Mathematics

 

In 1985, the Department of Mathematics was established at Government DegreeCollege, Paderu, with a mission to bolster scientific education among students in thesurrounding agency areas, thereby combating superstitions. Notably, the college activelyencouragedtheenrollmentoffemalestudentsinsciencecourses.Moreover,itsteadfastlyadvocated for every student to pursue advanced studies, thereby fostering a culture ofacademicexcellenceandknowledgeexpansion.

ProgrammeOutcomes:

➢     Acomprehensiveunderstandingofthefundamentalprinciplesandconceptsinmathematics,physics, and chemistry, including calculus, algebra, mechanics, thermodynamics, atomicstructure,chemical bonding,andorganicchemistry.

➢     Studentswillbeabletoapplymathematicaltechniques,physicallaws,andchemicalprinciples

toanalyzeandsolvecomplexproblemsindiversecontexts,includingtheoreticalcalculations,experimentaldataanalysis,andreal-worldapplications.

➢     Studentswilldevelopproficiency indesigning,conducting,andinterpretingexperimentsin

mathematics,physics,andchemistry,utilizingappropriatelaboratorytechniques,instrumentation,anddataanalysis methods.

➢     Studentswillbeabletorecognizeandappreciate theinterconnectednessofmathematics,

physics,andchemistry,andapplyinterdisciplinary approachestoaddressscientificchallengesandexplorenewresearchfrontiers.

➢     Studentswilldemonstrateeffectivecommunicationskills,bothorallyandinwriting,to

articulatemathematicalconcepts,physicalprinciples,andchemicalphenomenaclearlyandcoherentlytodiverseaudiences,includingpeers,instructors,andthebroadercommunity.

➢     Studentswilldevelopcriticalthinkingskillsandtheabilitytoanalyzeandevaluateexperimental

data,andtheoreticalmodels,

➢     Theseoutcomesprovidea frameworkforstudentstodevelopa well-roundedunderstandingofmathematics, physics, and chemistry and prepare them for various career paths in academia,industry,research, andbeyond.

CourseOutcomes:

Course1:ordinarydifferentialequations

Ø  After successful completion of this course, the student will be able to; Solve linear differentialequations

Ø  Convertnonexacthomogeneousequationstoexactdifferentialequationsbyusingintegratingfactors.

Ø  Knowthemethodsoffindingsolutionsofdifferentialequationsofthefirstorderbutnotofthefirstdegree

Ø  .4.Solvehigher-orderlineardifferentialequations,bothhomogeneousandnonhomogeneous,withconstantcoefficients.

Ø  Understandtheconceptandapplyappropriatemethodsforsolvingdifferentialequation

Course2:SolidGeometry

Ø  1.Gettheknowledgeofplanes.

Ø  2.Basicideaoflines,sphereandcones.

Ø  3.Understandtheproperties ofplanes,lines,spheresandcones.

Ø  4.Expresstheproblemsgeometricallyandthentogetthesolution.

Course3:ABSTRACTALGEBRA

Ø  Acquirethebasicknowledgeandstructureofgroups,subgroupsandcyclicgroups.

Ø  Getthesignificance ofthe notationofanormalsubgroups.

Ø  Getthebehaviorofpermutationsandoperationsonthem.

Ø  Studythehomomorphismsandisomorphismswith applications.

Ø  Understandtheringtheoryconceptswiththehelpofknowledgeingrouptheoryandtoprovethetheorems.

Ø  Understandtheapplicationsofringtheory invariousfield.

Course4:REALANALYSIS

Ø  Getclearideaabouttherealnumbersandrealvaluedfunctions.

Ø  Obtaintheskillsofanalyzingtheconceptsandapplyingappropriatemethodsfortestingconvergenceofasequence/series.

Ø  TestthecontinuityanddifferentiabilityandRiemannintegrationofa function.

Ø    Knowthegeometricalinterpretationofmeanvaluetheorems

Course5:LINEARALGEBRA

Ø  Understandtheconceptsofvectorspaces,subspaces,basises,dimensionandtheirproperties

Ø  Understandtheconceptsoflineartransformationsandtheirproperties

Ø  ApplyCayley-Hamiltontheoremtoproblemsfor findingtheinverseofamatrixandhigherpowersofmatriceswithoutusingroutinemethods

Ø  4.Learnthe propertiesofinnerproductspacesanddetermineorthogonalityininner    productspaces

Course6A:NUMERICALMETHODS

Ø  1.Understandthesubjectofvariousnumericalmethodsthatareusedtoobtainapproximatesolutions

Ø  2.Understandvariousfinitedifferenceconceptsandinterpolationmethods.

Ø  3.Workoutnumericaldifferentiationand integrationwheneverandwhereverroutinemethodsare        notapplicable.

Ø  4.Findnumericalsolutionsofordinarydifferentialequationsbyusingvariousnumericalmethods.

Ø  5.Analyzeandevaluatetheaccuracyofnumericalmethods.

Course-7A:METHEMATICALSPECIALFUNCTIONS

Ø  UnderstandtheBetaandGammafunctions,theirpropertiesandrelationbetweenthesetwofunctions, understand the orthogonal properties of Chebyshev polynomials and recurrencerelations.

Ø  Findpowerseriessolutionsofordinarydifferentialequations.

Ø  solveHermiteequationandwritetheHermitePolynomialoforder(degree) n,alsofindthegenerating function for Hermite Polynomials, study the orthogonal properties of HermitePolynomialsandrecurrencerelations.

Ø  SolveLegendreequationandwritetheLegendreequationoffirstkind,alsofindthegeneratingfunction for Legendre Polynomials, understand the orthogonal properties of LegendrePolynomials.

Ø  Solve Bessel equation and write the Bessel equation of first kind of order n, also find thegeneratingfunctionforBesselfunctionunderstandtheorthogonalpropertiesofBesselunction.

INTRODUCTION:

In 1985, the Department of Mathematics was established at Government DegreeCollege, Paderu, with a mission to bolster scientific education among students in thesurrounding agency areas, thereby combating superstitions. Notably, the college activelyencouragedtheenrollmentoffemalestudentsinsciencecourses.Moreover,itsteadfastlyadvocated for every student to pursue advanced studies, thereby fostering a culture ofacademicexcellenceandknowledgeexpansion.

ProgrammeOutcomes:

➢     Acomprehensiveunderstandingofthefundamentalprinciplesandconceptsinmathematics,physics, and chemistry, including calculus, algebra, mechanics, thermodynamics, atomicstructure,chemical bonding,andorganicchemistry.

➢     Studentswillbeabletoapplymathematicaltechniques,physicallaws,andchemicalprinciples

toanalyzeandsolvecomplexproblemsindiversecontexts,includingtheoreticalcalculations,experimentaldataanalysis,andreal-worldapplications.

➢     Studentswilldevelopproficiency indesigning,conducting,andinterpretingexperimentsin

mathematics,physics,andchemistry,utilizingappropriatelaboratorytechniques,instrumentation,anddataanalysis methods.

➢     Studentswillbeabletorecognizeandappreciate theinterconnectednessofmathematics,

physics,andchemistry,andapplyinterdisciplinary approachestoaddressscientificchallengesandexplorenewresearchfrontiers.

➢     Studentswilldemonstrateeffectivecommunicationskills,bothorallyandinwriting,to

articulatemathematicalconcepts,physicalprinciples,andchemicalphenomenaclearlyandcoherentlytodiverseaudiences,includingpeers,instructors,andthebroadercommunity.

➢     Studentswilldevelopcriticalthinkingskillsandtheabilitytoanalyzeandevaluateexperimental

data,andtheoreticalmodels,

➢     Theseoutcomesprovidea frameworkforstudentstodevelopa well-roundedunderstandingofmathematics, physics, and chemistry and prepare them for various career paths in academia,industry,research, andbeyond.

CourseOutcomes:

Course1:ordinarydifferentialequations

Ø  After successful completion of this course, the student will be able to; Solve linear differentialequations

Ø  Convertnonexacthomogeneousequationstoexactdifferentialequationsbyusingintegratingfactors.

Ø  Knowthemethodsoffindingsolutionsofdifferentialequationsofthefirstorderbutnotofthefirstdegree

Ø  .4.Solvehigher-orderlineardifferentialequations,bothhomogeneousandnonhomogeneous,withconstantcoefficients.

Ø  Understandtheconceptandapplyappropriatemethodsforsolvingdifferentialequation

Course2:SolidGeometry

Ø  1.Gettheknowledgeofplanes.

Ø  2.Basicideaoflines,sphereandcones.

Ø  3.Understandtheproperties ofplanes,lines,spheresandcones.

Ø  4.Expresstheproblemsgeometricallyandthentogetthesolution.

Course3:ABSTRACTALGEBRA

Ø  Acquirethebasicknowledgeandstructureofgroups,subgroupsandcyclicgroups.

Ø  Getthesignificance ofthe notationofanormalsubgroups.

Ø  Getthebehaviorofpermutationsandoperationsonthem.

Ø  Studythehomomorphismsandisomorphismswith applications.

Ø  Understandtheringtheoryconceptswiththehelpofknowledgeingrouptheoryandtoprovethetheorems.

Ø  Understandtheapplicationsofringtheory invariousfield.

Course4:REALANALYSIS

Ø  Getclearideaabouttherealnumbersandrealvaluedfunctions.

Ø  Obtaintheskillsofanalyzingtheconceptsandapplyingappropriatemethodsfortestingconvergenceofasequence/series.

Ø  TestthecontinuityanddifferentiabilityandRiemannintegrationofa function.

Ø    KnowthegeometricalinterpretationofmeanvaluetheoremsCourse5:LINEARALGEBRA

Ø  Understandtheconceptsofvectorspaces,subspaces,basises,dimensionandtheirproperties

Ø  Understandtheconceptsoflineartransformationsandtheirproperties

Ø  ApplyCayley-Hamiltontheoremtoproblemsfor findingtheinverseofamatrixandhigherpowersofmatriceswithoutusingroutinemethods

Ø  4.Learnthe propertiesofinnerproductspacesanddetermineorthogonalityininner    productspaces

Course6A:NUMERICALMETHODS

Ø  1.Understandthesubjectofvariousnumericalmethodsthatareusedtoobtainapproximatesolutions

Ø  2.Understandvariousfinitedifferenceconceptsandinterpolationmethods.

Ø  3.Workoutnumericaldifferentiationand integrationwheneverandwhereverroutinemethodsare        notapplicable.

Ø  4.Findnumericalsolutionsofordinarydifferentialequationsbyusingvariousnumericalmethods.

Ø  5.Analyzeandevaluatetheaccuracyofnumericalmethods.

Course-7A:METHEMATICALSPECIALFUNCTIONS

Ø  UnderstandtheBetaandGammafunctions,theirpropertiesandrelationbetweenthesetwofunctions, understand the orthogonal properties of Chebyshev polynomials and recurrencerelations.

Ø  Findpowerseriessolutionsofordinarydifferentialequations.

Ø  solveHermiteequationandwritetheHermitePolynomialoforder(degree) n,alsofindthegenerating function for Hermite Polynomials, study the orthogonal properties of HermitePolynomialsandrecurrencerelations.

Ø  SolveLegendreequationandwritetheLegendreequationoffirstkind,alsofindthegeneratingfunction for Legendre Polynomials, understand the orthogonal properties of LegendrePolynomials.

Ø  Solve Bessel equation and write the Bessel equation of first kind of order n, also find thegeneratingfunctionforBesselfunctionunderstandtheorthogonalpropertiesofBesselunction.