PROGRAMME OUTCOME:
• Enhance the analytical as well numerical ability.
• Know when there is a need for information, to be able to identify, locate, evaluate, and effectively use that information for the issue or problem at hand.
• Formulate and develop mathematical arguments in a logical manner.
• Acquire good knowledge and understanding in advanced areas of mathematics and statistics, chosen by the student from the given courses.
• Understand, formulate and use quantitative models arising in social science, business and other contexts.
• Apply the knowledge and skills to solve specific theoretical and applied problems in mathematics.
• Sufficient knowledge and skills enabling them to undertake further studies in mathematics and its allied areas on multiple disciplines concerned with mathematics.
• Develop a range of generic skills helpful in employment, internships and social activities.
• Mathematics is the mandatory ancillary course for four semesters in all Science streams.
COURSE OUTCOME :
1. Course Outcome of Calculus (Differentiation and Integration)
• Find Maxima and minima of function of two variables.
• Explain properties of definite integrals.
• Apply change variable method to find the value of double and triple integral.
• Explain properties of Beta functions.
• Evaluate integrals by using Beta and Gamma functions.
2. Course Outcome of Theory of Equation and Trigonometry
• Describe the relation between roots and coefficients.
• Transform the equation through roots multiplied by a given number, increase the roots, decrease the roots, removal of terms.
• Analyse the location and describe the nature of the roots of an equation.
• Expand sinnθ, cosnθ , tannθ cosnθ, sinnθ and
3. The course Outcome of Mechanics (Dynamics and Statistics)
• Define Resultant, Component of a Force, Coplanar forces, like and unlike parallel forces, Moment of a force and Couple with examples.
• Discuss Friction, Forces of Friction, Cone of Friction, Angle of Friction and Laws of friction.
• Find the tension at any point and discuss the geometrical properties of a catenary.
• Find the direct and oblique impact of smooth elastic spheres.
• Define Simple Harmonic Motion and find its Geometrical representation.
4. Course Outcome of Analytical Geometry 3D and Vector calculus
• Describe the various forms of equation of a plane, straight line, Sphere, Cone and Cylinder.
• Calculate the Shortest distance between two skew lines
• Interpret line, surface and volume integrals
5. Course Outcome of Real Analysis
• Define countable, uncountable sets.
• Define and recognize the concept of metric spaces, open sets, closed sets, limit points, interior point.
• Define and Illustrate the concept of completeness
• Determine the continuity of a function at a point and on a set.
• Characterize the concept of compactness in metric space.
6. Course Outcome of Complex Analysis
• Understand the significance of differentiability for complex functions and be
• Familiar with the Cauchy-Riemann equations.
• Write the bilinear transformation which maps real line to real line, unit circle to
• Unit circle, real line to unit circle.
• Classify singularities and poles.
7. Course Outcome of Modern Algebra
• Students will able to define subgroup, center, Normalizer of a subgroup.
• Define cyclic groups.
• Prove a group has no proper subgroup if it is cyclic group of prime order.
• Prove Cayley’s theorem, the fundamental theorem of homomorphism for groups.
• Define rings, zero divisors of a ring, integral domain, field and prove theorems.
8. Course Outcome of Linear Algebra
• Define Vector Space, Quotient space direct sum, linear span and linear independence, basis and inner product.
• Discuss the linear transformations, rank, nullity.
• Find the characteristic equation, eigen values and eigen vectors of a matrix.
9. Course Outcome of Numerical Analysis
• Define Basic concepts of operators Δ,Ε, ∇
• Find maxima and minima for differential difference equation.
• Derive Simpson’s 1/3 ,3/8 rules using trapezoidal rule
• Find the solution of the first order and second order equation with constant coefficient.
• Find the solution of ordinary differential equation of first by Euler,Taylor and Runge-Kutta methods.
10. Course Outcome of O.R
• Prove dual of the dual is primal.
• Find a basic feasible solution to the transportation problem by using North West corner rule, Vogel’s approximation method.
• Apply Modi method to solve transportation problem.
• Find the replacement period of equipment that fails suddenly/gradually
• Find inventory decisions costs using deterministic inventory problems with no shortages /with shortages
• Define basic components of Network and find critical path
• Define Two persons sum games , maximin-minimax principle, saddle points.
11. Course Outcome of Statistics
• Fit a straight line.
• Calculate the correlation coefficient for the given data.
• Define attributes, consistency of data, independence of data.
• Find index numbers for the given data.
• Derive Baye’s theorem.
• Define probability density function, probability distribution
• Derive mathematical expectation, binomial, poisson, normal distribution
12. Course Outcome of Sequence and Series
• Verify the given sequence in convergent and divergent by using behaviour of Monotonic sequence.
• Explain subsequences and upper and lower limits of a sequence.
• Discuss the behaviour of the geometric series.
13. Course Outcome of Differential equations and its applications
• Compute all the solutions of second and higher order linear differential equations with constant coefficients, linear equations with variable coefficients.
• Find the solution of First order partial differential equations for some standard types.
• Apply Laplace transform to solve second order linear differential equation and simultaneous linear differential equations.
14. Course Outcome of Graph Theory
• Discuss degree sequences and operations on graphs.
• Explain connectedness and components and some theorems.
• Derive some properties of planarity and Euler’s formula.
• Prove Five colour theorem.