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Jackpot Paus di PG Soft Hari ini 2023 Lucky Neko Situs Slot Gacor Pgsoft Hari Ini SITUS SABUNG AYAM SV388 ONLINE DAFTAR LINK LOGIN APK AGEN SV388 Daftar Judi Slot Online Indonesia Paling Gacor di Indonesia powergaming88 %PDF-1.7 % 1 0 obj <> endobj 2 0 obj <> /Subtype 7 0 R /XObject <> /ProcSet [/PDF /Text /ImageB /ImageC /ImageI] >> /Parent 9 0 R /MediaBox [0 0 380.0400 612.7200] >> endobj 3 0 obj <> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 4 0 obj <> stream q 380.04 0 0 612.72 0.00 0.00 cm /Obj502 Do Q endstream endobj 5 0 obj <> stream BT 3 Tr 0.00 Tc /F3 16.0 Tf 1 0 0 1 36.72 569.04 Tm <3F3220> Tj /F3 6.0 Tf 1 0 0 1 59.28 567.12 Tm <49> Tj 0.00 Tc /F3 7.5 Tf 1 0 0 1 73.68 569.04 Tm <435552524947554C554D20> Tj /F3 10.5 Tf 1 0 0 1 129.60 568.08 Tm <2D20> Tj /F3 7.5 Tf 1 0 0 1 136.32 569.52 Tm <42414348454C4F52275320> Tj /F3 7.0 Tf 1 0 0 1 187.68 569.76 Tm <44454752454520> Tj 1 0 0 1 221.04 570.00 Tm <494E20> Tj /F3 7.5 Tf 1 0 0 1 230.40 569.76 Tm <434F4D505554455220> Tj /F3 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<696E74656772616C73> Tj /F3 13.5 Tf 1 0 0 1 36.48 100.80 Tm <322E20> Tj /F3 8.5 Tf 1 0 0 1 54.00 100.56 Tm <54686520> Tj /F3 13.5 Tf 1 0 0 1 71.28 100.56 Tm <5A2D5472616E73666F726D20> Tj /F3 8.0 Tf 1 0 0 1 312.96 100.56 Tm <283920> Tj /F3 8.5 Tf 1 0 0 1 322.80 99.60 Tm <686F75727329> Tj /F3 13.5 Tf 1 0 0 1 54.48 87.12 Tm <322E3120> Tj /F3 9.0 Tf 1 0 0 1 78.96 87.12 Tm <6C6E74726F64756374696F6E> Tj /F3 13.5 Tf 1 0 0 1 54.24 76.32 Tm <322E3220> Tj /F3 8.0 Tf 1 0 0 1 79.20 76.32 Tm <50726F7065727469657320> Tj /F3 8.5 Tf 1 0 0 1 119.52 76.08 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 129.36 76.08 Tm <5A2D5472616E73666F726D> Tj /F3 13.5 Tf 1 0 0 1 54.24 65.52 Tm <322E3320> Tj /F3 8.0 Tf 1 0 0 1 78.48 65.52 Tm <5A2D20> Tj /F3 8.5 Tf 1 0 0 1 88.80 65.28 Tm <7472616E73666F726D20> Tj 1 0 0 1 127.68 65.28 Tm <6F6620> Tj 1 0 0 1 137.76 65.28 Tm <656C656D656E7461727920> Tj 1 0 0 1 182.88 65.04 Tm <66756E6374696F6E73> Tj /F3 13.5 Tf 1 0 0 1 54.24 54.96 Tm <322E3420> Tj /F3 8.5 Tf 1 0 0 1 78.96 54.72 Tm <4C696E65617269747970726F70657274696573> Tj /F3 13.5 Tf 1 0 0 1 54.00 44.16 Tm <322E3520> Tj /F3 7.5 Tf 1 0 0 1 78.96 44.16 Tm <466972737420> Tj /F3 8.5 Tf 1 0 0 1 96.72 43.92 Tm <7368696674696E6720> Tj 1 0 0 1 127.20 43.68 Tm <7468656F72656D2C20> Tj /F3 8.0 Tf 1 0 0 1 163.92 43.68 Tm <7365636F6E6420> Tj /F3 8.5 Tf 1 0 0 1 193.92 43.44 Tm <7368696674696E6720> Tj 1 0 0 1 223.92 43.44 Tm <7468656F72656D2C20> Tj /F3 9.0 Tf 1 0 0 1 261.60 43.20 Tm <6C6E697469616C20> Tj /F3 8.5 Tf 1 0 0 1 285.12 43.20 Tm <76616C756520> Tj 1 0 0 1 308.16 43.20 Tm <7468656F72656D2C> Tj 0.00 Tc /F3 7.5 Tf 1 0 0 1 81.12 502.32 Tm <33> Tj /F3 5.5 Tf 1 0 0 1 81.60 491.28 Tm <31> Tj /F3 9.0 Tf 1 0 0 1 80.88 480.48 Tm <30> Tj ET endstream endobj 6 0 obj <> endobj 7 0 obj <> stream ?2 I CURRIGULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEERING APPTIED MATHEMATICSsH 551 LectureTutorialPractical Year : llPart : ll Coutse ObjectiveThis course focuses on several branches of applied mathematics. The students areexposed to complex variable theory and a study of the Fourier and Z-Transforms,topics of current importance in signal processing. The course concludes withstudies of the wave and heat equations in Cartesian and polar coordinates.1. Complex Analysis (18 hours)1.1 Complex Analytic Functions1.1.1 Functions and sets in the complex plane1.1.2 Limits and Derivatives of complex functions1.1.3 Analytic functions. The Cauchy -Riemann equations1.1 .4 Harmonic functions and it's conjugate1.2 Conformal Mapping1.2.1 Mapping1.2.2 Some familiar functions as mappinp1.2.3 Conformal mappings and special linear functionaltransformations1.2.4 Constructing conformal mappings between given domains1.3 lntegral in the Complex Plane1.3.1 Line integrals in the complex plane1.3.2 Basic Problems of the complex line integrals1.3.3 Cauchy's integral theorem,l.3.4 Cauchy's integral formula1.3.5 Supplementaryproblems1.4 Complex Power Series, Complex Taylor series and Lauren series1.4.1 Complex power series1.4.2 Functions represented by power series1.4.3 Taylor series, Taylor series of elementary functions1.4.4 Practical methods for obtaining power series, Laurent series1.4.5 Analyticity at infinity, zeros, singularities, residues, Cauchy'sresidue theorem1.4.6 Evaluation of real integrals2. The Z-Transform (9 hours)2.1 lntroduction2.2 Properties of Z-Transform2.3 Z- transform of elementary functions2.4 Linearityproperties2.5 First shifting theorem, second shifting theorem, lnitial value theorem, 310 endstream endobj 8 0 obj <> >> stream Q[+ ?E: dB>@KDv7tA` s'"6̮;423D'j#A) 20a NL 4Tga;@"d$D H3aDBB MAU96I4\.YyEٌhv xIr0Y&I e h }NN[`B- YؐH2dRvdP""BTApixAׇv7[\*Qv82D.D2`B  chvO}CC5kAO#c!'"~߾ _Z/K~_鵯__~vA¿^F=}oK2:3(gqpJOx7;#~f8 {KޟIzUm/KApDD>o10?҃5!y|+[ݘ~KpK"zJaar^_Ĭ^!82ǯ^k ^kKK_ *e$6C@#S}m{$X-" 5W}A+1_wנm_oF$F6׿_GֵtoU7oo~E~DdxUwEsw+ ]!@"x߮D@=܊6D}^ ~d ~޻%P,TdZ ǵ"UoEɄF4*k#Gk]~kay b|B6ÇomP$}lt__~ߧ=iK ?]׿WoAw"gw?>z%oCpk~]OZ}_{^=__֨-{IuD_(z۫^+~{vץ va^v~{^vw*t#_ }vZUW_k_UjE︭h_/HηJIji}aM4݆w!?Aoj}_5K [i°[^BK rĖy? ml҆ a-tar_ ʅi6|1bvԸ1A0(:_U݆ e:6 >!H.9 _n1O_]?HC`A&;c$_Ȏ|w4 GA[{@_v*?8pλqlE[Ua5zz *ih! 0Ci#دa[_amxat""""#iPa a4 µDDHj6p|4 `T$ 0DJ_L,5 >aS@M˂9ܧ4lL^0 Ӱx'h   "JE B"ADDDD}Xa a!)Du0@dRTGep2"5zWj?R#R*͙G@ ##"3Ag2G@˖hb:%1#$'8쑜F0/fJGiڼFD50˙D|#:E.0U3;9&Ii # ͂ 28FMDܗ%lN3B##;.Pj/saˣa3b;2YG3`Y9 ˂vpR8GE:13DDDDbB'L3GFr3#yp9ˆP+ه"TPā3CM9~{ eap6C$50㜤P!r1s?5A* %-NDDDDF#2o 4\dtGDf{.3}C;Q,VUF"9E CEPs\9N2 ),'5-uL(ϠAg:FѼ D3@`"4uZ-aIk*r$ !hDVZ 5MӄD  ;W:h4 k}}߂4ACL - $U_ 5CC'VznC>79c):OI`JUV_Wjiw~SֽWUNmC~4}?WׯDwt_]=}>jwn^}&TBv#SWotAG!Ki!W7Vo"?]}{{]+=W׭תݿ~Vf+K xPt3>m/@X}po @K";zR DuZ2e ? 2ᔈg AMᮟ_ZXzֿZӯ*~;]gV^>_נmWK ݐW]'^O_Vl;K{~Ki~[J/!>_?5t C_0aP`_@KwY Pi5>.C*W߱V/_֞nk~VZn]a0m{u0 ~T0@mnT49>p!%AL"XeVD4a2%HC1ʳ`Dheq *`B#`1" L5P500Nw]:ҥKO /u \=R(__VL"\HQ;Ç[oh>orsy U` vobؿ(_)oI{_j VT맮Z^_kXᄢOHUzUaWapaC 0AL"J(`DGM([Q3^?c2THM4Ӷ)__-QM}t$fD C8 K-2M ۭ}Y ͺU"Ԍ / jLkm$tz-Uvv;+9!Bƈ{{7' Ba84Ay+W"UU 4AF v6a}?T4 M;_V[駻զ&<<$AWA-A|IW]kpAjka}& A&lQ?~ kj!h"S  5&Ek׿_z /@_ob! ^)3_׶vX!mol_{߭t]կgUaL-=4!]l0^>.4As2M"؆]{ ("&B !1D{?]2 ? & N4M%p0BT!^a2"aDDG+Ryd,D"zbi4!þ; }O庨#yf! # W.SA|߄7uK~ ]/}5 zȜ$4mZ: jU'v_TvƿȄDi"\u_p6 r& k"<0AMU_t_ R=~b?N_Z?__]ׄ޽_Ox}wMxj0 {}}nd{;m/i L&C0 xe>ŵ vv?V E`AhE0: ] `Db"""?S2AV rlBnD;; 3{A{O+j{ X;.}mZZM_$n3D]mS'بW Hla?oh4 ySڠ Ta<5%}}A}^ci"F 蠃wˣ.b=Vz0*_CzR\=x,W?:J~^z__/K]~~|iSunm_:p[V+^ ˵[ /~c`bl7na]]=8kd14d1i +A@A:Dr/`LFS!""#2>Ԏ9 CaørT68`P>ہ@ z| a ꟅVQ ^1: ҵAH>Tzo ,5H4M,i=7餟|IDjEOe6u2:)8jHMFo!j4BOP}C` !hE : 9) '4 % b4кinPވ W!#x"!mMCHDM'IA|z￷OI~Kb?^jQ_a oz/ B%_G}|G_ 1޿{~տW~z޵A\0 ]ߵ}Uv߾z=~xd\]{vI^t݆Cuk2!V}0a-%l'e[ۯocd4Z0N[nǯIب)tad˵ 1_N={aBWiiA’OM4b.A &a80Aa a A HXa" 6 )0B$"ݡ8>%J@e@NM i+2FRDHf@2 ;^Y S ԛ ?ފ3 4"/nJ莌"3ȶƋԞqȣ;AwЈ5^rZk;3 Dl׬djL[N6 /uX]C otb!4 /v Jpl!Jx@΁L %D'dr%`X "h:T [C9P@vXUƕjLג"‘!\*dB@PL \fb21Bj-SAONa?2/1tTBa)&dtB%DPR BSBYh |Y A8A"94 r 0@ 40B  ӰMXi<& 6D%̸9C4Dp@ !$A !' 0@D D1Y0 `΢x Bh q ' 0Ah=BaB~Mi 'MӋhC1HZ"E9A 4q  h8; ZA 8zzi ׋L&h; !a%CB{M0T P`4AxOz|\a;O O 8MhoCӑ1D?pM| 2oŦdtjW-Da4DxD=E C8D>c}kI Ӄ"tSzWժz!]C]M-D$Q"H-lC'!= ! 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<5072656E7469636520> Tj 1 0 0 1 294.72 251.28 Tm <48616C6C2E> Tj /F3 13.5 Tf 1 0 0 1 34.32 239.28 Tm <342E20> Tj /F3 8.5 Tf 1 0 0 1 52.80 239.52 Tm <4B2E20> Tj 1 0 0 1 63.60 239.28 Tm <4F676174612C20> Tj 1 0 0 1 92.88 239.28 Tm <2244697363726574652D54696D6520> Tj /F3 9.0 Tf 1 0 0 1 153.36 239.76 Tm <436F6E74726F6C20> Tj /F3 8.5 Tf 1 0 0 1 185.28 240.00 Tm <53797374656D272C20> Tj 1 0 0 1 222.00 240.24 Tm <5072656E7469636520> Tj /F3 9.0 Tf 1 0 0 1 256.56 240.48 Tm <48616C6C2C20> Tj /F3 8.5 Tf 1 0 0 1 278.40 240.48 Tm <456E676C65776F6F6420> Tj 1 0 0 1 324.24 240.48 Tm <436C696666732C> Tj 1 0 0 1 52.80 228.48 Tm <4E657720> Tj /F3 8.0 Tf 1 0 0 1 72.96 227.28 Tm <4A65727365792C20> Tj 1 0 0 1 101.52 228.72 Tm <313938372E> Tj ET endstream endobj 14 0 obj <> stream cuRRlcuLUM - BACHELOR',S DEGREE tN COMPUTER ENGTNEERING I 73 2.6 Final value theorem, Convolution theorem2.7 Some standard Z- transform2.8 lnverseZ-Transform2.9 Method for finding lnverse Z-Transform2.10 Application of Z-Transform to difference equations3. PartialDifferentialEquations (12 hours)3.1 Linear partial differential equation of second order, their classificationand solution3.2 Solution of one dimensional wave equation, one dimensional heatequation, two dimensional heat equation and Laplace equation(Cartesian and polar form) by variable separation method 4. Fourier Transform (6 hours)4.1 Fourier integral theorem, Fourier sine and cosine integral; complexform of Fourier integral4.2 Fourier transform, Fourier sine transform, Fourier cosine transformand their properties4.3 Convolution, Parseval's identity for Fourier transforms4.4 Relation between Fourier transform and Laplace transform References:1. S. K. Mishra, G. B. Joshi, S. Ghimire, V. Parajuli, ' A text book of AppliedMathematics", Dibya Deurali Prakashan.2. E. Kreyszig "Advance Engineering Mathematics", Fifth Edition, Wiley, NewYork.3. A. V. Oppenheim, "Discrete-Time Signal Processing", Prentice Hall.4. K. Ogata, "Discrete-Time Control System', Prentice Hall, Englewood Cliffs,New Jersey, 1987. endstream endobj 15 0 obj <> >> stream x/A1yd xldtEs.4! !TA9 B4Ftm*FV' L M0AB C e!Y@'9r)8elavрlJv?;A [ !k$`5C8QUOkD!A4DVn$ 4 @4AQ`DYVfR dh AO wޚv F3 k0 q2;;A?A?ރh=`;M PDDC82 dR84IB8|ӯ" {. wz!Twڄwa3Ӣ !mP n7"uD9?0{_=S[A l?{^z ܎P ܍>FaA  h;[OwxAޞA!oRoA7ނt#nAd ophjoڧZt'[|?MӯAAI$6ENiGD=k]';?:[{zOnvUxށF9@dJz!uK߫oJo'7aA7;ֻIzk믷M]w]}}MPKOMޫzOwҦ}I~uj}Q_wtu_~~TZ_ҾNzOޓv_KWnHw$]]W]/_J}?{}>K+10Zn}X{ߵ)"+)uAՐpO~OᅤWwd*!?߭^׷CgzMk\bd4 ." 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0 0 1 233.28 427.68 Tm <70726F6772616D6D696E6720> Tj /F3 8.0 Tf 1 0 0 1 286.80 427.20 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 303.12 427.20 Tm <6170706C69636174696F6E> Tj /F3 9.0 Tf 1 0 0 1 34.56 414.96 Tm <746F20> Tj /F3 8.5 Tf 1 0 0 1 44.88 414.96 Tm <7265616C697374696320> Tj 1 0 0 1 76.56 414.96 Tm <656E67696E656572696E6720> Tj 1 0 0 1 124.32 415.68 Tm <70726F626C656D732E> Tj /F3 13.5 Tf 1 0 0 1 35.28 394.80 Tm <6C2E20> Tj /F3 9.0 Tf 1 0 0 1 53.04 394.80 Tm <6C6E74726F64756374696F6E2C20> Tj 1 0 0 1 106.56 394.80 Tm <417070726F78696D6174696F6E20> Tj /F3 8.5 Tf 1 0 0 1 167.76 394.80 Tm <616E6420> Tj 1 0 0 1 184.80 394.80 Tm <6572726F727320> Tj /F3 9.0 Tf 1 0 0 1 210.48 394.80 Tm <6F6620> Tj /F3 13.5 Tf 1 0 0 1 221.04 394.80 Tm <636F6D7075746174696F6E20> Tj /F3 8.0 Tf 1 0 0 1 311.04 396.24 Tm <283420> Tj 1 0 0 1 321.12 395.28 Tm <686F75727329> Tj /F3 13.5 Tf 1 0 0 1 53.28 380.16 Tm <312E3120> Tj /F3 9.0 Tf 1 0 0 1 77.52 380.16 Tm <6C6E74726F64756374696F6E2C20> Tj /F3 8.5 Tf 1 0 0 1 129.60 380.16 Tm <6C6D706F7274616E636520> Tj /F3 9.0 Tf 1 0 0 1 174.96 380.16 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 185.52 380.16 Tm <4E756D65726963616C20> Tj 1 0 0 1 228.00 380.40 Tm <4D6574686F6473> Tj /F3 13.5 Tf 1 0 0 1 53.52 368.40 Tm <312E3220> Tj /F3 8.5 Tf 1 0 0 1 77.04 368.40 Tm <417070726F78696D6174696F6E20> Tj 1 0 0 1 137.04 368.40 Tm <616E6420> Tj /F3 8.0 Tf 1 0 0 1 154.08 368.40 Tm <4572726F727320> Tj /F3 8.5 Tf 1 0 0 1 178.80 368.40 Tm <696E20> Tj 1 0 0 1 188.16 368.40 Tm <636F6D7075746174696F6E> Tj /F3 13.5 Tf 1 0 0 1 53.52 356.64 Tm <312E3320> Tj /F3 8.5 Tf 1 0 0 1 77.04 356.64 Tm <5461796C6F72277320> Tj /F3 7.5 Tf 1 0 0 1 109.92 356.64 Tm <736572696573> Tj /F3 13.5 Tf 1 0 0 1 53.52 344.88 Tm <312E3420> Tj /F3 9.0 Tf 1 0 0 1 77.76 344.88 Tm <4E6577746F6E277320> Tj 1 0 0 1 118.32 344.88 Tm <46696E69746520> Tj /F3 8.5 Tf 1 0 0 1 143.28 344.88 Tm <646966666572656E63657320> Tj /F3 9.0 Tf 1 0 0 1 189.12 345.84 Tm <28666F727761726420> Tj /F3 11.5 Tf 1 0 0 1 225.12 343.20 Tm <2C20> Tj /F3 8.5 Tf 1 0 0 1 231.84 344.88 Tm <4261636B776172642C20> Tj /F3 9.0 Tf 1 0 0 1 275.52 344.88 Tm <63656E7472616C20> Tj /F3 8.5 Tf 1 0 0 1 305.52 344.88 Tm <646966666572656E63652C> Tj 1 0 0 1 77.28 333.12 Tm <6469766964656420> Tj 1 0 0 1 108.48 332.88 Tm <646966666572656E636529> Tj /F3 13.5 Tf 1 0 0 1 53.52 321.36 Tm <312E3520> Tj /F3 8.5 Tf 1 0 0 1 77.76 321.36 Tm <446966666572656E636520> Tj /F3 8.0 Tf 1 0 0 1 119.76 321.36 Tm <6F70657261746F72732C20> Tj /F3 8.5 Tf 1 0 0 1 160.56 321.12 Tm <736869667420> Tj /F3 8.0 Tf 1 0 0 1 178.80 321.12 Tm <6F70657261746F72732C20> Tj /F3 8.5 Tf 1 0 0 1 219.36 321.12 Tm <646966666572656E7469616C20> Tj /F3 8.0 Tf 1 0 0 1 262.80 321.12 Tm <6F70657261746F7273> Tj /F3 13.5 Tf 1 0 0 1 53.52 309.60 Tm <312E3620> Tj /F3 9.0 Tf 1 0 0 1 77.76 309.60 Tm <5573657320> Tj /F3 11.0 Tf 1 0 0 1 102.24 309.60 Tm <616E6420> Tj /F3 9.0 Tf 1 0 0 1 124.08 309.60 Tm <6C6D706F7274616E636520> Tj /F3 12.5 Tf 1 0 0 1 173.76 309.60 Tm <6F6620> Tj /F3 9.5 Tf 1 0 0 1 188.16 309.36 Tm <436F6D707574657220> Tj /F3 9.0 Tf 1 0 0 1 233.28 310.08 Tm <70726F6772616D6D696E6720> Tj /F3 13.0 Tf 1 0 0 1 292.08 309.60 Tm <696E20> Tj /F3 8.5 Tf 1 0 0 1 306.24 309.60 Tm <4E756D65726963616C> Tj 1 0 0 1 77.28 297.84 Tm <4D6574686F64732E> Tj 0.00 Tc /F3 13.5 Tf 1 0 0 1 35.04 277.68 Tm <322E20> Tj /F3 8.5 Tf 1 0 0 1 52.80 277.68 Tm <536F6C7574696F6E7320> Tj /F3 9.0 Tf 1 0 0 1 90.96 277.44 Tm <6F6620> Tj 1 0 0 1 101.76 277.68 Tm <4E6F6E6C696E65617220> Tj /F3 8.0 Tf 1 0 0 1 143.52 277.44 Tm <4571756174696F6E73> Tj /F3 13.5 Tf 1 0 0 1 52.80 263.04 Tm <322E3120> Tj /F3 8.5 Tf 1 0 0 1 77.76 263.04 Tm <426973656374696F6E20> Tj 1 0 0 1 114.96 263.04 Tm <4D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 52.80 251.28 Tm <322E3220> Tj /F3 8.5 Tf 1 0 0 1 77.76 251.28 Tm <4E6577746F6E20> Tj /F3 8.0 Tf 1 0 0 1 110.88 251.28 Tm <52617068736F6E20> Tj /F3 8.5 Tf 1 0 0 1 146.40 251.28 Tm <6D6574686F6420> Tj /F3 9.5 Tf 1 0 0 1 178.32 252.24 Tm <2874776F20> Tj /F3 8.5 Tf 1 0 0 1 199.68 251.04 Tm <6571756174696F6E20> Tj 1 0 0 1 236.16 251.04 Tm <736F6C7574696F6E29> Tj /F3 13.5 Tf 1 0 0 1 52.80 239.52 Tm <322E3320> Tj /F3 8.0 Tf 1 0 0 1 77.76 239.52 Tm <526567756C612D46616C736920> Tj /F3 8.5 Tf 1 0 0 1 125.52 239.52 Tm <4D6574686F6420> Tj 1 0 0 1 157.92 237.84 Tm <2C20> Tj /F3 8.0 Tf 1 0 0 1 162.96 239.28 Tm <536563616E7420> Tj /F3 8.5 Tf 1 0 0 1 190.56 239.28 Tm <6D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 52.80 227.76 Tm <322E3420> Tj /F3 8.0 Tf 1 0 0 1 77.52 228.00 Tm <466978656420> Tj /F3 9.0 Tf 1 0 0 1 100.80 228.24 Tm <706F696E7420> Tj /F3 8.5 Tf 1 0 0 1 123.36 227.76 Tm <697465726174696F6E20> Tj 1 0 0 1 157.20 227.52 Tm <6D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 52.80 216.00 Tm <322E3520> Tj /F3 7.5 Tf 1 0 0 1 77.76 216.00 Tm <5261746520> Tj /F3 8.5 Tf 1 0 0 1 96.48 215.76 Tm <6F6620> Tj 1 0 0 1 106.32 215.76 Tm <636F6E76657267656E636520> Tj 1 0 0 1 157.68 215.76 Tm <616E6420> Tj 1 0 0 1 174.48 215.76 Tm <636F6D70617269736F6E7320> Tj 1 0 0 1 225.36 215.52 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 235.20 215.52 Tm <746865736520> Tj /F3 8.5 Tf 1 0 0 1 257.76 215.52 Tm <4D6574686F6473> Tj 0.00 Tc 1 0 0 1 311.04 278.40 Tm <283520> Tj /F3 8.0 Tf 1 0 0 1 321.36 277.44 Tm <686F75727329> Tj 0.00 Tc /F3 13.5 Tf 1 0 0 1 34.80 195.84 Tm <332E20> Tj /F3 8.5 Tf 1 0 0 1 52.80 195.60 Tm <536F6C7574696F6E20> Tj /F3 9.0 Tf 1 0 0 1 87.36 195.60 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 97.92 195.60 Tm <73797374656D20> Tj /F3 9.0 Tf 1 0 0 1 126.72 195.36 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 137.52 195.36 Tm <6C696E65617220> Tj 1 0 0 1 161.76 195.36 Tm <616C6765627261696320> Tj 1 0 0 1 200.16 195.12 Tm <6571756174696F6E73> Tj /F3 13.5 Tf 1 0 0 1 53.04 181.20 Tm <332E3120> Tj /F3 8.0 Tf 1 0 0 1 77.28 180.96 Tm <436175737320> Tj /F3 9.0 Tf 1 0 0 1 102.72 180.96 Tm <656C696D696E6174696F6E20> Tj /F3 8.5 Tf 1 0 0 1 149.04 180.96 Tm <6D6574686F6420> Tj /F3 9.0 Tf 1 0 0 1 180.72 180.72 Tm <7769746820> Tj 1 0 0 1 200.16 181.20 Tm <7069766F74696E6720> Tj /F3 8.0 Tf 1 0 0 1 234.00 180.48 Tm <73747261746567696573> Tj /F3 13.5 Tf 1 0 0 1 52.80 169.44 Tm <332E3220> Tj /F3 7.5 Tf 1 0 0 1 77.28 169.44 Tm <47617573732D2E4A6F7264616E20> Tj /F3 8.5 Tf 1 0 0 1 130.32 169.20 Tm <6D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 52.80 158.16 Tm <332E3320> Tj /F3 8.0 Tf 1 0 0 1 77.76 158.16 Tm <4C5520> Tj /F3 8.5 Tf 1 0 0 1 91.20 158.16 Tm <466163746F72697A6174696F6E> Tj /F3 13.5 Tf 1 0 0 1 52.80 146.40 Tm <332E3420> Tj /F3 8.5 Tf 1 0 0 1 77.52 146.64 Tm <6C746572617469766520> Tj 1 0 0 1 110.40 146.40 Tm <6D6574686F647320> Tj /F3 8.0 Tf 1 0 0 1 145.68 147.12 Tm <284A61636F626920> Tj /F3 8.5 Tf 1 0 0 1 174.24 146.16 Tm <6D6574686F642C20> Tj /F3 8.0 Tf 1 0 0 1 208.32 145.92 Tm <43617573732D53656964656C20> Tj /F3 8.5 Tf 1 0 0 1 260.16 145.92 Tm <6D6574686F6429> Tj /F3 13.5 Tf 1 0 0 1 52.80 135.12 Tm <332E3520> Tj /F3 7.5 Tf 1 0 0 1 77.28 134.88 Tm <456967656E20> Tj /F3 8.5 Tf 1 0 0 1 100.08 134.88 Tm <76616C756520> Tj 1 0 0 1 123.60 134.64 Tm <616E6420> Tj /F3 8.0 Tf 1 0 0 1 140.40 134.64 Tm <456967656E20> Tj /F3 8.5 Tf 1 0 0 1 163.44 134.64 Tm <766563746F7220> Tj /F3 8.0 Tf 1 0 0 1 190.32 134.40 Tm <7573696E6720> Tj /F3 8.5 Tf 1 0 0 1 213.12 134.40 Tm <506F77657220> Tj 1 0 0 1 240.00 134.40 Tm <6D6574686F64> Tj 0.00 Tc 1 0 0 1 311.04 196.08 Tm <283820> Tj /F3 8.0 Tf 1 0 0 1 321.36 194.88 Tm <686F75727329> Tj 0.00 Tc /F3 13.5 Tf 1 0 0 1 34.32 115.20 Tm <342E20> Tj 1 0 0 1 52.80 115.20 Tm <496E746572706F6C6174696F6E20> Tj /F3 8.5 Tf 1 0 0 1 310.80 115.20 Tm <283820> Tj /F3 8.0 Tf 1 0 0 1 321.12 114.24 Tm <686F75727329> Tj /F3 13.5 Tf 1 0 0 1 52.08 100.80 Tm <342E3120> Tj /F3 8.5 Tf 1 0 0 1 77.52 100.56 Tm <4E6577746F6E277320> Tj 1 0 0 1 116.64 100.32 Tm <6C6E746572706F6C6174696F6E20> Tj /F3 7.0 Tf 1 0 0 1 168.00 101.04 Tm <2820> Tj /F3 8.5 Tf 1 0 0 1 172.56 100.08 Tm <666F72776172642C20> Tj /F3 8.0 Tf 1 0 0 1 207.36 99.84 Tm <6261636B7761726429> Tj /F3 13.5 Tf 1 0 0 1 52.08 89.04 Tm <342E3220> Tj /F3 8.0 Tf 1 0 0 1 76.80 88.80 Tm <43656E7472616C20> Tj /F3 8.5 Tf 1 0 0 1 106.80 88.56 Tm <646966666572656E636520> Tj 1 0 0 1 148.08 88.56 Tm <696E746572706F6C6174696F6E3A20> Tj 1 0 0 1 201.60 88.32 Tm <537469726C696E67277320> Tj 1 0 0 1 237.12 88.32 Tm <466F726D756C612C20> Tj /F3 8.0 Tf 1 0 0 1 274.08 88.08 Tm <42657373656C277320> Tj /F3 8.5 Tf 1 0 0 1 306.24 88.08 Tm <466F726D756C61> Tj /F3 13.5 Tf 1 0 0 1 52.08 77.52 Tm <342E3320> Tj /F3 8.5 Tf 1 0 0 1 77.28 77.28 Tm <4C616772616E6765696E746572706F6C6174696F6E> Tj /F3 13.5 Tf 1 0 0 1 52.08 66.00 Tm <342E3420> Tj /F3 7.5 Tf 1 0 0 1 77.28 65.76 Tm <4C6561737420> Tj /F3 8.5 Tf 1 0 0 1 99.12 65.52 Tm <73717561726520> Tj 1 0 0 1 127.92 65.52 Tm <6D6574686F6420> Tj /F3 9.0 Tf 1 0 0 1 160.08 65.28 Tm <6F6620> Tj 1 0 0 1 170.64 65.28 Tm <66697474696E6720> Tj /F3 8.5 Tf 1 0 0 1 196.08 65.28 Tm <6C696E65617220> Tj /F3 9.0 Tf 1 0 0 1 220.56 65.04 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 238.56 65.04 Tm <6E6F6E6C696E65617220> Tj 1 0 0 1 278.16 64.80 Tm <637572766520> Tj /F3 9.0 Tf 1 0 0 1 302.40 64.80 Tm <666F7220> Tj /F3 8.0 Tf 1 0 0 1 316.08 64.80 Tm <6469736372657465> Tj 1 0 0 1 76.56 54.00 Tm <6461746120> Tj /F3 8.5 Tf 1 0 0 1 95.04 54.00 Tm <616E6420> Tj 1 0 0 1 111.84 54.00 Tm <636F6E74696E756F757320> Tj 1 0 0 1 156.72 53.76 Tm <66756E6374696F6E> Tj /F3 13.5 Tf 1 0 0 1 51.84 42.72 Tm <342E3520> Tj /F3 8.5 Tf 1 0 0 1 76.56 42.48 Tm <53706C696E6520> Tj 1 0 0 1 103.20 42.48 Tm <6C6E746572706F6C6174696F6E20> Tj 1 0 0 1 154.80 43.20 Tm <28437562696320> Tj /F3 8.0 Tf 1 0 0 1 182.16 42.00 Tm <53706C696E6529> Tj ET endstream endobj 20 0 obj <> stream 74 I CURRTCULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEERING NUMERICAL METHODSsH 553 Lecture :3Tutorial : 1Practical :3 Year : llPart : ll Course objective:To introduce numerical methods used for the solution of engineering problems.The course emphasizes algorithm development and programming and applicationto realistic engineering problems.l. lntroduction, Approximation and errors of computation (4 hours)1.1 lntroduction, lmportance of Numerical Methods1.2 Approximation and Errors in computation1.3 Taylor's series1.4 Newton's Finite differences (forward , Backward, central difference,divided difference)1.5 Difference operators, shift operators, differential operators1.6 Uses and lmportance of Computer programming in NumericalMethods. 2. Solutions of Nonlinear Equations2.1 Bisection Method2.2 Newton Raphson method (two equation solution)2.3 Regula-Falsi Method , Secant method2.4 Fixed point iteration method2.5 Rate of convergence and comparisons of these Methods (5 hours) 3. Solution of system of linear algebraic equations3.1 Causs elimination method with pivoting strategies3.2 Gauss-.Jordan method3.3 LU Factorization3.4 lterative methods (Jacobi method, Causs-Seidel method)3.5 Eigen value and Eigen vector using Power method (8 hours) 4. Interpolation (8 hours)4.1 Newton's lnterpolation ( forward, backward)4.2 Central difference interpolation: Stirling's Formula, Bessel's Formula4.3 Lagrangeinterpolation4.4 Least square method of fitting linear and nonlinear curve for discretedata and continuous function4.5 Spline lnterpolation (Cubic Spline) endstream endobj 21 0 obj <> >> stream ު?,VZ?ui 4^ 0¢3'">GdDPd2 CHd'DiLi hd0!9R0Ai|"`/&d`ɃBC.4 ޟ-y;̎!!A a0wa>" o;;%HX5DXB"kA xw[ށ)VAr 2 ! =>]8_W ϾD##_AFGF N0A8ޘN/B/庰EڡLYwPe#A5A;Ao[t$! m{OI #9 @a848} k40i!bp|&B(  BCeL&z!àz9 pP%_@7o'Ci!ވrA!pA!z&>74z!hց2BE8] zMw_xAޟ =~ oo}{t^uo{!O?nY24z'&cޟ~ m'7OioC~/?[mh6}zCI_o}դz@_OoUlF?G/o/P !kzMVZ߯}6_- :'OOO_w߯/I-mtWki~/i^Koj/F [UҿރOW]uw"}N]_}?_ S/__M路m/K)?W#/VCadAo#/_~Uk?J?cg_׈߯oIoBr ci쎒d6 Lڈno 1"BO%zR5ʯ:F1I*0I?ߋֿ, a}w# IɹXw(o~ߑ}I~qT4 |HN"#"q2-kᐰo#SuЈ~+=߯ߵw~}J\_uzZ]ߤ_ 47g~~_}T߻y=ﶾݿ׻}Noۯvv֒lwXݯ[&?x8AWwi.~סxA{[ spqkNovB=l&8Ad۵NaaB@צoU׆NMSL ˲xDIhG5.TG,@B""""?kMmuiT 2 &oݦ@0@ Sa4 & "#0 i0 _A!#PFRxGa\LG qH$h'\1".1RI|h0,"..# @-TdYh_B""""@ Ɍ)h#'GT9 e@%7 2ZB-PʑP|s=v_6i0!p#o.D&fjjd 8#G`##Bb"""24!)\  ØFD#؈W\9GћGЈF0 %G"莈/z7F2xDDFM0DvjB""""""2 A٘Ⱥ#tb7DDh)A ? 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Tj /F3 6.0 Tf 1 0 0 1 191.52 312.72 Tm <2820> Tj /F3 8.0 Tf 1 0 0 1 195.60 311.52 Tm <7374616E6461726420> Tj /F3 8.5 Tf 1 0 0 1 229.92 311.76 Tm <6669766520> Tj 1 0 0 1 245.76 312.24 Tm <706F696E7420> Tj 1 0 0 1 267.36 311.76 Tm <666F726D756C6120> Tj /F3 9.0 Tf 1 0 0 1 298.80 311.52 Tm <7769746820> Tj /F3 8.5 Tf 1 0 0 1 318.24 311.52 Tm <697465726174697665> Tj /F3 8.0 Tf 1 0 0 1 79.68 300.24 Tm <6D6574686F6429> Tj /F3 13.5 Tf 1 0 0 1 55.20 288.48 Tm <372E3320> Tj /F3 8.5 Tf 1 0 0 1 79.44 288.24 Tm <536F6C7574696F6E20> Tj /F3 9.0 Tf 1 0 0 1 113.52 288.24 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 123.84 288.24 Tm <506F6973736F6E20> Tj /F3 8.5 Tf 1 0 0 1 155.28 288.24 Tm <6571756174696F6E20> Tj 1 0 0 1 191.76 289.20 Tm <2866696E69746520> Tj 1 0 0 1 215.52 288.24 Tm <646966666572656E636520> Tj 1 0 0 1 256.08 288.00 Tm <617070726F78696D6174696F6E29> Tj /F3 13.5 Tf 1 0 0 1 55.20 276.48 Tm <372E3420> Tj /F3 8.5 Tf 1 0 0 1 79.20 276.48 Tm <536F6C7574696F6E20> Tj 1 0 0 1 113.52 276.48 Tm <6F6620> Tj 1 0 0 1 123.60 276.48 Tm <456C6C697074696320> Tj 1 0 0 1 152.16 276.24 Tm <6571756174696F6E20> Tj /F3 10.5 Tf 1 0 0 1 188.64 276.24 Tm <627920> Tj /F3 8.0 Tf 1 0 0 1 203.04 276.48 Tm <52656C61786174696F6E20> Tj /F3 8.5 Tf 1 0 0 1 245.52 276.48 Tm <4D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 55.20 264.72 Tm <372E3520> Tj /F3 8.5 Tf 1 0 0 1 79.20 264.72 Tm <536F6C7574696F6E20> Tj 1 0 0 1 113.52 264.72 Tm <6F6620> Tj 1 0 0 1 123.36 264.72 Tm <6F6E6520> Tj 1 0 0 1 140.16 264.72 Tm <64696D656E73696F6E616C20> Tj /F3 8.0 Tf 1 0 0 1 190.32 264.72 Tm <4865617420> Tj /F3 8.5 Tf 1 0 0 1 210.48 264.72 Tm <6571756174696F6E20> Tj 1 0 0 1 246.96 264.48 Tm <627920> Tj 1 0 0 1 258.72 264.72 Tm <5363686D69647420> Tj 1 0 0 1 292.56 264.72 Tm <6D6574686F64> Tj 0.00 Tc 1 0 0 1 36.96 241.20 Tm <50726163746963616C3A> Tj /F3 9.0 Tf 1 0 0 1 36.24 226.56 Tm <416C676F726974686D20> Tj /F3 8.5 Tf 1 0 0 1 77.28 226.32 Tm <616E6420> Tj 1 0 0 1 94.32 227.04 Tm <70726F6772616D20> Tj 1 0 0 1 128.64 226.56 Tm <646576656C6F706D656E7420> Tj 1 0 0 1 181.92 226.56 Tm <696E20> Tj 1 0 0 1 191.28 226.56 Tm <4320> Tj 1 0 0 1 200.16 227.04 Tm <70726F6772616D6D696E6720> Tj /F3 8.0 Tf 1 0 0 1 254.40 226.56 Tm <6C616E677561676520> Tj /F3 8.5 Tf 1 0 0 1 290.88 226.56 Tm <6F6620> Tj /F3 9.0 Tf 1 0 0 1 300.72 226.56 Tm <666F6C6C6F77696E673A> Tj /F3 13.5 Tf 1 0 0 1 37.20 209.04 Tm <312E20> Tj /F3 8.0 Tf 1 0 0 1 54.48 208.80 Tm <43656E657261746520> Tj /F3 8.5 Tf 1 0 0 1 91.92 209.04 Tm <646966666572656E636520> Tj /F3 8.0 Tf 1 0 0 1 132.72 209.04 Tm <7461626C652E> Tj /F3 13.5 Tf 1 0 0 1 36.48 197.04 Tm <322E20> Tj /F3 8.5 Tf 1 0 0 1 54.24 197.04 Tm <417420> Tj /F3 7.5 Tf 1 0 0 1 65.28 197.04 Tm <6C6561737420> Tj /F3 8.5 Tf 1 0 0 1 83.76 197.04 Tm <74776F20> Tj 1 0 0 1 99.84 197.04 Tm <66726F6D20> Tj /F3 8.0 Tf 1 0 0 1 120.24 197.04 Tm <426973656374696F6E20> Tj /F3 8.5 Tf 1 0 0 1 157.20 197.28 Tm <6D6574686F642C20> Tj 1 0 0 1 191.04 197.04 Tm <4E6577746F6E20> Tj /F3 8.0 Tf 1 0 0 1 223.68 197.28 Tm <52617068736F6E20> Tj /F3 8.5 Tf 1 0 0 1 258.48 197.52 Tm <6D6574686F642C20> Tj /F3 7.5 Tf 1 0 0 1 292.08 197.28 Tm <536563616E7420> Tj /F3 8.5 Tf 1 0 0 1 319.20 197.52 Tm <6D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 36.72 185.52 Tm <332E20> Tj /F3 9.0 Tf 1 0 0 1 54.24 185.76 Tm <417420> Tj /F3 7.5 Tf 1 0 0 1 65.52 185.76 Tm <6C6561737420> Tj /F3 8.0 Tf 1 0 0 1 84.24 185.52 Tm <6F6E6520> Tj /F3 8.5 Tf 1 0 0 1 100.56 185.76 Tm <66726F6D20> Tj /F3 8.0 Tf 1 0 0 1 120.72 185.52 Tm <436175737320> Tj /F3 9.0 Tf 1 0 0 1 145.92 185.52 Tm <656C696D696E6174696F6E20> Tj /F3 8.5 Tf 1 0 0 1 192.00 185.76 Tm <6D6574686F6420> Tj /F3 8.0 Tf 1 0 0 1 223.20 185.52 Tm <6F7220> Tj /F3 7.5 Tf 1 0 0 1 233.28 185.52 Tm <476175737320> Tj /F3 8.0 Tf 1 0 0 1 258.00 184.56 Tm <4A6F7264616E20> Tj /F3 8.5 Tf 1 0 0 1 285.84 185.76 Tm <6D6574686F642E20> Tj 1 0 0 1 319.68 185.76 Tm <46696E64696E67> Tj /F3 8.0 Tf 1 0 0 1 54.96 174.00 Tm <6C61726765737420> Tj 1 0 0 1 81.84 174.00 Tm <456967656E20> Tj /F3 8.5 Tf 1 0 0 1 104.88 174.24 Tm <76616C756520> Tj 1 0 0 1 128.16 174.00 Tm <616E6420> Tj 1 0 0 1 144.96 174.00 Tm <636F72726573706F6E64696E6720> Tj 1 0 0 1 202.32 174.24 Tm <766563746F7220> Tj 1 0 0 1 228.96 174.24 Tm <627920> Tj /F3 8.0 Tf 1 0 0 1 241.20 174.24 Tm <506F77657220> Tj /F3 8.5 Tf 1 0 0 1 267.84 174.24 Tm <6D6574686F642E> Tj /F3 13.5 Tf 1 0 0 1 36.24 162.48 Tm <342E20> Tj /F3 8.0 Tf 1 0 0 1 57.36 162.48 Tm <4C616772616E676520> Tj /F3 8.5 Tf 1 0 0 1 94.32 162.48 Tm <696E746572706F6C6174696F6E2E20> Tj 1 0 0 1 147.84 162.48 Tm <437572766520> Tj /F3 9.0 Tf 1 0 0 1 173.28 162.72 Tm <66697474696E6720> Tj /F3 8.5 Tf 1 0 0 1 197.76 162.48 Tm <627920> Tj /F3 7.5 Tf 1 0 0 1 210.00 162.48 Tm <4C6561737420> Tj /F3 8.0 Tf 1 0 0 1 231.36 162.72 Tm <73717561726520> Tj /F3 8.5 Tf 1 0 0 1 259.20 162.72 Tm <6D6574686F642E> Tj /F3 13.5 Tf 1 0 0 1 36.72 150.96 Tm <352E20> Tj /F3 9.0 Tf 1 0 0 1 54.96 150.96 Tm <446966666572656E74696174696F6E20> Tj /F3 10.5 Tf 1 0 0 1 115.44 150.96 Tm <627920> Tj /F3 9.0 Tf 1 0 0 1 130.32 150.96 Tm <4E6577746F6E277320> Tj /F3 10.0 Tf 1 0 0 1 171.60 150.96 Tm <66696E69746520> Tj /F3 9.0 Tf 1 0 0 1 195.84 150.96 Tm <646966666572656E636520> Tj /F3 10.5 Tf 1 0 0 1 239.76 151.20 Tm <6D6574686F642E20> Tj /F3 9.0 Tf 1 0 0 1 282.00 151.20 Tm <6C6E746567726174696F6E20> Tj /F3 8.0 Tf 1 0 0 1 328.08 151.20 Tm <7573696E67> Tj 1 0 0 1 54.48 139.20 Tm <53696D70736F6E277320> Tj /F3 8.5 Tf 1 0 0 1 96.00 139.20 Tm <332F3820> Tj 1 0 0 1 110.88 139.44 Tm <72756C65> Tj /F3 13.5 Tf 1 0 0 1 36.48 127.68 Tm <362E20> Tj /F3 8.5 Tf 1 0 0 1 54.48 127.68 Tm <536F6C7574696F6E20> Tj /F3 9.0 Tf 1 0 0 1 88.56 127.68 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 99.36 127.92 Tm <312220> Tj /F3 8.5 Tf 1 0 0 1 109.44 127.68 Tm <6F7264657220> Tj 1 0 0 1 132.48 127.68 Tm <646966666572656E7469616C20> Tj 1 0 0 1 176.16 127.68 Tm <6571756174696F6E20> Tj 1 0 0 1 212.64 127.92 Tm <7573696E6720> Tj /F3 7.5 Tf 1 0 0 1 235.68 128.16 Tm <524B2D3420> Tj /F3 8.5 Tf 1 0 0 1 256.32 127.92 Tm <6D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 36.72 116.16 Tm <372E20> Tj /F3 8.0 Tf 1 0 0 1 54.72 116.40 Tm <5061727469616C20> Tj /F3 8.5 Tf 1 0 0 1 80.88 116.16 Tm <646966666572656E7469616C20> Tj 1 0 0 1 124.56 116.16 Tm <6571756174696F6E20> Tj /F3 8.0 Tf 1 0 0 1 161.04 117.36 Tm <284C61706C61636520> Tj /F3 8.5 Tf 1 0 0 1 194.88 116.16 Tm <6571756174696F6E29> Tj /F3 13.5 Tf 1 0 0 1 36.24 104.64 Tm <382E20> Tj /F3 8.5 Tf 1 0 0 1 54.72 104.64 Tm <4E756D65726963616C20> Tj 1 0 0 1 97.44 104.64 Tm <736F6C7574696F6E7320> Tj /F3 8.0 Tf 1 0 0 1 134.40 104.64 Tm <7573696E6720> Tj /F3 8.5 Tf 1 0 0 1 156.96 104.88 Tm <4D61746C61622E> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 36.48 81.60 Tm <5265666572656E6365733A> Tj /F3 13.5 Tf 1 0 0 1 36.96 67.20 Tm <312E20> Tj /F3 9.0 Tf 1 0 0 1 54.72 67.20 Tm <44722E20> Tj /F3 8.5 Tf 1 0 0 1 69.84 66.96 Tm <422E532E47726577616C2C20> Tj /F3 9.5 Tf 1 0 0 1 118.08 66.72 Tm <224E756D65726963616C20> Tj /F3 8.5 Tf 1 0 0 1 167.28 67.20 Tm <4D6574686F647320> Tj /F3 9.0 Tf 1 0 0 1 203.52 67.20 Tm <696E20> Tj /F3 8.5 Tf 1 0 0 1 213.60 67.20 Tm <456E67696E656572696E67616E6420> Tj /F3 8.0 Tf 1 0 0 1 278.40 67.44 Tm <536369656E636520> Tj /F3 9.0 Tf 1 0 0 1 310.80 67.68 Tm <222C20> Tj /F3 8.0 Tf 1 0 0 1 319.68 67.44 Tm <4B68616E6E61> Tj /F3 8.5 Tf 1 0 0 1 54.72 55.44 Tm <5075626C69636174696F6E2E> Tj ET endstream endobj 26 0 obj <> stream CURRICULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEERING 175 5. Numerical Differentiation and lntegration (6 hours)5.1 Numerical Differentiation formulae5.2 Maxima and minima5.3 Newton{ote general quadrature formula5.4 Trapezoidal, Simpson's 113,318 rule5.5 Rombergintegration5.6 Caussian integration ( Caussian - Legendre Formula 2 point and 3point) 6. Solution of ordinary differential equations (6 hours)6.1 Euler's and modified Euler's method6.2 Runge Kufta methods for lst and 2nd order ordinary differentialequations6.3 Solution of boundary value problem by finite difference method andshooting method. 7. Numerical solution of Partial differential Equation (8 hours)7.1 Classification of partial differential equation(Elliptic, parabolic, andHyperbolic)7.2 Solution of Laplace equation ( standard five point formula with iterativemethod)7.3 Solution of Poisson equation (finite difference approximation)7.4 Solution of Elliptic equation by Relaxation Method7.5 Solution of one dimensional Heat equation by Schmidt method Practical:Algorithm and program development in C programming language of following:1. Cenerate difference table.2. At least two from Bisection method, Newton Raphson method, Secant method3. At least one from Causs elimination method or Gauss Jordan method. Findinglargest Eigen value and corresponding vector by Power method.4. Lagrange interpolation. Curve fitting by Least square method.5. Differentiation by Newton's finite difference method. lntegration usingSimpson's 3/8 rule6. Solution of 1" order differential equation using RK-4 method7. Partial differential equation (Laplace equation)8. Numerical solutions using Matlab. References:1. Dr. B.S.Grewal, "Numerical Methods in Engineeringand Science ", KhannaPublication. endstream endobj 27 0 obj <> >> stream ^?&],K"P0W3P kT1AڦHAbc(}=4L Ah v( O}ݦwPe"(8oAh2`C"F? 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Tm <6F7220> Tj /F3 9.0 Tf 1 0 0 1 285.60 125.52 Tm <6C6971756964732C20> Tj /F3 9.5 Tf 1 0 0 1 317.52 126.24 Tm <704820> Tj /F3 8.0 Tf 1 0 0 1 333.12 125.76 Tm <616E64> Tj /F3 9.0 Tf 1 0 0 1 106.56 114.72 Tm <68756D69646974792E> Tj /F3 10.5 Tf 1 0 0 1 78.24 103.68 Tm <332E332D3320> Tj /F3 8.5 Tf 1 0 0 1 106.32 103.92 Tm <4D6561737572656D656E7420> Tj /F3 11.0 Tf 1 0 0 1 163.92 103.92 Tm <6F6620> Tj /F3 9.5 Tf 1 0 0 1 176.88 103.92 Tm <62696F706879736963616C20> Tj /F3 9.0 Tf 1 0 0 1 228.72 104.16 Tm <7661726961626C657320> Tj /F3 10.0 Tf 1 0 0 1 268.32 104.16 Tm <626C6F6F6420> Tj /F3 8.5 Tf 1 0 0 1 296.16 104.88 Tm <707265737375726520> Tj /F3 8.0 Tf 1 0 0 1 333.12 104.40 Tm <616E64> Tj /F3 8.5 Tf 1 0 0 1 106.32 93.12 Tm <6D796F656C65637472696320> Tj 1 0 0 1 153.84 93.84 Tm <706F74656E7469616C73> Tj /F3 13.5 Tf 1 0 0 1 35.04 73.92 Tm <342E20> Tj /F3 9.5 Tf 1 0 0 1 53.28 73.92 Tm <746C656374726963616C20> Tj /F3 8.0 Tf 1 0 0 1 92.16 73.92 Tm <5369676E616C20> Tj 1 0 0 1 118.32 73.92 Tm <50726F63657373696E6720> Tj 1 0 0 1 162.24 73.92 Tm <616E6420> Tj /F3 13.5 Tf 1 0 0 1 178.80 73.92 Tm <7472616E736D697373696F6E20> Tj /F3 8.0 Tf 1 0 0 1 312.00 75.36 Tm <283520> Tj /F3 8.5 Tf 1 0 0 1 322.08 74.40 Tm <686F75727329> Tj /F3 12.5 Tf 1 0 0 1 52.80 62.88 Tm <2E342E3120> Tj /F3 8.0 Tf 1 0 0 1 78.24 60.24 Tm <426173696320> Tj /F3 9.5 Tf 1 0 0 1 100.56 60.24 Tm <4F70616D7020> Tj /F3 8.0 Tf 1 0 0 1 134.64 60.24 Tm <636861726163746572697374696373> Tj /F3 13.5 Tf 1 0 0 1 53.28 49.44 Tm <342E3220> Tj /F3 8.5 Tf 1 0 0 1 78.48 49.44 Tm <6C6E73747275726E656E746174696F6E20> Tj /F3 9.0 Tf 1 0 0 1 140.40 49.44 Tm <616D706C6966696572> Tj ET endstream endobj 38 0 obj <> stream CURHICULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEEBING 177 INSTRUMENTATION IEE 552 !.ecture :Tutoria! :Practical : 3I312 Year : llPart : ll Course Objectives:To provide comprehensive treatment of methods and instrument for a wide rangeof measurement problems 1. lnstrumentatlons Systems (2 hours)1.1 Functions of components of instrumentation system introduction,signal processing, Signal transmission,output indication1,2 Need for electrical, electronics, pneumatic and hydraulic workingmedia systems and conversion devices1.3 Analog and digital systems2. Theory of measurernent (10 hours)2,1 Static performanc parameters - accuracy, precision, sensitivity,resolution and linearity2.2 Dynamic performance parameters - response time, frequency responseand bandwidth2,3 Error in measurement2.4 Statistical analysis of error in measurement2.5 Measurement of voltage & current (moving coil & moving ironinstruments)2,6 Measurement of low, high & medium resistances2.7 AC bridge & measurcment of inductance and capacitance3. Transducer (g hours)3.1 lntroduction3,2 Classification3.3 Application3.3.1 Measurement of mechanical variables, displacement, strain.velocity. acceleration and vibration3. 3.2 Measurcment of process variables - temperature pressure, level,fluid flow, chemical constituents in gases or liquids, pH andhumidity.3.3-3 Measurement of biophysical variables blood pressure andmyoelectric potentials4. tlectrical Signal Processing and transmission (5 hours).4.1 Basic Opamp characteristics4.2 lnstrurnentation amplifier endstream endobj 39 0 obj <> >> stream 4Qxm,(l(CQhP@1Z_rJgh# FtEZ*6?F# H#ٚ;,EuEHH8M "eVPLu&wPn Ќ!!Sj+pA"U2& oW2"r.?piA &LB "uÕGt"$hYB~mm>","&&@BF91E$QSND  eֱ"A %QqѴahKAޟ-4A 0lbSPD\New_Ma4 &zCj [[8%ٯzL3AH":%SEˑu0fж [?xNdP d%XPjD- ;1yBv"C㇧~ ӴAd$1f,A3dDR;IZat!u}v: 7"V$Dz`;[UȘ5HȀ h35o6'U?AAz"@YwAL4 !ŧVC˧>Wn&0&IđU zavfύ0@7}}Ǥ&|7{GA C[U[ iz>^A  $`={[uo߾n S臟'V~jIInF$nhUkz^umoIUA7 D9և.ۯ'o o}]$kI~T[I޿"Iq0[DcI> `~ m*d@'V;Z;zݯ}zE ?~*A-꾟"J&]/}uO_ /տݿi{]8.V|{nK]?!G}w\LJ_Poגz}%ת!xKZIKw;" JB<Kֺ:7U0uq,HI^ڤ֒_ W"*KfiwKJul %T-__0ټI: yTIF56ajQ=f/mz\B=P/$ +B 1gi?Z߄#wr 9 u{DR]]?hl D~vwr`I׿/}_/otȐ {K91ȰonXhz]j[ftdI]/B#r(ã~Zz+p~=bZ;~#"̨+_KC YWH!ߺAG-6kz!~~ԍ;- RMq/v޿o}{LK<λUz^Bzj"!oB֮uGy*ݥoUiiv[^߯k{N_}aڭ­:,[{[i*j6KEfjjVj}+v# 0waKC~~L*[]uH|3aXqًix6Ukm0 M; ~ 튧b #">gUj_w_ Ll&w amuaj!_09 "4KݰQ`I 4V {U?< ݰ,H"DAEIa5L/j_ݍ0 a+h:\u.1*9nhP[ b"A%BGixcAʋrZ}~5ė^}#Ðᕧm~"" !MS]5S|EĄ h0Aj2pvCqĖA0vWIT""  ivo""! 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78 I CUnntCULUM - BACHELOR',S DEGREE lN COMPUTER ENGINEERING 4.3 Signal amplification, attenuation, integration, differentiation, networkisolation, wave shaping4.4 Effect of noise, analog filtering, digital filtering4.5 Optical communication, fibre optics, electro-optic conversion devices5. Analog - Digital and Digital - Analog Conversion (5 hours)5.1 Analog signal and digital signal5.2 Digital to analog convertors - weighted resistor type, R-2R ladder type,DAC Errors5.3 Analog to digital convertors - successive approximation type, ramptype, dual ramp type, flash type, ADC errors6. Digital lnstrumentation (5 hours)5.1 Sample data system, sample and hold circuit6.2 Components of data acquisition system6.3 lnterfacing to the computer7. Electrical equipment (8 hours)7.1 Wattmeter7.1.1 Types7.1 .2 Working principles7.2 Energy meter7.2.'l Types7.2.2 Working principles7.3 Frequency meter7.3.1 Types7.3.2 Working principles7.4 Power factor meter7.5 lnstrumenttransformers Practical:1. Accuracy test in analog meters2. Operational Amplifiers in Circuits- Use of Op amp as a summer, inverter, integrator and differentiator3. Use resistive, inductive and capacitive transducers to measure displacement- Use strain gauge transducers to measure force4. Study of Various transducers for measurement of Angular displacement,Angular Velocity, Pressure and FJow- Use optical, Hall effect and inductive transducer to measure angulardisplacement- Use tacho - generator to measure angular velocity- Use RTD transducers to measure pressure and flow5. Digital to Analog Conversion- Perform static testing of D/A converter6. 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D.M Considine "Process lnstruments and Controls Handbook" McGraw Hill.2. S. Wolf and R.F.M. Smith "Students Reference Manual for Electronicslnstrumentation Laboratories", Prentice Hal l.3. E.O Deobelin "Measurement System, Application and Design" Mccraw Hill.4. A.K Sawhney "A Course in Electronic Measurement and lnstrumentation "DhanpatRai and Sons.5. C.S. Rangan, C.R Sharma and V.S.V. Mani, "lnstrumentation Devices andSystems" Tata McGraw Hill publishing Company Limited New Delhi.6. J.B. Cupta. "A Course in Electrical & Electronics Measurement &' lnstrumentation, Kataria& Sons. endstream endobj 51 0 obj <> >> stream u@}:Bu@}ӏQ&umn@|n(wSCHF?EVXK)htޥ2́CPZ&gaA3XkX␂AN wX"FPF]Z #K;. 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Tj 1 0 0 1 128.40 140.64 Tm <5472616E73666F726D6572733A20> Tj 1 0 0 1 187.44 140.40 Tm <506F74656E7469616C20> Tj 1 0 0 1 227.04 140.16 Tm <5472616E73666F726D657220> Tj 1 0 0 1 280.08 140.88 Tm <2850542920> Tj /F3 10.5 Tf 1 0 0 1 300.96 139.92 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 321.84 139.68 Tm <43757272656E74> Tj 1 0 0 1 81.12 130.08 Tm <5472616E73666F726D657220> Tj /F3 7.5 Tf 1 0 0 1 130.08 130.80 Tm <28435429> Tj /F3 10.5 Tf 1 0 0 1 56.88 119.52 Tm <322E313220> Tj /F3 8.5 Tf 1 0 0 1 81.12 119.52 Tm <4175746F20> Tj 1 0 0 1 102.00 119.28 Tm <7472616E73666F726D65723A20> Tj 1 0 0 1 150.72 119.04 Tm <636F6E737472756374696F6E2C20> Tj /F3 9.0 Tf 1 0 0 1 203.04 119.04 Tm <776F726B696E6720> Tj /F3 8.5 Tf 1 0 0 1 237.36 119.28 Tm <7072696E6369706C6520> Tj 1 0 0 1 273.60 118.56 Tm <616E6420> Tj /F3 8.0 Tf 1 0 0 1 290.64 118.56 Tm <437520> Tj 1 0 0 1 303.84 118.56 Tm <736176696E67> Tj /F3 10.5 Tf 1 0 0 1 56.88 108.96 Tm <322E313320> Tj /F3 8.0 Tf 1 0 0 1 81.12 108.72 Tm <546872656520> Tj 1 0 0 1 105.60 109.20 Tm <706861736520> Tj 1 0 0 1 130.08 108.48 Tm <5472616E73666F726D657273> Tj 0.00 Tc /F3 13.5 Tf 1 0 0 1 38.64 78.96 Tm <332E20> Tj /F3 8.5 Tf 1 0 0 1 56.88 78.96 Tm <444320> Tj 1 0 0 1 72.00 78.72 Tm <47656E657261746F72> Tj /F3 13.5 Tf 1 0 0 1 56.64 65.28 Tm <332E3120> Tj /F3 8.5 Tf 1 0 0 1 80.88 65.28 Tm <436F6E737472756374696F6E616C20> Tj 1 0 0 1 139.68 65.04 Tm <44657461696C7320> Tj 1 0 0 1 168.48 64.80 Tm <616E6420> Tj 1 0 0 1 185.28 64.80 Tm <41726D617475726520> Tj /F3 9.0 Tf 1 0 0 1 223.44 64.56 Tm <57696E64696E67> Tj /F3 13.5 Tf 1 0 0 1 56.64 54.48 Tm <332E3220> Tj /F3 9.0 Tf 1 0 0 1 80.88 54.48 Tm <576F726B696E6720> Tj 1 0 0 1 116.88 54.96 Tm <7072696E6369706C6520> Tj /F3 8.5 Tf 1 0 0 1 153.36 54.00 Tm <616E6420> Tj 1 0 0 1 170.16 54.00 Tm <436F6D6D757461746F7220> Tj 1 0 0 1 220.80 53.76 Tm <416374696F6E> Tj /F3 13.5 Tf 1 0 0 1 56.64 43.68 Tm <332E3320> Tj /F3 7.5 Tf 1 0 0 1 81.12 43.68 Tm <454D4620> Tj /F3 8.5 Tf 1 0 0 1 100.08 43.44 Tm <6571756174696F6E> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 82.80 501.84 Tm <33> Tj /F3 6.0 Tf 1 0 0 1 83.28 491.28 Tm <31> Tj /F3 7.5 Tf 1 0 0 1 83.28 480.24 Tm <333132> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 315.36 78.96 Tm <283620> Tj /F3 8.5 Tf 1 0 0 1 325.20 78.00 Tm <686F75727329> Tj ET endstream endobj 56 0 obj <> stream 80 | CURRTCULUM - BACHELOR',S DEGREE lN COMPUTER ENGINEERING ETECTRICAL MACHINESEE 554 LectureTutorialPractical Year: llPart : ll Course Objectives:To impart knowledge on constructional details, operating principle andperformance of Transformers, DC Machines, l-phase and 3-phase lnductionMachines, 3-phase Synchronous Machines and Fractional Kilowatt Motors.1. Magnetic Circuits and lnduction (4hours)1.1 Magnetic Circuits1.2 Ohm's Law for Magnetic Circuits1.3 Series and Parallel magnetic circuits1.4 Core with air gap1.5 B-H relationship (Magnetization Characteristics)1.6 Hysteresis with DC and AC excitation1.7 Hysteresis Loss and Eddy Current Loss1 .8 Faraday's Law of Electromagnetic lnduction, Statically and Dynamicallylnduced EMF1.9 Force on Current Carrying Conductor2. Transformer (8 hours)2.1 Constructional Details, recent trends2.2 Working principle and EMF equation2.3 ldeal Transformer2.4 No load and load Operation2.5 Operation of Transformer with load2.6 Equivalent Circuits and Phasor Diagram2.7 Tests: Polarity Test, Open Circuit test, Short Circuit test and EquivalentCircuit Parameters2.8 Voltage Regulation2-9 Losses in a transformer2.10 Efficiency, condition for maximum efficiency and all day efficiency2.11 lnstrument Transformers: Potential Transformer (PT) and CurrentTransformer (CT)2.12 Auto transformer: construction, working principle and Cu saving2.13 Three phase Transformers 3. DC Generator3.1 Constructional Details and Armature Winding3.2 Working principle and Commutator Action3.3 EMF equation 31312 (6 hours) endstream endobj 57 0 obj <> >> stream W???3z! 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1 200.64 60.00 Tm <6D6F746F72> Tj /F3 11.0 Tf 1 0 0 1 79.68 48.48 Tm <372E332E3220> Tj /F3 8.0 Tf 1 0 0 1 107.52 48.48 Tm <52656C756374616E636520> Tj 1 0 0 1 152.16 48.72 Tm <737461727420> Tj /F3 8.5 Tf 1 0 0 1 170.64 48.96 Tm <6D6F746F72> Tj ET endstream endobj 62 0 obj <> stream cuRRrcuLUM - BACHELOR'S DEGREE rN COMPUTER ENGINEERTNG I 81 3.4 Method of excitation: separately and self excited, Types of DCCenerator3.5 Characteristics of series, shunt and compound generator3.6 Losses in DC generators3.7 Efficiency and Voltage Regulation4. DC Motor (6 hours)4.1 Working principle and Torque equation4.2 Back EMF4,3 Method of excitation, Types of DC motor4.4 Performance Characteristics of D.C. motors4.5 Starting of D.C. Motors: 3 point and 4 point starters4.6 Speed control of D.C. motors: Field Control, Armature Control4.7 Losses and Efficiency5. Three Phase Induction Machines (7 hours)5.1 Three Phase lnduction Motor5.1.1 Constructional Details and Types5.1.2 Operating Principle, Rotating Magnetic Field, SynchronousSpeed, Slip, lnduced EMF, Rotor Current and its frequency,Torque Equation5.1.3 Torque,Slip characteristics5.2 Three Phase lnduction Cenerator5.2.1 Working Principle, voltage build up in an lnduction Cenerator5.2.2 Power Stages6. Three Phase Synchronous Machines (8 hours)6.1 Three Phase Synchronous Generator6.1.1 Constructional Details, Armature Windings, Types of Rotor,Exciter6.1.2 Working Principle6.1.3 EMF equation, distribution factor, pitch factor6.1 .4 Armature Reaction and its effects6.1.5 Alternator with load and its phasor diagram6.2 Three Phase Synchronous Motor6.2.1 Principle of operation6.2.2 Sarting methods5.2.3 No load and Load operation, Phasor Diagram6.2.4 Effect of Excitation and power factor control7. Fractional Kilowatt Motors (6 hours)7.1 Single phase lnduction Motors: Construction and Characteristics7.2 Double Field Revolving Theory7.3 Split phase lnduction Motor7.3.1 Capacitors start and run motor7.3.2 Reluctance start motor endstream endobj 63 0 obj <> >> stream ZeHڏh8KQ)_-B|L:r[I֯ V6vi!P`ah3X Sa0@*ȔAsh`Yڰ@aD2 Kih0Aa ;2 2`A20 g#.FVe$FD jj 0L 0A@q FhB@ ɜirAÇ {ijpM0#C'aG#~#h֌H.?[M;A4@0BB"Kf j2d%9  @!{KiM?;v;᧪hjaQ ښ` zkWoDtxA}Aih4}?Eݠ$D(mB!Ȝ9uw! ]l4a pKkM}`auh+ %gTYaI m/kuklWikk!U|^ B qȨ 2# rWl00Wvߪدc*Cc Ɇh m{ /a}]a&Tݥڭ1LU0*kibv-mH.1;XUkwmXau`aB~5 c \\DTA`(M4pk ;T4{ p*auoL/݉ޟH8ǖBqCPTa 8&@a!]30n &A@D&i]S_>Oe""b"""!r=dЈ_4G2L80D ˣhXA0h0|0ި4aDO`Ў4"""'Љ, 4M>'0aq ܿ#B`L `Ei]` ~外yf3Q ; +[A"&wM0Y*S!s;0BD bzR[!c e;ȬwoZzjI_D T8`SG X47z~ނy, '[?:2H&ďA 0/Vh(MN}!g k*[GWȕOkN[VI~ IZ~G_i5K_&zW^|dH$[k¥IwAau R4} LA "h.C.d:dB'"@pD3A띂ZJA BM3lNAd`0k`00@"&aȌ!&Ƀ#_va 'waa0M ڂ 0AvjD8"%D˜a'2 hAbxSAi/T  ?8(N-==:a=0Aaa4 ]5Maa?j C臆HBG$=4DzވWtX}ń0 tB T aAݺTdcM= !m }IւD'1 "4;T0 4\2m'ȆI'ŦIj?NN"O7h"7U5޴>J]C$&&-GTz i]7M>rx@A7BHHBD/?ƈOhYۭ+麦tmPOI>F鴃MqI `BmIOA@5Kx~{ޞ'a}7t:Nu tڴ utMZMvCuп_pkW^ߧI p^U{M+Im'nkIҵI;":إ G~ZW'WUaiw}p~":Z릵wwӤkmqߡo~OK wH{~pk_# Z֓y&O߰qN ?GviuJNwU_wD 4d gA^k޼O#GфMg_ Q^>w_DZ뺽n_ax]?ނ/o+[y{_-Im}i7}_~&_km{mtt3U~$kvkMk}vtִJ4m~{jKm0}MkZҶgnZM %mJa {kkk cOjԬ:m>Kܧvf~$ uLLlt<+l%a&* 7az`&¤h>+յM'[&)LA; إpl[`QWb/ M(a/aJ/Xa#@am&\S ¥k酵Vl6!Ci5a(d+0V0^aXhXa`"8bw a5һ[ Gگh0 ^0)41[ b1 "h4AAa h0§a0P 0M4'd}ujA4_4""B ;G2!a h0L ` a h`i&N݄g}uL&CAxc!$pC2]>B A 0 0 a hB0b  hTN<#aHg R#KJ"""4)1ǎ":ꖣI/֩zz]_TaSF@f<6 4HAT!>NΨGAVvƮ!h h'55VIl3NFH gQ gQBa2@h0aBMqaBvh"s A E d0d:n7I]'i=+rTЍ {N a_~t}zӏ^u@^T{DOh-mrʡ^I bBGKh7ޕ5]{ֵ#/1z i noj[!턫l%`8ub1[õ\qh0Nd2M K8!v@ !e4Fšqdq `A>M PC;5,gR+ `YA MWа+x_ 7m/_DKx@z| ސ>dTmuk;ZZ +}EEG y]ejKkUE!נKuuό !@H"s\GB B!B"C$d\h&E‘ A2Z?j&0D4[04@:p 3>20akd! `JCr6!/";%#6!DLA00A0a54AŦ43X 9`AH#H@L9Y" VC/3vZqI S8 N ! 0AA 0`PPAA„ 0 Z"wAXOTMVޝaMNаB-40) mkh"ΈIiD%(B{tBE$Dﴈ=KGv?T}) $`}iOȁᤃ i y [ 4r@ ôAHޮRA;OI7]54 ۮ*xAt$| 8 mh!x$DAG6!l>Y 7U!NO!Uir k_kzo7t 70~A:M>RoH;8N6nkMtUx4׵֓]6~tuz &꜋n^uki}ޛ_9nAw,:_i=U7wu]{ߥuBV7cP_]>Ct#08W?[tu ]/T֗ï+uW{\,.?ƽ`h3IoAztV @#AUg7ᅯEap%!ӿઽ _^?^)߄np^ 6\'_ w/{Z BhV~ aH(r)rIoD>_腛*G7ȂZ]ԂAE0Ykk]T+?aB)~'^too)Ak/Iw/K~{4_#B{5B_a~:_AzvJm]Bk?Ik}鿿kWZ, WwU}߫uV{p~JHi6Oղ;D_j+WD, [zSmzm6}:{lkidk ?R;u{ml]ե7#?34j [ / +ka[T鴴ՆTM/d?Xa[KW_ua~?] h0n>.[l'ڰ֡ ]_Ïa[Nm(km}v.(1Zcdw?☭4g]샨~m/+iG0 { .GRwvM4݇maڦ)EhWC`lB`om xضA& `{ ײ dӰxj^ªkݐ M;MuOX{ VV6+kpa4& 5MM0{M+MS!UM0NaaOwAMBmߖBopy &a4ADb! 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1 0 0 1 152.88 370.08 Tm <636861726163746572697374696320> Tj /F3 8.0 Tf 1 0 0 1 205.92 371.28 Tm <284F43432920> Tj /F3 8.5 Tf 1 0 0 1 232.56 370.32 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 242.40 370.32 Tm <6120> Tj /F3 8.5 Tf 1 0 0 1 249.60 370.56 Tm <444320> Tj /F3 8.0 Tf 1 0 0 1 264.72 370.32 Tm <7368756E7420> Tj 1 0 0 1 288.00 371.28 Tm <67656E657261746F72> Tj /F3 13.5 Tf 1 0 0 1 52.56 359.04 Tm <2D20> Tj /F3 8.0 Tf 1 0 0 1 70.56 358.80 Tm <546F20> Tj /F3 9.0 Tf 1 0 0 1 83.04 358.80 Tm <6472617720> Tj /F3 8.5 Tf 1 0 0 1 105.36 359.04 Tm <6C6F616420> Tj /F3 8.0 Tf 1 0 0 1 124.08 358.80 Tm <636861726163746572697374696320> Tj /F3 8.5 Tf 1 0 0 1 176.64 359.04 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 186.72 359.28 Tm <7368756E7420> Tj 1 0 0 1 210.00 360.00 Tm <67656E657261746F72> Tj /F3 13.5 Tf 1 0 0 1 34.80 342.00 Tm <342E20> Tj /F3 8.5 Tf 1 0 0 1 53.04 342.24 Tm <444320> Tj /F3 9.0 Tf 1 0 0 1 68.16 342.24 Tm <4D6F746F72> Tj /F3 7.5 Tf 1 0 0 1 70.80 331.44 Tm <537065656420> Tj /F3 8.5 Tf 1 0 0 1 96.00 331.44 Tm <636F6E74726F6C20> Tj 1 0 0 1 125.28 331.44 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 135.36 331.68 Tm <444320> Tj 1 0 0 1 149.76 331.44 Tm <5368756E7420> Tj /F3 8.5 Tf 1 0 0 1 173.76 331.68 Tm <6D6F746F7220> Tj 1 0 0 1 198.24 331.68 Tm <627920> Tj /F3 7.0 Tf 1 0 0 1 210.00 332.88 Tm <28612920> Tj /F3 8.0 Tf 1 0 0 1 220.80 331.92 Tm <61726D617475726520> Tj /F3 8.5 Tf 1 0 0 1 256.80 331.92 Tm <636F6E74726F6C20> Tj 1 0 0 1 286.32 331.44 Tm <6D6574686F6420> Tj /F3 7.5 Tf 1 0 0 1 317.52 333.36 Tm <28622920> Tj /F3 8.5 Tf 1 0 0 1 329.04 332.40 Tm <6669656C64> Tj /F3 9.0 Tf 1 0 0 1 70.80 320.40 Tm <636F6E74726F6C20> Tj /F3 8.5 Tf 1 0 0 1 100.80 320.64 Tm <6D6574686F64> Tj /F3 13.5 Tf 1 0 0 1 52.56 309.84 Tm <2D20> Tj /F3 9.0 Tf 1 0 0 1 70.80 309.84 Tm <546F20> Tj /F3 8.5 Tf 1 0 0 1 84.72 309.60 Tm <6F62736572766520> Tj /F3 9.0 Tf 1 0 0 1 118.08 309.84 Tm <74686520> Tj /F3 8.5 Tf 1 0 0 1 134.16 309.84 Tm <65666665637420> Tj /F3 10.0 Tf 1 0 0 1 158.64 309.84 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 170.16 310.08 Tm <696E6372656173696E6720> Tj /F3 9.0 Tf 1 0 0 1 213.12 310.08 Tm <6C6F616420> Tj /F3 10.0 Tf 1 0 0 1 233.28 310.08 Tm <6F6E20> Tj /F3 9.0 Tf 1 0 0 1 247.44 310.32 Tm <444320> Tj 1 0 0 1 263.76 310.08 Tm <7368756E7420> Tj 1 0 0 1 288.72 310.32 Tm <6D6F746F72277320> Tj /F3 8.0 Tf 1 0 0 1 321.36 310.56 Tm <73706565642C> Tj 1 0 0 1 70.80 298.80 Tm <61726D617475726520> Tj /F3 8.5 Tf 1 0 0 1 107.28 298.80 Tm <63757272656E742C20> Tj /F3 8.0 Tf 1 0 0 1 139.44 299.04 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 156.00 299.04 Tm <6669656C6420> Tj 1 0 0 1 175.20 299.04 Tm <63757272656E742E> Tj /F3 13.5 Tf 1 0 0 1 35.04 282.24 Tm <352E20> Tj /F3 8.0 Tf 1 0 0 1 53.04 282.24 Tm <332D706861736520> Tj /F3 8.5 Tf 1 0 0 1 85.20 282.48 Tm <4D616368696E6573> Tj /F3 13.5 Tf 1 0 0 1 52.80 271.92 Tm <2D20> Tj /F3 9.0 Tf 1 0 0 1 70.80 271.68 Tm <546F20> Tj /F3 8.5 Tf 1 0 0 1 84.24 271.44 Tm <6472617720> Tj 1 0 0 1 106.32 271.44 Tm <746F7271756527737065656420> Tj /F3 8.0 Tf 1 0 0 1 159.60 271.68 Tm <63686172616374657269737469637320> Tj /F3 8.5 Tf 1 0 0 1 216.48 271.68 Tm <616E6420> Tj /F3 9.0 Tf 1 0 0 1 234.00 271.68 Tm <746F20> Tj /F3 8.5 Tf 1 0 0 1 244.80 271.68 Tm <6F62736572766520> Tj /F3 9.0 Tf 1 0 0 1 277.68 271.92 Tm <74686520> Tj /F3 8.5 Tf 1 0 0 1 293.04 271.92 Tm <65666665637420> Tj /F3 9.5 Tf 1 0 0 1 317.04 271.92 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 328.08 272.16 Tm <726F746F72> Tj /F3 13.5 Tf 1 0 0 1 35.52 259.92 Tm <2E20> Tj /F3 8.0 Tf 1 0 0 1 71.52 260.64 Tm <726573697374616E636520> Tj /F3 8.5 Tf 1 0 0 1 110.88 260.64 Tm <6F6E20> Tj 1 0 0 1 123.12 260.64 Tm <746F727175652E737065656420> Tj /F3 8.0 Tf 1 0 0 1 175.44 260.88 Tm <63686172616374657269737469637320> Tj /F3 8.5 Tf 1 0 0 1 231.60 260.88 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 241.44 260.88 Tm <6120> Tj 1 0 0 1 248.64 260.88 Tm <332D706861736520> Tj /F3 9.0 Tf 1 0 0 1 280.80 261.12 Tm <6C6E64756374696F6E20> Tj 1 0 0 1 319.68 261.12 Tm <4D6F746F72> Tj /F3 8.5 Tf 1 0 0 1 71.04 249.84 Tm <546F20> Tj 1 0 0 1 84.00 249.84 Tm <737475647920> Tj 1 0 0 1 107.52 249.84 Tm <6C6F616420> Tj /F3 8.0 Tf 1 0 0 1 126.48 249.84 Tm <63686172616374657269737469637320> Tj /F3 9.0 Tf 1 0 0 1 183.12 249.84 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 193.44 249.84 Tm <73796E6368726F6E6F757320> Tj 1 0 0 1 244.56 250.56 Tm <67656E657261746F7220> Tj /F3 9.5 Tf 1 0 0 1 283.68 250.08 Tm <7769746820> Tj /F3 8.0 Tf 1 0 0 1 303.60 251.28 Tm <28612920> Tj 1 0 0 1 315.84 250.32 Tm <726573697374697665> Tj /F3 8.5 Tf 1 0 0 1 71.52 239.04 Tm <6C6F616420> Tj /F3 8.0 Tf 1 0 0 1 90.48 240.00 Tm <28622920> Tj /F3 8.5 Tf 1 0 0 1 103.20 239.04 Tm <696E6475637469766520> Tj 1 0 0 1 141.12 239.04 Tm <6C6F616420> Tj 1 0 0 1 159.84 239.04 Tm <616E6420> Tj /F3 7.5 Tf 1 0 0 1 176.88 240.00 Tm <28632920> Tj /F3 8.5 Tf 1 0 0 1 188.40 239.04 Tm <6361706163697469766520> Tj /F3 8.0 Tf 1 0 0 1 229.92 239.28 Tm <6C6F6164> Tj /F3 13.5 Tf 1 0 0 1 35.28 222.24 Tm <362E20> Tj /F3 8.5 Tf 1 0 0 1 53.52 222.24 Tm <4672616374696F6E616C20> Tj /F3 9.0 Tf 1 0 0 1 95.04 222.48 Tm <4B696C6F7761747420> Tj 1 0 0 1 130.32 222.48 Tm <4D6F746F7273> Tj /F3 13.5 Tf 1 0 0 1 52.80 211.68 Tm <2D20> Tj /F3 8.5 Tf 1 0 0 1 71.04 211.44 Tm <546F20> Tj /F3 8.0 Tf 1 0 0 1 83.76 211.44 Tm <737475647920> Tj /F3 8.5 Tf 1 0 0 1 106.32 211.44 Tm <74686520> Tj /F3 8.0 Tf 1 0 0 1 120.96 211.44 Tm <65666665637420> Tj /F3 8.5 Tf 1 0 0 1 144.00 211.44 Tm <6F6620> Tj /F3 7.5 Tf 1 0 0 1 154.08 211.44 Tm <6120> Tj /F3 8.5 Tf 1 0 0 1 160.80 211.44 Tm <636170616369746F7220> Tj 1 0 0 1 198.48 211.44 Tm <6F6E20> Tj 1 0 0 1 210.72 211.44 Tm <74686520> Tj /F3 8.0 Tf 1 0 0 1 225.60 211.68 Tm <7374617274696E6720> Tj /F3 8.5 Tf 1 0 0 1 255.60 211.68 Tm <616E6420> Tj 1 0 0 1 272.64 211.68 Tm <72756E6E696E6720> Tj 1 0 0 1 304.56 211.68 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 314.64 211.68 Tm <6120> Tj /F3 8.5 Tf 1 0 0 1 321.60 211.68 Tm <73696E676C652E> Tj /F3 8.0 Tf 1 0 0 1 71.28 201.36 Tm <706861736520> Tj /F3 9.0 Tf 1 0 0 1 96.24 200.64 Tm <696E64756374696F6E20> Tj /F3 8.5 Tf 1 0 0 1 135.12 200.64 Tm <6D6F746F72> Tj /F3 13.5 Tf 1 0 0 1 52.80 190.08 Tm <2D20> Tj /F3 8.0 Tf 1 0 0 1 71.52 189.84 Tm <526576657273696E6720> Tj /F3 8.5 Tf 1 0 0 1 110.64 189.84 Tm <74686520> Tj 1 0 0 1 125.28 189.84 Tm <646972656374696F6E20> Tj /F3 9.0 Tf 1 0 0 1 161.76 189.84 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 172.08 189.84 Tm <726F746174696F6E20> Tj 1 0 0 1 203.76 189.84 Tm <6F6620> Tj /F3 7.5 Tf 1 0 0 1 213.84 189.84 Tm <6120> Tj /F3 8.5 Tf 1 0 0 1 220.56 189.84 Tm <73696E676C6520> Tj /F3 8.0 Tf 1 0 0 1 245.52 190.56 Tm <706861736520> Tj /F3 8.5 Tf 1 0 0 1 270.00 189.84 Tm <636170616369746F7220> Tj 1 0 0 1 307.92 190.08 Tm <696E64756374> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 35.52 168.24 Tm <5265666572656E6365733A> Tj /F3 6.5 Tf 1 0 0 1 35.76 157.68 Tm <276C20> Tj /F3 13.5 Tf 1 0 0 1 40.56 154.80 Tm <2E20> Tj /F3 7.5 Tf 1 0 0 1 53.52 155.04 Tm <6C2E4A2E20> Tj /F3 8.5 Tf 1 0 0 1 66.00 154.80 Tm <4E61677261746820> Tj /F3 9.0 Tf 1 0 0 1 98.88 154.80 Tm <2620> Tj /F3 8.5 Tf 1 0 0 1 108.00 154.80 Tm <442E502E4B6F74686172692C2220> Tj /F3 8.0 Tf 1 0 0 1 161.04 154.80 Tm <456C656374726963616C20> Tj /F3 8.5 Tf 1 0 0 1 198.00 154.80 Tm <4D616368696E6573222C20> Tj /F3 8.0 Tf 1 0 0 1 243.36 155.04 Tm <5461746120> Tj /F3 9.0 Tf 1 0 0 1 262.08 154.80 Tm <4D634772617720> Tj /F3 9.5 Tf 1 0 0 1 298.56 155.04 Tm <48696C6C> Tj /F3 13.5 Tf 1 0 0 1 35.28 139.92 Tm <322E20> Tj /F3 7.5 Tf 1 0 0 1 53.28 139.92 Tm <532E20> Tj /F3 8.0 Tf 1 0 0 1 63.12 139.92 Tm <4B2E20> Tj 1 0 0 1 73.44 139.92 Tm <4268617474616368617279612C20> Tj /F3 8.5 Tf 1 0 0 1 127.68 139.44 Tm <22456C656374726963616C20> Tj 1 0 0 1 168.24 139.92 Tm <4D616368696E6573222C20> Tj /F3 8.0 Tf 1 0 0 1 213.84 139.92 Tm <5461746120> Tj /F3 8.5 Tf 1 0 0 1 232.56 139.92 Tm <4D634772617720> Tj /F3 9.5 Tf 1 0 0 1 268.80 139.92 Tm <48696C6C> Tj /F3 13.5 Tf 1 0 0 1 35.52 125.04 Tm <332E20> Tj /F3 8.0 Tf 1 0 0 1 53.52 125.04 Tm <422E20> Tj /F3 7.5 Tf 1 0 0 1 64.08 125.04 Tm <4C2E20> Tj /F3 8.0 Tf 1 0 0 1 72.72 125.04 Tm <54686572616A6120> Tj 1 0 0 1 103.92 125.04 Tm <616E6420> Tj /F3 9.0 Tf 1 0 0 1 120.48 125.04 Tm <412E20> Tj /F3 7.5 Tf 1 0 0 1 132.00 125.04 Tm <4B2E20> Tj /F3 8.5 Tf 1 0 0 1 141.84 125.04 Tm <54686572616A612C20> Tj 1 0 0 1 175.68 124.56 Tm <22456C656374726963616C20> Tj 1 0 0 1 216.24 125.04 Tm <546563686E6F6C6F677920> Tj 1 0 0 1 264.24 126.00 Tm <28566F6C2D6C6C29222C20> Tj /F3 7.5 Tf 1 0 0 1 298.56 125.04 Tm <532E20> Tj /F3 8.0 Tf 1 0 0 1 308.16 125.04 Tm <4368616E64> Tj /F3 13.5 Tf 1 0 0 1 35.04 110.16 Tm <342E20> Tj /F3 8.0 Tf 1 0 0 1 53.52 110.16 Tm <48757361696E20> Tj 1 0 0 1 82.56 110.16 Tm <41736866617120> Tj /F3 9.5 Tf 1 0 0 1 111.36 108.48 Tm <2C2220> Tj /F3 8.0 Tf 1 0 0 1 120.48 110.16 Tm <456C656374726963616C20> Tj /F3 8.5 Tf 1 0 0 1 157.44 110.16 Tm <4D616368696E6573222C20> Tj 1 0 0 1 203.52 110.16 Tm <4468616E7061745261692620> Tj /F3 7.5 Tf 1 0 0 1 257.28 109.92 Tm <536F6E73> Tj /F3 13.5 Tf 1 0 0 1 35.52 95.28 Tm <352E20> Tj /F3 9.0 Tf 1 0 0 1 53.04 95.28 Tm <412E452E20> Tj /F3 8.5 Tf 1 0 0 1 72.96 95.28 Tm <4669747A676572616C642C20> Tj 1 0 0 1 116.64 95.04 Tm <432E4B696E67736C65794A7220> Tj /F3 9.0 Tf 1 0 0 1 167.04 95.04 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 185.28 95.04 Tm <5374657068656E20> Tj /F3 10.0 Tf 1 0 0 1 220.80 95.04 Tm <442E20> Tj /F3 8.5 Tf 1 0 0 1 234.24 95.04 Tm <556D616E732C22456C65637472696320> Tj 1 0 0 1 299.28 95.28 Tm <4D616368696E657279222C> Tj /F3 8.0 Tf 1 0 0 1 52.80 84.48 Tm <5461746120> Tj /F3 9.5 Tf 1 0 0 1 71.76 84.48 Tm <4D636372617720> Tj 1 0 0 1 108.00 84.48 Tm <48696C6C> Tj /F3 13.5 Tf 1 0 0 1 35.28 69.60 Tm <362E20> Tj /F3 8.5 Tf 1 0 0 1 53.52 69.60 Tm <422E522E20> Tj /F3 9.0 Tf 1 0 0 1 72.72 69.36 Tm <477570746120> Tj /F3 8.5 Tf 1 0 0 1 100.32 69.36 Tm <2656616E64616E6153696E6768616C2C20> Tj 1 0 0 1 174.96 69.12 Tm <2246756E64616D656E74616C7320> Tj /F3 9.5 Tf 1 0 0 1 235.44 69.36 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 246.72 69.36 Tm <456C656374726963616C20> Tj 1 0 0 1 285.12 69.60 Tm <4D616368696E65732C20> Tj 1 0 0 1 328.56 69.60 Tm <4E6577> Tj 1 0 0 1 53.04 59.04 Tm <41676520> Tj 1 0 0 1 70.80 59.04 Tm <496E7465726E6174696F6E616C> Tj /F3 13.5 Tf 1 0 0 1 35.76 44.16 Tm <372E20> Tj /F3 7.5 Tf 1 0 0 1 53.52 44.16 Tm <502E20> Tj 1 0 0 1 63.12 43.92 Tm <532E20> Tj /F3 8.5 Tf 1 0 0 1 72.72 44.16 Tm <4268696D6272612C20> Tj 1 0 0 1 110.16 43.44 Tm <22456C656374726963616C20> Tj /F3 9.0 Tf 1 0 0 1 150.96 43.92 Tm <4D616368696E657322274B68616E6E6120> Tj /F3 8.0 Tf 1 0 0 1 228.72 44.16 Tm <5075626C697368657273> Tj ET endstream endobj 68 0 obj <> stream 82 I CURRICULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEERING 7.47.5 Alternating Current Series motor and Universal motorSpecial Purpose Machines: Stepper motor, Schrage motor and Servomotor Practical:1. Magnetic Circuits- To draw B-H curve for two different sample of lron Core- Compare their relative permeability2. Two Winding Transformers- To perform turn ratio test- To perform open circuit (OC) and short circuit (SC) test to determineequivalent circuit parameter of a transformer and hence to determine theregulation and efficiency at full load3. DC Generator- To draw open circuit characteristic (OCC) of a DC shunt generator- To draw load characteristic of shunt generator4. DC MotorSpeed control of DC Shunt motor by (a) armature control method (b) fieldcontrol method- To observe the effect of increasing load on DC shunt motor's speed,armature current, and field current.5. 3-phase Machines- To draw torque'speed characteristics and to observe the effect of rotor. resistance on torque.speed characteristics of a 3-phase lnduction MotorTo study load characteristics of synchronous generator with (a) resistiveload (b) inductive load and (c) capacitive load6. Fractional Kilowatt Motors- To study the effect of a capacitor on the starting and running of a single.phase induction motor- Reversing the direction of rotation of a single phase capacitor induct References:'l . l.J. Nagrath & D.P.Kothari," Electrical Machines", Tata McGraw Hill2. S. K. Bhattacharya, "Electrical Machines", Tata McGraw Hill3. B. L. Theraja and A. K. Theraja, "Electrical Technology (Vol-ll)", S. Chand4. Husain Ashfaq ," Electrical Machines", DhanpatRai& Sons5. A.E. Fitzgerald, C.KingsleyJr and Stephen D. Umans,"Electric Machinery",Tata Mccraw Hill6. B.R. Gupta &VandanaSinghal, "Fundamentals of Electrical Machines, NewAge International7. P. S. 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0.00 Tc /F3 16.0 Tf 1 0 0 1 78.96 502.32 Tm <49> Tj /F3 9.0 Tf 1 0 0 1 78.72 491.52 Tm <30> Tj 1 0 0 1 78.72 481.20 Tm <30> Tj ET endstream endobj 80 0 obj <> stream $fl GUHEiGULUi' = BAOHELOH'S DEGREE IN COMPTJTEH ENGINEEHING DISERETE STRUCTUREcT 55r tdrture !Tutorial iPractital : Year ; llPart : ll ourse ObfectivesrTo gaih knowledge in disci'ete mathematics and finite state automata in analgorithmic approach and to Eain fundamental and conceptual clarity in the areaof Logic, Rearoning, Algorithms, Recurrence Relation, Graph Theory, and Theoryof Automatal. lo8ir, inductlon and Reasoning (12 hours)1.1 Ptoposition and Truth funolort1,2 Pnopositlonal Logic1.3 Expressihg statemenB ih Logic Propositional Logic1.4 The predicate Logic1.5 Validity1.6 lnformal Deduction in Predicate Logic1,7 Rules of lnfurence and Proofs1.8 lnformal Proofs and Foitndl Pbofs1.9 Elertrentary lnduction and Complete lnduction.l.10 Methods of Tableaux1.1 'l Cortsistency and Completefless of the System2. Flnite Stiite AUtomata (10 hours)2.1 Sequential Circuits and Finite state Machine2.2 Finite State Automata2,3 Language and Crarnmars2.4 Non-deterministic Finite State Autorrata2.5 Language arid Autotnata2,6 Regular Expressiorr and lB characleristicsi. Recurrcnce Relation (8 hourc)3.1 RecUrsiVe ULefinition Of SeqUeirces3.2 Solution of Linear redrirence rclations3.3 Solutlon to Nonlinar Recurrense Relations3.4 Application to Algorithm Ailalysis4. 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C. Bi*hoff, T.C. Bartee, "Modern Applled Algsbra", CB$ Pghliohers.3. R. Johnsonbaugh, "Discrete Mathem.atles', Prentice Hall lnc.4, C,Charand, B.R.Oller Mann, 'Applied ard Algori*rrnlc Graph Thgow',McCraw Hill5. Joe L. Mott, AbrahanlGndel, and Thesdore P. 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8.5 Tf 1 0 0 1 146.64 258.96 Tm <64796E616D696320> Tj /F3 8.0 Tf 1 0 0 1 182.88 258.96 Tm <6C69737420> Tj 1 0 0 1 195.84 258.72 Tm <737472756374757265> Tj /F3 7.0 Tf 1 0 0 1 79.20 248.16 Tm <332E3120> Tj /F3 13.5 Tf 1 0 0 1 91.68 248.16 Tm <2E3220> Tj /F3 8.5 Tf 1 0 0 1 107.04 248.16 Tm <417272617920> Tj 1 0 0 1 130.80 248.16 Tm <696D706C656D656E746174696F6E20> Tj /F3 9.0 Tf 1 0 0 1 193.20 247.92 Tm <6F6620> Tj /F3 7.5 Tf 1 0 0 1 203.76 247.92 Tm <6C69737473> Tj /F3 11.0 Tf 1 0 0 1 79.20 237.36 Tm <332E312E3320> Tj /F3 8.0 Tf 1 0 0 1 107.04 235.68 Tm <51756575657320> Tj 1 0 0 1 139.20 237.12 Tm <617320> Tj 1 0 0 1 150.24 237.36 Tm <6C697374> Tj 0.00 Tc /F3 13.5 Tf 1 0 0 1 36.24 218.16 Tm <342E20> Tj /F3 8.5 Tf 1 0 0 1 54.72 218.16 Tm <4C696E6B656420> Tj /F3 8.0 Tf 1 0 0 1 82.80 217.92 Tm <6C69737473> Tj /F3 13.5 Tf 1 0 0 1 54.00 204.48 Tm <342E3120> Tj /F3 9.0 Tf 1 0 0 1 79.20 204.24 Tm <44796E616D6963696D706C656D656E746174696F6E> Tj /F3 13.5 Tf 1 0 0 1 54.00 193.68 Tm <342E3220> Tj /F3 8.5 Tf 1 0 0 1 78.72 193.44 Tm <4F7065726174696F6E7320> Tj /F3 9.0 Tf 1 0 0 1 124.32 193.20 Tm <696E20> Tj /F3 8.5 Tf 1 0 0 1 134.16 193.20 Tm <6C696E6B656420> Tj 1 0 0 1 160.32 193.20 Tm <6C697374> Tj /F3 13.5 Tf 1 0 0 1 54.00 182.88 Tm <342E3320> Tj /F3 8.5 Tf 1 0 0 1 79.20 182.64 Tm <4C6972696B656420> Tj /F3 9.0 Tf 1 0 0 1 107.04 182.40 Tm <737461636B20> Tj /F3 8.0 Tf 1 0 0 1 132.00 182.40 Tm <616E6420> Tj 1 0 0 1 148.56 182.88 Tm <717565756573> Tj /F3 13.5 Tf 1 0 0 1 54.00 172.08 Tm <342E3420> Tj /F3 9.0 Tf 1 0 0 1 79.20 171.84 Tm <446F75626C7920> Tj 1 0 0 1 110.40 171.60 Tm <6C696E6B656420> Tj /F3 8.0 Tf 1 0 0 1 136.80 171.60 Tm <6C6973747320> Tj /F3 8.5 Tf 1 0 0 1 153.12 171.36 Tm <616E6420> Tj /F3 7.5 Tf 1 0 0 1 170.40 171.36 Tm <69747320> Tj /F3 8.5 Tf 1 0 0 1 180.72 171.36 Tm <6170706C69636174696F6E73> Tj /F3 13.5 Tf 1 0 0 1 36.00 152.88 Tm <352E20> Tj /F3 8.0 Tf 1 0 0 1 54.48 152.88 Tm <526563757273696F6E> Tj /F3 13.5 Tf 1 0 0 1 54.24 139.44 Tm <352E3120> Tj /F3 8.5 Tf 1 0 0 1 78.96 139.44 Tm <5072696E6369706C6520> Tj /F3 9.0 Tf 1 0 0 1 114.96 139.20 Tm <6F6620> Tj /F3 8.5 Tf 1 0 0 1 125.28 139.20 Tm <726563757273696F6E> Tj /F3 13.5 Tf 1 0 0 1 54.24 128.64 Tm <352E3220> Tj /F3 9.0 Tf 1 0 0 1 78.24 128.64 Tm <544F4820> Tj /F3 9.5 Tf 1 0 0 1 100.08 128.40 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 119.76 128.40 Tm <4669626F6E6163636920> Tj /F3 8.0 Tf 1 0 0 1 159.36 128.16 Tm <73657175656E6365> Tj /F3 13.5 Tf 1 0 0 1 54.24 118.08 Tm <352E3320> Tj /F3 8.5 Tf 1 0 0 1 78.24 118.08 Tm <4170706C69636174696F6E7320> Tj /F3 9.0 Tf 1 0 0 1 128.64 117.84 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 138.96 117.84 Tm <726563757273696F6E> Tj /F3 13.5 Tf 1 0 0 1 36.00 99.12 Tm <352E20> Tj /F3 8.0 Tf 1 0 0 1 53.52 99.12 Tm <5472656573> Tj /F3 13.5 Tf 1 0 0 1 53.76 85.44 Tm <362E3120> Tj /F3 8.5 Tf 1 0 0 1 78.24 85.44 Tm <436F6E63657074> Tj /F3 13.5 Tf 1 0 0 1 53.76 74.88 Tm <362E3220> Tj /F3 8.5 Tf 1 0 0 1 78.24 74.64 Tm <4F7065726174696F6E20> Tj /F3 9.0 Tf 1 0 0 1 120.24 74.64 Tm <696E20> Tj /F3 8.0 Tf 1 0 0 1 130.08 74.64 Tm <42696E61727920> Tj 1 0 0 1 156.72 74.40 Tm <74726565> Tj /F3 13.5 Tf 1 0 0 1 53.76 64.08 Tm <362E3320> Tj /F3 8.5 Tf 1 0 0 1 78.00 64.08 Tm <547265657365617263682C20> Tj 1 0 0 1 127.44 63.84 Tm <696E73657274696F6E2F64656C6574696F6E73> Tj /F3 13.5 Tf 1 0 0 1 53.76 53.28 Tm <362E3420> Tj /F3 8.0 Tf 1 0 0 1 78.00 53.28 Tm <5472656520> Tj 1 0 0 1 97.20 53.28 Tm <74726176657273616C7320> Tj 1 0 0 1 135.60 54.00 Tm <287072652D6F726465722C20> Tj 1 0 0 1 178.32 53.52 Tm <706F73742D6F7264657220> Tj /F3 10.0 Tf 1 0 0 1 219.36 52.80 Tm <616E6420> Tj /F3 8.0 Tf 1 0 0 1 239.28 52.80 Tm <696E2D6F7264657229> Tj /F3 13.5 Tf 1 0 0 1 53.52 42.72 Tm <362E3520> Tj /F3 8.5 Tf 1 0 0 1 78.48 42.72 Tm <4865696768742C20> Tj 1 0 0 1 109.20 42.48 Tm <6C6576656C20> Tj /F3 8.0 Tf 1 0 0 1 129.60 42.24 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 146.16 42.24 Tm <646570746820> Tj /F3 11.0 Tf 1 0 0 1 170.88 42.00 Tm <6F6620> Tj /F3 7.0 Tf 1 0 0 1 183.36 42.00 Tm <6120> Tj /F3 8.0 Tf 1 0 0 1 189.84 42.00 Tm <74726565> Tj 0.00 Tc /F3 7.5 Tf 1 0 0 1 307.68 218.40 Tm <2820> Tj /F3 8.5 Tf 1 0 0 1 312.72 217.20 Tm <3520> Tj 1 0 0 1 320.40 217.44 Tm <686F75727320> Tj /F3 7.5 Tf 1 0 0 1 344.40 216.24 Tm <29> Tj 0.00 Tc /F3 7.0 Tf 1 0 0 1 307.68 152.88 Tm <2820> Tj /F3 9.0 Tf 1 0 0 1 312.48 151.92 Tm <3420> Tj /F3 8.5 Tf 1 0 0 1 320.40 151.92 Tm <686F75727320> Tj /F3 7.5 Tf 1 0 0 1 344.40 150.96 Tm <29> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 307.44 99.12 Tm <2820> Tj 1 0 0 1 312.72 98.16 Tm <3720> Tj /F3 8.5 Tf 1 0 0 1 319.92 98.16 Tm <686F75727320> Tj /F3 7.5 Tf 1 0 0 1 343.92 97.20 Tm <29> Tj ET endstream endobj 92 0 obj <> stream 86 | CUnRCUUM - BACHELOR',S DEGREE lN COMPUTER ENGINEERING DATA STRUCTURE AND ATGORITHMSct 552 Lecture :3Tutorial : 0Practica! :3 Year: llPart : ll Course Objectives:To provide fundamental knowledge of various data structures and theirimplementation and to provide ttre fundamental knowledge of various algoritrms andtheiranalpist. Concept of data structure (2 hours)1.1 lntroduction: data types, data structures and abstract data types1.2 lntroduction to algorithms 2. The Stack and Queue (5 hours)2.1 Stack operation2.2 Stack application: Evaluation of lnfix, Postfix and Prefix expressions2.3 Operations in queue, Enqueue and Dequeue2.4 Linear and circular queue2.5 Priority queue 3. List3.1 ( 3 hours ) Definition3.1.1 Static and dynamic list structure3.1 .2 Array implementation of lists3.1.3 Queues as list 4. Linked lists4.1 Dynamicimplementation4.2 Operations in linked list4.3 Liriked stack and queues4.4 Doubly linked lists and its applications5. Recursion5.1 Principle of recursion5.2 TOH and Fibonacci sequence5.3 Applications of recursion5. Trees6.1 Concept6.2 Operation in Binary tree6.3 Treesearch, insertion/deletions6.4 Tree traversals (pre-order, post-order and in-order)6.5 Height, level and depth of a tree ( 5 hours ) ( 4 hours ) ( 7 hours ) endstream endobj 93 0 obj <> >> stream :Q ?XQ (C^?-Q\Bb8Tdw>#4RPIc^@T@ 0)ؠ28B]ˑ0^a5#Hr%9|B8@hDH? 0[C 0bAH**Hp@0.DQk$9 (`Ai?8 `srX p%! ѫM4 i=~^pAڠA9QdL)̘30=?!g oD1?7V{}7]#.;A>OM_t]Q/Iޛ =Jwިu-7~ߤ׷|v׷y_uo~݅M4t7Sb]?Տ>~~ wu}iiM[a]j_}z^~uU7׶!5| CzV_aӿUKdpoD~ߏ]I5%Րrk3B" ^1^ 6*-__W# ;jG?&]߄"BMm׷BCDfh`+~x80I7E2 ĿE_]O⢶ ?0Zo_w-IT#@}~_ȣa-<z>ޝ]WKC?܎B0dcei!7#C!Zkr ϭ!@1#v~1{~ wwd d_&;ğ7="jo?҂}b?^Ick)?tߠ^D]A]w\p{_mbL[۶ܫojw'<O￷k_v߾k߻qOwbwk}߭;t]_ޭ/W_Nҷzد}u_~i߯uҶwҴmW mmnտ[Z_/_m}! k_Ӱaii~V5]]pw~4Uc?!Bw {[[ !r*KUmK᥂[ /L4 v"BC1Xa- 2 A{vap[5&_qa?aLCݻ^wNaXI8I; ~f² E,THD\H\ئ"^+v x馮Aܧ_!!]Pwﰿvh0OjMnW݆[_ޞ &ô 0 ko馶Z,5_0 'iB"""""@U~n݅ -ja00 j vVNa   τTESM}> _SL&Sp0B$X(Pb"""#i[ aPa4he b"""6 a VbA 0E )H_ ,ԣ ,$Ԉ;2Eѯ!hhhyKag-$EVvBGf"r9 9';""""gFB'#Gd|.e#r#*2wh8"Drtl>a \9pdr#t{:d(RJ0C6 t` aG.0FtGGs#h$"]B"""""2lQG 6  R9ѸEo6>o@A|!p.g3yUqLЈ9+. 1˂BA*C@TyrLnAl$9nCC͆!ma<@>""# (G@t_ ;PY,tvje22 Df $\)l0H2\丈0AX2 5#k2%m f @UrpsXB2md|R.Y@.EBCQB JB i a,h S#ba `h?A [F pSe`;L4׭MU wwڮޝ}}Zzt(<" ﯽ {Hw_߾mC[@ a3@Z~hwUwAz;:OAk})d5 FkAgЁr pP _߆tv~wNޣI'mzzN~4_ݿk'ozCmw~)7V׽ק {]$}To}ӽoow^ȃW~׻ O#}/귯" u~^oۃ}/t5T׷?֡*K[_W%݂ZV][}{/ooakW!?^Ukm&M\/Wꂿ }VDM)_ޕaս+}" }{Z>oG/iXL\moߵὪaUاߡoOׯ/[@u=krl]}=0}!Wݿ{?}oO}%~K_z{ZW[}[$޶o7׿ W.}Uwr!K 1}Wu_oV]oJKokOڿiw׾t_RzimVn}/{u]_I&KoI'm-TUڶ_|/{ Xa{V۵I-Ia{Ҷ.Ok~ 0a- aOI7 aQ ou\KIKۆeou{/خЭ]i}LQWz '1]8oI/xIxh0׶u{ n{Ã]K ^vA0 [zU ;4ᦁA/Ao!X h4DDN׶ `NӴYEAY  a}XB!""$ p4L& 3o@GfeFY BJeұ@pG03B c\j@(D`1 h8O oӢVpD"ȱBAŐBz ?~[UJ)Q}rB/zZu˅Ă_u.~Am-m<'cm/K[JI+zzzgT/J%MU%`iZK VJUE! 饆aPh00@TÉRdXc'~?rd0ӻeTn-0A=%M7S&34h>LH TfH aGD_AڢB]OT;:!0配>@ A:.i"B0-K`;4iA+M?M7O]xzNaCMkޗ/ taWȸ0KPMW^Z_V}oC:hCC_o믽F zC}"1 ׷ЯOߴ__Aw_BQ ?^ёK!_0MWd3߮loa!͐/di(md!Xav8LLa3O~IbMA4 i@v 0VDs5#XA$ :f""Fw$2]PqÐM͒]i;|dZ -kC_aO {k+Z{dW "4*O0  1:CMM5*c=Bu$%q qqD"NCebDNE| @ҾD)4P Mt?ґ/:u_ ?_?ވ|~#W êE'O_;_ ᯯr|km}X]p/z5boA_ _]:_UD0/ ֿ_^'?}u7kuuK}/]O._i{5y?P04l+{"E!X2 =¬2}´[@C0Q $,DUi@_Ġk0 v  {Z%Zo5{-J V5 @A | &TBh< jia=SOT:a{ ^pA-BU^Jt!Ȥȸ/'J'a?ibm'׼2~ ~]RvfDP_hr AW(1o x./~.? _~o}/K_߯ _ӵZkWo}ldaXw0WV/ozoikOAxAŦ0A0M4 a4h0Qh`Ad%Ye؈Z ?^?@TmGR-G,U-h'B`8M4 5LdDW-NM#q Qs@0 0TTA +T4 J TƓW7SWgcgA p` bd̉BNQs@ACa :A4hA@ M40@A~3Ati44z :TުO׽WD܉! ?z!q ;[6u2]&Io~FK=GAIo麶о_>n]}߭E}}Q5/p#aꯍ_һ /{۽o^׽u믹 1_V{CijA?@-noՃߥ\?uǷ}n;w߻z_tB}{[kM¨Am]_Ҵ"a;am(lKa[ lE^KX*8iv;IKj=cQ]دvvݪ{Mh=PLAaa0x0 A al j aA  !1 % 0p"*[NF0Rm"qDJ[DDF"#%J -(6M:aG ?;HTӖ#2Ru - fvJgaDW$ wABa4MBwC^ z_2/Z+;_SYn ͇Nu[#D!; k*qlaP\.2,J̌*-__o;SvL wXHR@R% ߿ &vJӊw<"d`S AS0(C<9ӓ $ 5 ` h3P^[y/D|yDPC B1/HR#! @A BY '#9C %P`H3̰g d|S jK Au#A d12DABAa<'zanijL'ń=vA# xAL(L0A0 L`顅L~5U? 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0 1 206.64 82.56 Tm <717565756573> Tj /F3 13.5 Tf 1 0 0 1 40.32 70.80 Tm <332E20> Tj /F3 8.5 Tf 1 0 0 1 58.08 70.80 Tm <536F6C7574696F6E7320> Tj 1 0 0 1 95.76 71.04 Tm <6F6620> Tj /F3 9.0 Tf 1 0 0 1 105.60 71.04 Tm <544F4820> Tj /F3 8.5 Tf 1 0 0 1 127.68 71.04 Tm <616E6420> Tj 1 0 0 1 144.72 71.04 Tm <4669626F6E6163636920> Tj /F3 8.0 Tf 1 0 0 1 184.32 71.04 Tm <73657175656E636520> Tj /F3 8.5 Tf 1 0 0 1 223.20 71.28 Tm <627920> Tj /F3 8.0 Tf 1 0 0 1 235.20 71.52 Tm <526563757273696F6E> Tj /F3 13.5 Tf 1 0 0 1 39.84 60.24 Tm <342E20> Tj /F3 8.5 Tf 1 0 0 1 58.56 60.24 Tm <6C6D706C656D656E746174696F6E7320> Tj /F3 9.0 Tf 1 0 0 1 124.56 60.24 Tm <6F6620> Tj 1 0 0 1 134.88 60.48 Tm <6C696E6B656420> Tj /F3 8.5 Tf 1 0 0 1 161.52 60.48 Tm <6C6973743A20> Tj 1 0 0 1 176.88 60.48 Tm <73696E676C7920> Tj 1 0 0 1 201.60 60.48 Tm <616E6420> Tj /F3 9.0 Tf 1 0 0 1 218.40 60.48 Tm <646F75626C7920> Tj 1 0 0 1 248.16 60.96 Tm <6C696E6B656420> Tj /F3 8.5 Tf 1 0 0 1 274.56 61.20 Tm <6C697374> Tj /F3 13.5 Tf 1 0 0 1 40.32 49.44 Tm <352E20> Tj /F3 8.5 Tf 1 0 0 1 58.56 49.44 Tm <6C6D706C656D656E746174696F6E20> Tj 1 0 0 1 121.20 49.68 Tm <6F6620> Tj /F3 8.0 Tf 1 0 0 1 131.04 49.68 Tm <74726565733A20> Tj /F3 8.5 Tf 1 0 0 1 153.84 49.92 Tm <41564C20> Tj /F3 8.0 Tf 1 0 0 1 172.80 49.68 Tm <74726565732C20> Tj /F3 8.5 Tf 1 0 0 1 195.84 49.68 Tm <616E6420> Tj 1 0 0 1 212.88 49.92 Tm <62616C616E63696E67> Tj ET endstream endobj 98 0 obj <> stream cuRRrcuLUM - BACHELOR',S DEGREE tN COMPUTER ENGTNEERTNG | 87 6.6 AVL balanced trees and Balancing algorithm6.7 The Huffman algorithm6.8 B-Tree6.9 Red Black Tree 7. Sorting ( 5 hours )7.1 Types of sorting: internal and external7.2 lnsertion and selection sort7.3 Exchange sort7.4 Merge and Redix sort7.5 Shell sort7.6 Heap sort as a priority queue7.7 Big 'O' notation and Efficiency of sorting8. Searching ( 5 hours )8.1 Search technique8.2 Sequential, Binary and Tree search8.3 Ceneral search tree8.4 Hashing- 8.4.1 Hash function and hash tables8.4.2 Collision resolution technique9. GroMh Functions ( 2 hours)Asymptotic notations: e, O, Q, o, co notations and their properties10. Graphs ( 6 hours )10.1 Representation and applications10.2 Transitive closure10.3 Warshall's algorithm10.4 Graphs type10.5 Graph traversal and Spanning forests10.5.1 Depth FirstTraversal and Breadth FirstTraversal10.5.2 Topological sorting: Depth first, Breadth first topological sorting10.5.3 Minimum spanning trees, Prim's, Kruskal's and Round-Robinalgorithms10.6 Shortest-path algorithm1 0.6.1 Greedy algorithm'l 0.6.2 Dijkstra's Algorithm Practical:There shall be 10 to 12 lab exercises based on C or C+ +1. lmplementation of stack2. lmplementations of linear and circular queues3. Solutions of TOH and Fibonacci sequence by Recursion4. lmplementations of linked list: singly and doubly linked list5. lmplementation of trees: AVL trees, and balancing endstream endobj 99 0 obj <> >> stream n& &&* >lMG6H͋Q'0r P2@eqJ.M 4aN)) RdJ@u&""4fP9Ld5 GDpo>MSTᦈ4`L @Da`\d> jaOxiUB P 203 `ֈ5$6ՐqB>o pvpTIA rBDAA*)"ޟקza4C02f ؉Af j`F E!84ѶaOj A ߭~Vi4 4!aU O [a#&ENDCGtyM;[> ۢ7_Zt@$rI܊=d6 {D,!f=?[ UMx~7pIWz ;D}pOOn ߯߷֓{nxmu&M~FF6Hc} Ԇ G ?$'zMzAX7VFHL?tA_?{ӿ&}vA?k߿^ޕi7^߽_]l26*Mi7{^ߚ_"2SZkW_]'}:]>ޓt=zmoKZމ'J=ik__}붿??w܌z_- ߫V~OoIoﴗ_tW}o U/O~׷ _+A_f샂}tzkoNJK]z^HI`o_T/mO/'S kLEJCD|s_q>r#z_W߯V봿!ߥ_iY~Bo*9VBR~P_Nw/COO/hkk5y얁T^4wG]t{~k N^Uԅ(Sq*vTC$6HZO _քB!mr6T}HƘd(4_znMv{{#eAt HLzb~ooOF&d?b u,}[rOVp߿H:ukj"=^w}6]?o/kDZ뻾]/ww]o޿[j߿~mU__OuJ$^_kk[~k[[ ?֪mZ_}omke!__ޘ0$վU]]zMk}zk"Wmu]vmmx}7^ֿ5}~a/[KKmm/KǺkk=& >l0K pJjm}IekMm_^|_j0J Y.vm/b>Mu5m}WQ!pfaHNWPLKm~wak &zV^lB" "DW $[0e?kA`aS aV_.څ1LWċ@ 0U %xfo }0]a jC,;AV…~[^#"$L2'"""Qbh"" .DN 7 /zik؊WpL#xM i z|5^""$]!4¦ ߧ &wa=0""!!0MM5N^DDDHG 8CA2莈莎T-Hjs6b=`1#ǣ\`fFB$D"DDDDDDDDDgfF876P1asqp;oR8}$.U6*gD$xA|`ap<4""""""""#i'# ,u*ޚ (ₑ#'[^,$|wPFF0N{@ d ^U}U!+u@A"-O'kTN'+Bm__JɽqR"q{&2]֖Bc&$`9P)9 B!hB`[\ Pk„@ 5 `֑N Hؤ!Tiia=mSAA3Q %.Br&PF E <Ј5i_4a44jqa L v0PS`g  3Gm}>v_!!1(2.;]SiP 0 Ttm8A6 D/#\jza8'!-7p@ !MznA=|%7 ~# :D&8.ӡI~CKI֩:Oy6~C& o@ uq{Iim]]/;i7CMi=S{OAnto /;Hj'GzI_M]BxMֿ UmTKK^ׯ}Dպ^w~u_DmW_MZmm~uk^ٯpeeAAa _n:' $i!!w4ME7!5`Ooxa/a}tL' 0 aH1dcD bEA\tA wAi &T aM8a; 0TE;a{ """""""$@eș0C'cႦa4h4_"""""""Kϱl00M4p5M;5qIc k^][Ja&VV`+LBj )M(2fu2& -ޗgRj!ȴ)*HE`B!Ut&5l XB!AC!=z hxUһ@) |W' ^%~u;_FE/k/RԆDc3D BA~BNAH`0!@t Ba0`1\3XB 0@Za;4PvXOPuŧXDh(Ͼ:nC !C| H` U@MhAx#0>~P,~A8WKa=7=7{$/ ~뤵xC5%I_q?޿}zK޷m/JZm_C=~_K6Z?]p_ /K"%@i5Hl_u/ $تI  _[Uo_ҭw_H޿׫zK_jH/_^*UD-o^_ZkZi}k/Z߰®#'avK_ }m%__ @{ @3D5;_X0a{]l'}: Y LB"DaN L it MNii'!W5 " !XV aP°GȲ)S4ք D20 w;D,;|$nD; R=PI>Z+{_*L#GLPAYQ&L(A >Z k"M,< 'I6*pդ&W!COMлp̈́Ci>@Nyt Jޛ>|q+?[׿D"Z_{OZ^}S#ȎVXK[NJV {ja.Q^Xa+P ױLT[ Ph06, (p0@DDGF;:idZ8Ȳ)S# / o\ z p}I9 !Np9 fA?TUI_W*~}_ʀN"u R Lu`hLd/H&O]0zXM=.4zI1!sw"X|ӻD$% Az z $zm'&o m']==t?\ ZM8IZ_./[뵼vK -U.; ^D;ؑa XKC o_/Gw^t  [}@|}@&AGR q[~h-wZK5vۿݺO2 zNFYT%j{ M_[[iYKm¶` j[ ᄶaaᅶXalW3ؒ[l} Mn5km(1P5 k 5Mi &N\00 aDH6" dDC"G Y /rȰ &\,& $ -y6vu“ޤ'Z[zAդN/ֱK:_pΟK.ZX!&25]`5 5XA0Nf2!DA"@WP p 9PPi!L 0h6{ 0}#邪h}&mDNW~7?V i7^ 1}6  Mރ}Ӯ9C]oP޿mH>ul'?KOVko~_o_~A;]/~~Z=jPQMM~_v^kFJUm>m/Ba.}1c;i{e_ $_ /j00^!xb)( ' tFdN Axh5ᄱ` aU-a")}F6t[J5vhp†–u4bM`K"x`[L 8P3yeM7^$A}tY9 %^LO]LJ_ _Qk/E{aTdd%ԅf|)V-  H`ilrNdJLF5 a`P0L&aKYR3  :aD\ x gA}3.)P"0z_4za;[Ai4 M0;4Ӱ: үP8O i<&AڨAA'4GD>'XAZxN-$DZqń_AA$A C1MTz"| n'm+WI&LH7|s( A9& Ț&C^oU&nC=$IztoU)_7C?nr }MӤkr4?KW7N§׷]juMXN]=V/׽i׫m-}o{]_ﺻi={u}z{v;_?]/kOZ]{kjN޺|2V ྩ?__5̋ur\0\A|(o+ _o(E&," ^D)|6oJ=BzP} _렾;&z_ [O{u}% }m/}RkӪփ~6UOi7+)>7h>}~+{kVXkڶlץMKM&_^i{a{Ӵa&T $ \4 v }mRomwz_S.*+d{v=Պav kaSUAov~l{ AߦnianZt/{{ݰaT&Ia 4AM4;UT ݐAN0deˊh0M4h4a1A0MQHDJ|DDDDDD0]b"#]}?/K%l%JRVӃ $[gb[-!GΪ4G`Y 6"H"kt"AqP}| ,Z D^@d#~wO6>4 "XN|(~WӥV)VD%!Ƞ(B&27"D| *O ->H:AA7!rp^ZW!t6MM$'kI⻧Kzy_muI M֕}:O]%/W_A~:UtK}ثۮ+^%u'!C-q ( S$`nڃƩդ}>?-~X__am.D)HAWr5mVzjt?ۮׯ\/N{H#]茛t?nvw߷z_H}Vވ7v뻷6P!rHM֗?Oi{m?~׷N] 6@^ՆVVVJm/ F m X*[^~ձ]L=Xa7a&[}EV!~h}!pG@Axzv 魈v 04M 4ӆM8aOJL/d4:!^Xa4VDDN2&bU#KiXa+!X tu9?吤Caa=DZ5z_Ԝ֮Y Zz_]jHJ(_28\$0 4e}*nOU;Q-?M8"EĈJA}LmttτP1Ä ~XC`w8IaȔv{c@íu;A&olj# [Wo%__Zw_/{Z֑5zA_kS$IZiI[ka(a+%KpL /% {-@/Mxa};0a>ao,aB B `,@8LG9!,Fv吩a0i V}״_M,ZAxZ1h%C4 ܂A?!^/UUɁHe TԕI-j"\A#\l `))‘ DQA 4 0A f>0@(L`ɉxj@`4M8P/[[Mh5!G 5D,=T'@x# DD?I!/艎w 6I7!ȂH:O GNmoD'}scA=7 tt7^~Hwo}P z[kQ IZֿۧҹ }&&_cX/M֓[OWTA}?W_^I_#@v](O"${?]_^K­pko^K|B *jdvG7Kdw &"_ |7a,%KD!" 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lmplementation of Heap References1I. Y. Langsam, M. J. Augenstein and A. M Tenenbaurn, 'Data Structures usingCand C+ +", PHI12. T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein, "lntroduction toAlgorithrns', PFll13. G.W. Rowe, "lntroduction to Data Structure and Algorithms with C andC+ +', PHIl,t. R. L. Krure, B" P. l-eung C. L. Tondo, "Data Structure and Program design inC', PHI15. G. Brassard and P. 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146.40 66.72 Tm <4F7065726174696F6E73> Tj /F3 7.0 Tf 1 0 0 1 70.32 54.00 Tm <332E3120> Tj /F3 13.5 Tf 1 0 0 1 83.04 54.00 Tm <2E3420> Tj /F3 8.0 Tf 1 0 0 1 98.64 54.00 Tm <5365676D656E7420> Tj 1 0 0 1 133.68 54.24 Tm <616E6420> Tj /F3 8.5 Tf 1 0 0 1 150.24 54.24 Tm <4F666673657420> Tj /F3 8.0 Tf 1 0 0 1 175.92 54.24 Tm <41646472657373> Tj /F3 13.5 Tf 1 0 0 1 45.84 41.52 Tm <332E3220> Tj /F3 8.5 Tf 1 0 0 1 69.84 41.52 Tm <41646472657373696E674D6F64657320> Tj /F3 8.0 Tf 1 0 0 1 143.28 41.52 Tm <6F6620> Tj 1 0 0 1 152.64 43.92 Tm <2C38303836> Tj ET endstream endobj 110 0 obj <> stream CURRICULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEERING 180 MICROPROCESSORSEX 551 Lecture :3Tutorial : IPractical : 3 Year : llPart : ll Course Objective:To familiarize students with architecture, programming, hardware and applicationof microprocessor 1. lntroduction (4 hours)1.1 lntroduction and History of Microprocessors1-2 Basic Block Diagram of a Cornputer1.3 Organization of Microprocessor Based System1.4 Bus Organization1.5 Stored program Concept and Von Nzumann Machine1.6 Processing Cycle of a Stored Program Computer1.7 Microinstructions and Hardwired/Microprogrammed Control tJnit1.8 lntroduction to Register Transfer Language 2. Programming with 8085 Microprocessor (fO hours)2.1 lnternal Architecture and Features of 8085 rnicroprocessor2.2 lnstruction Forrnat and Data Format2.3 Addressing Modes of 80852.4 lntel 8O85 lnstruction Set2.5 Various Programs in 8O852.5.1 Simple Programs with Arithmetic and Logical Operations2.5.2 Conditions and Loops2.5.3 Array and Table Processing2.5.4 Decimal BCD Conversion2.5.5 Multiplicafion and Division 3. Programming with 8O85 Microprocessor (I2 ttoqs)3.1 lnternal Architecture and Features of 8O86 Microprocessor3.X.1 BIU and Components3.1 .2 EU and Components3.1.3 EU and BIU Operations3.1 .4 Segment and Offset Address3.2 AddressingModes of ,8086 endstream endobj 111 0 obj <> >> stream )x2r82xG 4 @j#`dqi<L:#G!lMrL\1! 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Displaying Numbers in Binary and Hexadecimal Formats 3.63.73.83.93.10 4. Microprocessor System (10 hours)4.1 Pin Configuration of 8085 and 8086 Microprocessors4.2 Bus Structure4.2.1 Synchronous Bus4.2.2 Asynchronous Bus4.2.3 Read and Write Bus Timing of 8085 and 8086 Microprocessors4.3 Memory Device Classification and Hierarchy4,4 lnterfacing l/O and Memory4.4.1 Address Decoding4.4.2 Unique and Non Unique Address Decoding4.4.3 l/O Mapped l/O and Memory Mapped l/O4.4.4 Serial and Parallel lnterfaces4.4.5 l/O Address Decoding with NAND and Block Decoders (8085,8086)4.4.6 Memory Address Decoding with NAND, Block and PROMDecoders (8085, 8086)4.5 Parallel lnterface4.5.1 Modes: Simple, Wait, Single Handshaking and DoubleHandshaking endstream endobj 117 0 obj <> >> stream G@|Iq"c*:ҎT*ڬej?d"B(OR cd"ڎA 7S_AA5_zk_r ^?An(##\ +XN@a\d%!( ƲQAEeYAip+ i)";2GEفK\˂"\  a;ODAB/*  ̉e0hDDEg5S~j*;1!6NE! h0iڧ!MBLs!BR) 5VЉ j"M; w}ߺ!,䨋Fk>"0 iD? 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cuRRtcuLUM - BACHELOR',S DEGREE rN COMPUTER ENGTNEEBTNG I 91 4.5.2 lntroduction to Programmable Peripheral lnterface (PPl)4.6 Serial lnterface4.6.1 Synchronous and Asynchronous Transmission4.6.2 Serial lnterface Standards: RS232, RS423, RS422, USB4.6.3 lntroduction to USART4.7 lntroduction to Direct Memory Access (DMA) and DMA Controllers 5. lnterruptOperations5.1 Polling versus lnterrupt5.2 lnterrupt Processing Sequence5.3 lnterrupt Service Routine5.4 lnterrupt Processing in 80855.4.1 lnterrupt Pins and Priorities5.4.2 Using Programmable lnterrupt Controllers (PlC)5.4.3 lnterrupt lnstructions5.5 lnterrupt Processing in 80865.5.1 lnterrupt Pins5.5.2 lnterrupt Vector Table and its Organization5.5.3 Software and Hardware lnterrupts5.5.4 lnterrupt Priorities (5 hours) 6. Advanced Topics (4 hours)6.1 MultiprocessingSystems6.1.1 Real and Pseudo.Parallelism6.1 .2 Flynn's Classification6.1.3 lnstruction Level, Thread Level and Process Level Parallelism6.1.4 lnterprocess Communication, Resource Allocation andDeadlock6.1.5 Features of Typical Operating System6.2 Different Microprocessor Architectures6.2.1 Register Based and Accumulator Based Architecture6.2.2 RISC and CISC Architectures6.2.3 Digial Signal Processors Practical:There will be about 12 lab exercises to program 8085 and 8086 microprocessors' endstream endobj 123 0 obj <> >> stream >4ZPn >ʳ?@~E@}IG۪t%QJ >l( .62[QL()_,ңȀ#PFY#粪vZr@b E iЈ0D@@b'AB!vP)IAr@Dy:X9': ;NCH:M=4L ih3`f hH "GPd@e5";@r$ 4M5>B @4 &d\3 "$dPRmGN#$Kqt'h=| pAi̓Q"|ɆACdi18@vOTӽ;ӿAݧzii C &?nO[}>kv}vo#MWD"2prCG wUa?OzjhO%T~ttK Br1B C^T> !9"i77AA7Adiߝ28n諭C z {Mtz}ߋPB22!6}܌HPG_@a9ᓁzMA_}76{T߯A4AoA wIoowIO~ _M^Mٚ]w֖iv߷?'z׵zޗW}z_w/Zo]wM_amF=!ޓ_^QAw׫ c]'WJ]_hzU_oRa׷{zUzuB/g_8Lm~U{~?Q_+nDF4ݫ!޾jF^־Kz練H5X9_WUr}uLdy+_^_o_jtuNDWWa/fR _mA2w@:oE:|#7p/oי/zm_zzz\WEZߔ˷|ȻG-#d!Ɏú֫ߪo׷8gdiPH"F%@Ĉ;^{~K]_Lߔ o|u}]=m !ܤ9AR6B*; F6bV#Om[},67׷_r,e9R4nFn={B"> ^HG}m[_mz썖n{+MN_}ߦoVGw~}%^{}7u]J{߷~5XkK[zӮڙl-hio{]~m</3h+gW.ٽ;^}mշ1UAab"Imi]Z[a{W_K{{TU[mI{]v׿^5_~%iI¿{ [5?ګi~Ad=+IU_{ Pjkk+vC:r T JAQRH!;אk3OWWmm.)؈[^P؉?C` -iy}jpiMmoV][_1_Ćef`F!(sЇ[{tkau׆^P0ݦخDI`}esA4ӆ&M?NUTa{ i߯0Tk{XX( ab:6iC` `N$9A0 a5N{Aa~SO2'*DDJDDDb$\A\( n \DDDDD, v¦}TD"""%@QSx.g  3 """"8`[HN,bA/qd WRn1pGt\rF"8B>G9/々p-4DDDDDDDDDDDDDDDDDDDDIO#8A"""%}5сN4"%Q-Ͳ 6 xCGrF;d$Qk: "Yf?̸ySS 0C ޻Yȸ.?U@`AGZ9Ɔ?V~E L3(}a;T fhwO+kNBxO;19!hXwߤ<"!/W*{2[몽kzWUK}knu:G‚ BZ2!(A2)LF2& C: D5dXq__K4D[`f 31A@9G3 $Dx@s0D%d2@&x.A0aSMmB 0Lz P@ &4aS<)>)0!gRL**_u_\^kk?C58Zh< z:<2A" GlЁAC:A!ǯ߄'0q N4 Pi& a]/.A/mRh"!z@kD'; ZD'4C©qhzH4>.-8~< Bh0ׇ\N D҂ >0]oKA 1@ wDO!_]OOӌ&~m' Bo]&m ~CxAޒ 9!q?tKu"D/D*MzoIn H i:M7M'8AnC>AAKKu^_pˁ %oxC]5Oz tIdBOAҿ kzVүxJMݜҹ.AOI7!it߂XKpu^z_Mct7 M+TWVwW*Io^ڽ[\ub/]~K'_ [ _AO]ׂW_K~ Z XOFD_r 1|_}//_" ֿ]v[wy\wI}V}3^˻ϦVimX(sSm?V4}턐0 Wj l0\lTE{ݗHv!l.<50Ad-tgZh0A Q 0 a4 CL!i  "dj2+4""KQVYD*""""#@|Mxj%he- C/!,~TWK9&IpiA\B'A4] M: z,Mk}BAR{Tת Ua_]aU/F#VDk#3e+62_AffχHs͇"$@"vaF(F`ܤv8%DL Aj@ 1rY? މIr<03X2`3ɀvYoq"/|XN- ; 0 iLaB 0 #X!%C>Ddfjg (@@2 }Zv8M4 a`N0 hAAsa0AL'^C"lZqiꞆ S 8x}p ?hm4C'shBB5l|{A5 Oh&&1x w1'=oiiB"!p;=a:A7!$W<&i=]U MP}C΂ M|Aީק=7=:NC6Sr a%t'֟7  @A+.!;~znm^ujB֕< 0M_MwUN{/?}t;}5M>!\=K_'uVoN[7}ijMKmv]W^-+Ӈj֓}{5-w~___`Zp/~ }H9pd;Ճ Ѓj~ڶEgn0c@J#_L? gnNz_oWhw&۵Uw7|/6nߢ8o]_}=}8Vh0NNI_i}}RXh.~DHw!Q nJҴ߽uJh4o ov@ D$ԕ!?%GN҇ZUKi]tZAO  ZiH7^aViuJ> [M5OI7!~Ӱ}7Azty^_K CJxJL:x[OޯzztäkQL_q ᴮV+ªzx]S 0^_MX l<]uqI$0R u_rkW Pk%atAo A ( K꽸HRtcan6Kpthn r#tצ^xPjC@޿@#2[:0Hym-k}i _ /ʰ uu}t% >@ ἗ vtARol:!4?Ih-в>~A^z w/VIoI:q%T~_߽--a^R0/IﶒU )v*_^koKKo]I-.F+H5*P$z Koj Bi]6FizkkiI[* tf#ia kO_[z[m?JgDPTKD]a}^VmSIc>dTA>-3S[I5ҧIVIVaX݅B-4M{ilKtZ!aKX0_ {a~8a/xi- %pm ja+ `حh1^< x _qK *}IVIvu iE|0id3a{lSL6L솁mZZVRB5J jMjAm0N1alӵ[ Wz)-I*4 M20NR&AӰMaA;  & iZ Q 0B'd}B dMA0(0A`#!a2``ʰd8};^׸i """""Lb""""""SX@Pa&A!!)6J 9p@`"#Bj!"% `#*ZUUUTqK[PMDGj8O~YƝ10БB] l)^Y! qehcMuMBjpMoB!yZ9yK;Y^~ T'pMޝv렚}p 5{JU~W)k/_#1YIE_|("Aȩ#䤉UeK& `@&4! x9 9O7ivzKMp&>%8Okz^j 6^!&BsאO`ȄPAA M.D;ixKѰtIi?6Z0d]~-0 OruҪOO X o>~Kwu;~ڼ. ;_z _KH7fm6Ik zN*Y[HY ?!~W{W׭Iu{k{MEt )uO>JZz߽եuWo Ұ~ګI5vm/￧zWٍm[:%I4W /m+ՆյmXaa^% w_ᄘ80[a+L&!\uCC# }L4I\+i=ñt[ؠA* d{O OT0 a;p w!d(B 0x0Bi h4 0"""""""!3DF"#6,QYeL[K#&u.vi+ ++:YXajHd#+#Ef`2X>Y L/pJl3NԲ5+ɺPDzji$1Y|;Tv' 5M~vZڪ" ZyChS[SDOҫ 6+zNA;؅RaN[&?]w iN"ӪkzkKm?o[T륺j_}wޫ-|6y4˚dR,;#3lk}>uNtFb 0rNG` @bE*8&|BS !!0R;#` BL׿W;Z]/kGpAΠ0 &= \! 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Ramesh S. Gaonkar, "Microprocessor Architecture, Programming andApplication with 8085', Prentice Hall2. Peter Abel, "lBM PC Assembly Language and Programming', PearsonEducation lnc.3. D. V. Hall, iMicroprocessor and lnterfacing, Programming and Hardware",Tata McGraw Hill4. John Uffenbeck, 'Microcomputers and Microprocessors, The 808O, 8085 andZ-80 Programrning lnterfacing and Troubleshooting', Prentice Hall5. Waller A. Triebel and Avtar Singh, "The 8088 and 8086 Microprocessors,Programming, lnterfacing, Software, Hardware and Appl ications', PrenticeHall6. 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