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1 M101 MATHEMATICS M101 2 M201 MATHEMATICS M201 3 M301 MATHEMATICS M301 4 M302 MATHEMATICS M302 5 M303 MATHEMATICS(MECHANICAL& M303 PRODUCTION) 6 M315 MATHEMATICS–III M315 7 M401 MATHEMATICS M401 8 MM101 DISCRETEMATHEMATICALSTRUCTURE M(MCA)101 9 MM301 STATISTICS&NUMERICALTECHNIQUES M(MCA)301 10 MM391 STATISTICS&NUMERICALANALYSISLAB M(MCA)391 (PRACTICAL) 11 CS312 NUMERICALMETHODS&PROGRAMMING M(CS)312 12 CS382 NUMERICALMETHODS&PROGRAMMINGLAB M(CS)382 (PRACTICAL) 13 CS402 OPERATIONRESEARCH&OPTIMIZATION M(CS)402 TECHNIQUES 14 CS511 OPERATIONRESEARCH&OPTIMIZATION M(CS)511 TECHNIQUES 15 CS581 OPERATIONRESEARCHLAB(PRACTICAL) M(CS)581 16 CE301 CIVILENGINEERING%IIISEMESTER M(CE)301 MATHEMATICS 17 MB105 QUANTITATIVEMETHODS%1 M(MBA)105 18 MB203 QUANTITATIVEMETHODS M(MBA)203 19 MB205 OPERATIONSRESEARCH M(MBA)205 20 M(CT)301 APPLIEDMATHEMATICS M(CT)301 21 CS(CT)401 COMPUTERSCIENCE&OPERATIONRESEARCH M[CS(CT)]401 1 Code:M101 Contacts:3L+IT=4 Credits:4 Sequence,convergence&divergenceofinfiniteseries–andtypical 1L examplesofconvergentanddivergentseries. Comparisontest(statementonly)andrelatedproblems 1L Ratiotest(statementonly)&relatedproblems 1L Cauchy’sroottest(statementonly)&relatedproblems 1L AlternatingseriesLeibnitz’stheorem(withoutproof),absoluteconvergence 2L &relatedproblems ! Reviewoflimit&continuityanddifferentiability 1L Successivedifferentiation,Leibnitz’stheorem[withoutproofbutwithproblems 3L ofthetypeofrecurrencerelationsinderivativesofdifferentorders&alsotofind (y )o]: Rolle’stheorem(statementonly);Meanvaluetheorems%Lagrange&Cauchy 6L (statementonly),Taylor’stheorem(withoutproofandproblemsinrespectof directuseandapplicationsofthetheoremonly),expansionsoffunctionsby Taylor&Maclaurinseries.Maclaurin’sseriesexpansionininfiniteseriesofthe functionslog(1+x), ,sinx,cosx,(a+x),nbeinganegativeintegerorafraction L’Hospital’sRule(statementonly)andrelatedproblems. Integrationof 2L π / 2 π/2 π/2 π/2 ∫ cos χdχ, ∫ sin χdχ, ∫ cos χsin χdχ, ∫cosmχsinnχdχ,m,narepositiveintegers 0 0 0 0 Application: Rectification 1L "# #$%& 2 Directioncosine,directionratio;Equationofaplane(generalform,normalform&4Linterceptform);Equationof astraightlinepassingthroughonepoint&twopoints; Pairofintersectingplanesrepresentingastraightline. Elementaryideasofsurfaceslikesphere,rightcircularconeandrightcircularcylinder (throughgeometricalconfiguration)andequationinstandardforms. ! Introductionoffunctionofseveralvariables&examples 2L Knowledgeoflimit&continuity Partialderivative&relatedproblemsHomogeneousfunctions&Euler’stheorem (statementonly)&problemsupto3variables. 3L Chainrulesandrelatedproblems. Differentiationofimplicitfunctions&relatedproblems. 4L Totaldifferentials&relatedproblems Maxima,minimaandsaddlepoints–definition,conditionofextremaandproblems 2L fortwovariables.Lagrange’smultipliermethod–problemsrelatedtotwovariables only. Lineintegral,doubleintegral,tripleintegral–discussionw.r.t.differenttypesoflimits 3L &problems;momentofinertia,centreofgravity. Jacobian–definition&relatedproblemsfortwovariables. 2L Applicationtoareas&volumes,surfaceareaofrevolution. Scalarandvectorfields–definitionandterminologies;products:dot,cross,box, 2L vectortripleproduct. Gradient,directionalderivative,divergence,curl(withproblems). 2L Tangentplanesandnormalsandrelatedproblems. 1L Statementsof Green’stheorem,divergencetheorem,Stokes’theoremwithapplications. 4L '() 3 *+, " -. .+."#/.).$0/$ #$123 /2 //4$52-6(7. 8. , 20/91:;2!"2 <2-6=6. >. +.. <099"#12."/;.2<". '. 92;,"? 7. /$:.@.A 3. 9"9!:)";$ =. 9"9!2 "";",!$ (. 9"9!2+/;"/ 6. 2$; "" -B. 92$; "" --. 99"#2..C#/ -8. /$2,; ->. D/9/99.".:E2, -'. 99".-282>:),"#2, -7. !:/$ ..%<9& -3. :"#.%<9& -=. 9F"#.%<9& -(. #"/9: A.@.%<9& -6. *+,99."-;.8:.%<9& 8B. / /99."#+$..2$!" 4
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