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
