All years Course outcomes of B.Sc

MATHEMATICS COURSE OUTCOMES OF B.Sc

SEMESTER I

Paper: Differential calculus & Integral calculus

After completion of this course, students will be able

1.      Compare and contrast the ideas of continuity and differential.

2.      Evaluate integrals of rational functions by partial fraction

3.      Calculate the length of an arc of curve whose equations are given in parametric &polar form.

4.      Evaluate the area of surfaces of revolution.

5.      Identify different types of differential equations and solve them

6.       Obtain equations for surfaces and curves in there dimensions.

7.      Form the partial differential equation by elimination of constants &elimination of function.

SEMESTER II

Paper: Differential equations

On successful completion of the course, students will be able to:

1.      Student will be able to solve first order differential equations utilising the standard     

Techniques for separable, exact, linear, homogeneous, or Bernoulli cases.

2.      Student will be able to find the complete solution of a non homogeneous differential

  Equation as a linear combination of the complementary function and a particular Solution.

3.      Define ordinary differential equations

4.      Apply the fundamental concepts of ordinary differential equations and partial differential equations for the resolution

5.      Demonstrate understanding of the meaning of ODE, its order, its general solution and its particular solution

6.      Apply the method of undermined coefficient to solve non homogeneous linear differential equations with constant coefficients

SEMESTER III

Paper: Real Analysis

After completion of this course, students will be able

1.      Describe fundamental properties of the real numbers that lead to the formal development of Real Analysis.

2.      Demonstrated an understanding of limits and how that are used in sequences series and differentiation

3.       Determine whether or not real series are convergent by comparison with standard series by using the ratio test

4.      Give the essence of the proof of bolzanoweistrass theorem the contraction theorem as well as existence of convergent sub sequence using equi continuity.

5.      Describe the basic difference between the rational and real number

SEMESTER IV

Paper: Abstract Algebra

1.      Learn about the fundamentals concept of Groups, Sub groups, normal subgroups, isomorphism theorems, Cyclic and permutations groups

2.      To classify numbers into number sets

3.      To combine Polynomial by Addition or Subtraction

4.      To Solve problems of simple inequalities

5.      Interpret basic absolute value Expression

6.      To simplify algebraic expression using the commutative, Associative and distributive Properties

SEMESTER V

paper: LINEAR ALGEBRA (PAPER V)

1.      Define vector space and subspace

2.      Understand the concept of base and dimension of the vector space

3.      Understand algebraic and geometric representations of vectors

4.      Describes coordinates of a vector relative to a given basis

5.      Discuss spanning sets s for vectors

6.      Use characteristic polynomial to compute eigenvalues and eigen vectors

7.      Explain the relationship between the row space and column space of a matrix

8.      Recognize and use basic properties of subspaces and vector space

COURSE TITLE: SOLID GEOMETRY (PAPER VI(A ))

1. To understand geometrical terminology for sphere, cones, concoid and cylinder.

2. Able to recognise line and rotational symmetries.

3. Use geometric results to determine unknown angles.

4. Get basic knowledge about circle, cone, sphere, concoid and cylinder.

5. Understand the concepts and advance topics related to two and three dimensional geometry.

6.  Find the area of triangles, quadrilaterals and circles and shapes based on these.

SEMESTER VI

COURSE TITLE: NUMERICAL ANALYSIS (PAPER: VII)

1. The theoretical and practical aspects of the use of numerical analysis.

2. Proficient in implementing numerical methods for a variety of multidisciplinary applications.

3. To establish the limitations, advantages and disadvantages of numerical analysis.

4.To derive numerical methods for various mathematical operations and tasks, such 5.As interpolation, differentiation, integration, the solution of linear and non linear equations, and the solution of differential equations.

To understand of common numerical analysis and how they are used to obtain approximate solution to otherwise intractable mathematical problems.

To understand appropriate numerical methods to solve probability based problems

COURSE TITLE: VECTOR CALCULUS ( PAPER: VIII(A))

1. Define vector equations for lines and planes

2. Compute limits or derivatives of functions of two and three variables

3. Analyse vector functions to find limits, derivatives and integrals

4. Determine gradient vector fields and find potential function

5. Apply fundamental theorem of line integrals, green’s and divergence theorem to evaluate integrals

6. Compute partial derivatives, derivatives of vector valued function and gradient functions

7. Calculate directional derivatives and gradient

8. Explain the concept of conservative vector field and describes applications to physics