30 hours)
IV
ALGEBRA
II
{1Sh.{arlts)
Text: Set thecry and P.elated Topios - Scha'xn's Seriss Chapters - 7,. 8. 9, 10
qrperations,
Further rheory of ,{ers - rlge,bia o1- sets, Itinoiplc oi D,:aiity, Lrdexeci sets, {tnelatiTscl
parlitions, Equirralelce relatisrs and patitir-'ps. Furth,;r tfieor-v uf fuitcti,-rr5 Llpil'atioilu - Functit-'u and
diagrams. sei functions, Real vaiued fiinctioq rl,lgebra of real viiiueci flrnciions, Rules of maximurn
Oomalt, Charactcristic functions. Choicc funciion, Cpcrations. Cornmutativc opcr-'aiions, .dssociativc
operations, DisUibutive operations. Iilcrriily olornents, ln-uerse elemuflts, operaiiorr aiid subsets. Cardinai
numben - F,quivalent rits, I)enumerable sets, Continuurn, CarCinal numbers. Cardinal arithmeticInequalities and cardinal ourrrbers, Cantor's theorem, SchroEder Bernstein theorem, Cofif,rilum
hypothesis. Partially and Totalty ordered se.ts * Pafiially ordered sets, Totally ordered sets, Subsets'of
ordered sets, Totally crdersd subsets. First and. last elomer.ts, L,Iaximai ancl rninima! elements. Upper
and lower hound-s, Similar sets. Order types.
(3Cll{alks)
Itr GROIIPS AND Ril\GS (60 hours)
'fext: JohB F'raleigtr: AFirst Course in Abstract Algebra - 3 rdEdn.Llhapters'.1-7,11- 13, 23 &24
Crroups - Binary opirrrtirm. N'Iotir,ntiorq Dcfinition and'propcttios, Tatrlcs, Gtoups. lv{ot'*atio'4
Delirrition and elemerrtr-v'Froperiies! Firiite groups, and Groups and group tables. Subgroups - )Jotation
and terminolog-v. sub sets and sub groups, Llclic sub groups. Perrnutarions - Function and perrnutation,
Groups of permutatiorq Tu'o important exampies, Cycles and cyclio notation, Even and odd
perrnr:tations, The alteraating groups. Clclic groups - Elernentary properties, The classification of
L)NJIT
c_vclic groups, Sutrgroups of finite cyclic groups. Isomorphi-"m - Definition and slemcntary properties,
Htrw to solve the groups arc isomoqriiic and not isomorphic, Cayic,v's tlreorem
Group of cose;ts - Introdrrctir.rq Cosets, Applic;--rns. Nornal sub groups anii Factor gErfups - L-lriteria
ftrr the existence of a coset iEr.rup, hurer automorphisms and nonr,ul gr'oups, Factor gloups! Simpie
groups and applications. Homomorptisms - Definition and elementary properties, The Fundamental
homomoiphism thooicnl Applicatlons
Rings - Definitrons anC basic properties, Multipiicative questicns. Fields. Integral Dornains - Divisors
of zoro and cancellation, integral Domains, Charactenslic of a rhg, Ferunflt's theorenq Euler's
generalization
I.INITUI
L,IMEARPROGR,It'A{ING(30hours)
(151\{arks)
Text: P.K.Gupta bnd lr.{anmohan: Lineu progranrming and Theory of Games
JaI.--J
--; a^6d
!rrutu 4rtu
uvlas
-
9th ECition
-
Sulthan
Formulation of a Linear Programming Problenr. The Linear Piogramming Problenr. Graphioal solution,
General Linear Programming Problerrl Simplex \.Iothod, Dualitl, in . Lineiu Programrning; The
Transpnrtation Prohlem. The Assigrpeni Prcbienr (irfeihod a1d Theorern - without proo!
Sections:O.4,2.1-2;4,3.1-3,7, 4.1-4.f-r. 5.1-:5.3,6,1-6.5, 6-9^ 11.i
-
11.9; 11.11,
fZl - 12.3
Reference books:
c'
@
a
4
+-
(lorrlernporarr, Atr-<iraci Aigehra 4th E<in. Naro.qa Puh Co.
F.B-Bhali;,cli;:r5a - i,K.iaii. d,. il.R i'ragFal - Ba.sic Atrstract ,{lgei;r;i - /d Edn.CLIP India edn.
F-rarrii A-veis Jr. X.{uiiein Alg=bra Schaurn's series
.Ttiseph A Gaii:ari
-
P.}i.Guple ( )oer::tion Resea.rctr. Iiashna Prakasan
r-r,,ra--.;
, a- o,.-,].-,.-.^
.i.ir,.)iidiiiiii
- Lrirr;i.iiiu
P.Looinba
_-
-r'L..-d,
,..-"..!;^or.i.--^
.*,1 nlil:ir9allvrtD,
r rt[Uj y .lriii
rJ,r..,:-.-^t.
i.\-:.)v.i.rvii
Lutear Prosran'::nixg.
P.s_PEli_
T-I|!fT
n {^^.-;!t4lvldelltlllalll
I
1r
REAL A_N-ALi'-{IS
(Z+i*adis,i
- Sciiucncci ard sci'ics, Tr'pc.logi of R
hiiiociuctiori ii i{<'al ,inalysis -- G. Bariis, Donalti R. Siierbert (Third Edn)
Scction-*r" 2.1. 2.2,'.!.3. .t.t,.2.5. 3.L. 3.2.3.3.3.4, 3.5. 3.7. g.l.g.Z, g.3.11.1. I1'2, 1i.3
R+al nuinhors
Trrl:
r
.
iarrili l-lrr
{24Niar*si
Coirtinr:ousfunctioni;, Rcittiiiurlategrais Scctions: 5.3, J.+. i.1,i.7, 1.:.,
I'ert: .biirooucticn tc i<e el Analysis -- G. Ba$le. Donald }t. Sherb:rt (I'hird Ectn)
t,,r!!
L:tPt'c'P' 61 Ini t ina
i;-r
rf Rtal
Sectic'irs: i .9; i.iC
Test:
i'.i*tlhoris
r.-rr*i1'sis
-
F i,:irat',i Grridirrrg
Bota anil Ganima F'rtrr;i'ioni
us . ir.{uiicar,'ricliagoi:r Piiliii,
Secti,ons: 2.i. 2,?-" 2.3.'J. 4. 5
Tcxt : tla lcui
t riqlE:-l: iIT
1-t:I.iI l..i-r
i'"Tar;yanarr
r ! 11 iir*l :.\
\(-avl.!rtr'jr,
SecluencE of Fur,.cilons. Pornt rvise and.L:niforrn Convergepcer [nterc.hange of limits
Texi: Introducricn t+ R.:r1 .'\reiysis - f-i. Emtie, Donnkl R. Shert:ert (Third Edn)
Seutiorts: A.i . F,.7, 9.t,
irtis-
i'€ llt';eSl
f^.L-....-ti^.!
f,-:-^:--!..c
-f'1.r\ad(rr*ill4Livdr
l. I iiivil.rrvD ui
l,4athemetical,tuialysili
Maihenm tical A;irlvsis
,:.:-.1-,';i-"1
ilild
- \\, IiUdin
-'.t. l'ri .P,p<,'siol
- F'.G.3:r';:lcte
P.l,PflR \"'l
'I'ext: ()cmoles \ial;abias rnC ,r,ppllcation
,1-.,,=.1^;ii
i-r,,.* ^1i.^-.i'i
Ui.:i\rrJ11 utltllrdllvlacr
r:.1LLui.
- (-lnLrI'l"EX .4]irLl'SIS
- throl \r Churchil
aad Janies WarC Brc"vrr
- Fiiih ECn. Mc
,,r6r.4".i o't
I T\-i'i 1
(--omplex nufiii,ers --Aieei:r'aic iin:pertics, Georneh-ic irtet1:retatii,rt, Triangie inequalitv, Poiar f<rrm,
E.qri:rr;::rii;1 forrl i]';v;tr: a-rrd roois,.Regioos iu compl+.< 1;!an.:
;lraif ii.; Fulci-iu;ir; - Liiiiits. Coni'iluii.r.. Ded-ratives. Cauchl' - Rieutarur Equatiorrs. atmlltic fiutctiotrs.
,
\,vvjrlrlrlll
Ilarrr',i;iii r: fu nci i r;r
,./a
r;.
'filnctir-rns, 'The
F,lenrerr[nry functions - F.rporrenliai filrcrions. Triganrtrleiric fui'rctions, H1'peri;tiiic
logariiirnic flu-ruti+n irn<! its Bra-nrhes, Cr:lr1rlex exlrcilsiits- Tnverse Trigoiiot-r:eiri+ iud H,"pc-'-holiu
funclioris.
Chapters 1,2&3.
LI}{TT
iI
)ll\,fori,c i
\ & .lrlalr 1\o /
r'
Complex intcpgals - Comple.x vaiueci luneticrns, (,-onloltr inltgrais, ,'inlicit-,t'irrati.rss, Ca,icir)' Gcrr;rsal
T'!.rc*reiir ir*iilr,:ut 1:q,-'uf), Siinply zrrri! l&rltipl,v Ctuul'=,:it,i D+tlafuts, C;ruch-n,' I'tiegl':r! Fatritr:la.
Derivativcs of ,+ruiytic iurrciions, tlorera's Theulm,-Liouvilis's theorenr, Furtdamental Ther-,rem of
Algchra.
Series
-
Lauiuiii series (ii''iilioutproof),
Powel seriEs. Integfaticn Dif,f'erentisticn cf Pot*/or ser-iss,
Coi-i-vei'gencs ci's*queiice and sc-,rie,i, Ta-'vior's serits, F,xainl:les,
Absolute and l-Inifbnn Ccnvergenoe
I-Tniquenes s ol series repre sen'*tion.
cf
Chapter 4 omitting sections Jd &37 and chapter 5.
I lr\r t !
lll
, -!t!\^af?oI
1! -'+rrrtAJ-,
B-esidues and Poles
-
I:er:ciurrs, F-esidue lheorern, Prlncipie part r-rf a funt:ticrn. R-esiclues af Ptries, Ze.ros
Ptles, Erraluatiou uf ftu!>r,.'p;r F-Eal Trrtsgl'als, Trnprcper' irlt;g!'ais ilt..ro1.,.utg sittrs aud L:osilrs,
Definite intcgrais invoiyil* sines iutd cosilrs, i.inear Frasrional Transfonrrariorl Corrfonnal h,Iapping
anc!
Chapter 5 seotions 5-3 to t!0
Chapter 7 secti:ns ,64 io 66,
A1---L-,n,--r:
O
LIralplEI 6 sirutirJlls-4- /-i rX -ar*
f{ef,erence Books:
\i Kanrnekaran - Complex analtsis. f,larosa lfublislring l{ouse
Letrenscn anC ReChefiel Cornplex \;arinhies - Teia lvic,Glaw Hiii Pubiishing Cornpanl'
S Ponnusamy - FoLrno-ations of Compiex anai,vsis Narosa Put'iisiiurg House
J
l.I Shauira
-
Fuuctiols of a Corupl*:r, \,'a.riatrle, Iii"qlui+
PAPEB.
\'iI
Pia1"-asan ir4a-r:riil
I/IICTOR. .{N.AT,YSIS .{ND DIFFEEJEI.ITIAI, EQTIATIONS
tIi\IIT I \'ECTCR,LNALI,ISIS (201t{ar*s)
Text Book: Litroduction io \"ccior Analr,;sis - Harry F l)a'r;is, Ar.licr David Siiidcr:
i{ quick Relier!- of producls o1'veutoi's and tlieir ph_1'sical inierpreiaiioi-rs
Chapter
l.
Sections 1.9,, 1.12. i.11.
-
6tt'Fldn.
l.Ij
Ye;icr Punctiors cf'a single l,,irirbie, Ileri',aii'"';s of
:'.
i.erior w.r.i a singte per;:r:etcl, Derivatir,'es of
procriucts, Spac.e Cunres, \ielocities anci T'angents, Frerurets Fonnulas
e)
2.i.2-2, ?-3, Z-4
Seiikr aiicl Ve':to:r f:ri*1r. ,5,:a1rrr f,iqij-q, Isotrnii.,: srrrfa,:.es, Gratlients, Ve,ltcr fie1,J; al1,J Flcr.t lurcs.
-tr-=uti'ir Itle'-' -lties
Divcr gence, Curl. Dcl i.iotatiot.
Chapier 3 ssciit;ns 3.1.3.?.3 +" 3.5- 3-6- 3.9
Inoiational Vecior Function, Scalar I'ot;ritie! (Del-;nition.onll') Solenoidal Vector Field (Deftnition on11')
Chapter 2 Seclirrns
Cha,.^tel'4 Sectioirs 4.4. '1.6
lntegraticn of Ysotors, Line integrris
i,',.--l[li.::;.tu,,ou
zri,J Exarttples (Ph;r"*icitl
tsaritpies':r*itttd)
Scciiou.l.9
\.'olunic intcgt'ai
Sgullutl) +. 1V
'I'heorern t-c'r'a plane and
Staremer.r ot'tlcuss,s'l'heorern. Stoiie's=fheorern anil Green's
their simple
appiicaticns (I'-:levant stciicns irom chapter 4)
LI}'iiT
II
{irdinr4'DifferentielEqtutions
(20h'iarks)
Basic ,loiicepts and irjeas- Ge,trlelti; consiiierations, Isoclines, Separatile equationr Equaiii:ns redocible
to separal;le fi;ini. E;<aut Qiftrer-riiai Equaiions. irrteguating faciors. Linear ftrsi'otder equatiorx,
frariaiion of Pariiineiqs. Farailies of curves, Ottftogonal T'rajeotories, Pieard's iteration methods,
E;iisience iiid uniiiueiiess of s+iutions, Homogsneous linear eqr:ations of seconil cr':10r, Hoinogoneous
sccond crcler equations of constant coeit-rcients. ,jenelal sclutions. Basis. Initial rrslgg problem, real
rcots. Complex rco'.s. D,:u$le roots sf cirarircterisiic equation, Diffelenriai operirtors, Cauctry equation,
Ncrn - homogeneous eqilations, Strirrirrg non h<lmcgenee)us iinear er$rations, S)'ste.ms of rii.fferential
r,1U:riiurtS,
IINIT
III
I*rplacc's Tranitbrm. Fauiicr scrics and.Partir-l lliffcrcnrial
F.quations (ZON{arks)
ffanstqnri, Linearity' Laplace trar-r'ifbrm of Derilativis and lntegtals'
Laplact Trar,sioirn.
Shifting of tha s- a>;is. Shifiing of the t- axis, Unit step function Differentiation and integration of
fansibims, Convclutioe Farrraffractions, Periodi; function:i, Fr:ether Apptiqations.
Fourier serie.s - Perio<iic. functionb, Trigonometric. series. Fourier series, Euier tbrmula. Funetiors
hi':.4ng ubitri:ry perioti. Even and cdct f,urctions, Helf - range Expansions,
Fartiai Iiifierentiai Equations - Rasic ooncepts, Separation of variairles, I)'Aicmirert's Solution of thtr
ir.-n'erse
iq61a Fr:1uaii1i1-- (lirl di.r'nerrsirrna! Haat-Flov,,,
Text for Urut 1l & unii
i-!r^*r-rT_
S-r!_;ar.'-.!i.:i-'i-i
i- J-.r:vii:'i
-i
Ss.r-:tiorr.s L
-8,
i
ilI
aplace's equation. Potegtial.
E F'rci'zig : idvanoad Engg. it'tatheiiiaiics
.lt1 t1 i''hrntrr
l-'iidl;ivr
-
s
-- i!,
O.ii-:
C.hapter
i
ltl-Sec'rions
I
se-iirrnc- i'iJ1 7 iiJt
L
'
"
-5, Chaprer 1l -Sce-'tions
ke!'eretrce Ec.oi<s:
i;dtelential Equaticns -S. Nara','anln
I-:i,.it ta' t Tracsf'rnns - S chaut'i-l' s seiies
i;,:r-!ner tnailsis ' Scir-aum's Series
'.,'-;ci,- ri,&inlysis -'-i c!', itul:i' s s rrits
.niectot Anal-vsis ii E l\reatirst bum
Eletrrentar-v
i2, Chapfef -i - Section
i - j'
1, Chtpter
i,,:
P'LPERVIII -PROGF{'\hi}IING
UiiIT L - tr'R'ilG-lL\Ir'f"{tNC
AI\ALIISIS
IN C fu iD i{Lr'\iE'i{iCAL
(30lv1ar1ig)
INC
r' Li'urar'v Fulctrons'
t'iNIT
{sor'tarxs)
i-^+r-nrl P''{:u
R,,{ri*a- Falsi }'{othod'
mathod'
Bisection
i"""'"* -
rI
S
lvrethcd
1
ii:;
;1
:,.::H"'if''['.i;;il,,r-s, \1etlori't !'6nrl?rrl
Differauce
arid Backward'
C)Peiators'
l^.,
t**,',^rr"r,".,
D'rffore
(h''{ikre's} }'4eth^ods'
TE:(T
EsclKs
cf
i.Th=cry and Pror:ieir''s
. l.;u;;''i;al
Mcri'ois
'Ref,uremces:
Prcg
scien
rrrirh
(
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c
ii,.rlt*"-
B1,s,3n *.
K'
eil TainM
san'li
"iit
Prograuuiiirg Lairguiigc
N'i Riiciric Thc -r
2''d ec"ii'
ika s Pubiishing
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N Vedaia":t"#ijr
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