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.