Govenment Degree College, Ravulapalem

MATHEMATICS

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Course Outcomes 2024-25

First B.Sc, Semester - II Differential Equations Course -1

After successful completion of this course, the student will be able to

1. solve first order first degree linear differential equations.

2. convert a non-exact homogeneous equation to exact differential equation by using an

integrating factor.

3. know the methods of finding solution of a differential equation of first order but not of first

degree.

4. solve higher-order linear differential equations for both homogeneous and non-homogeneous,

with constant coefficients.

5. understand and apply the appropriate methods for solving higher order differential equations.

Second B.SC SEMESTER -III Group Theory Course-2

After successful completion of this course, the student will be able to

1. acquire the basic knowledge and structure of groups

2. get the significance of the notation of a subgroup and cosets.

3. understand the concept of normal subgroups and properties of normal subgroup

4. study the homomorphisms and isomorphisms with applications.

5. understand the properties of permutation and cyclic groups

Second B.Sc Semester -IV Ring Theory Course-3

After successful completion of this course, the student will be able to

1. acquire the basic knowledge of rings, fields and integral domains

2. get the knowledge of subrings and ideals

3. construct composition tables for finite quotient rings

4. study the homomorphisms and isomorphisms with applications.

5. get the idea of division algorithm of polynomials over a field.

Second B.Sc. Semester-IV Real Analysis Course-4

Aftersuccessfulcompletionofthiscourse,thestudentwillbeableto

1. get clearideaabouttherealnumbersandrealvaluedfunctions.

2. obtaintheskillsofanalysingtheconceptsandapplyingappropriatemethodsfortesting convergence of a sequence/ series.

3. testthecontinuityand differentiabilityandRiemannintegrationofafunction.

4. knowthegeometricalinterpretationofmeanvalue theorems.

5. know about the fundamental theorem of integral calculus

Third B.Sc Semester-V Linear Algebra Course-5

After successful completion of this course, the student will be able to

1. understand the concepts of vector spaces, subspaces

2. understand the concepts of basis, dimension and their properties

3. understand the concept of linear transformation and its properties

4. apply Cayley- Hamilton theorem to problems for finding the inverse of a matrix and higher powers of matrices without using routine methods

5. learn the properties of inner product spaces and determine orthogonality in inner product spaces.

Third B.Sc Semester-V Vector Calculus-6

Studentsaftersuccessfulcompletionofthecoursewillbeableto

1. Learnmultipleintegrals asanaturalextensionofdefiniteintegraltoafunctionoftwovariables inthecaseofdoubleintegral/threevariables inthecaseoftripleintegral.

2. Learnapplicationsintermsoffindingsurfaceareabydoubleintegralandvolumebytripleintegral.

3. Determinethegradient,divergenceandcurlofavectorandvectoridentities.

4. Evaluateline,surfaceandvolumeintegrals.

5. understand relation between surface and volume integrals (Gauss divergence theorem),relationbetweenlineintegralandvolumeintegral(Green’stheorem),relationbetweenlineandsurfaceintegral(Stokestheorem)