||Name of the Paper
|After the completion of the course, the students will be able:
||Foundations of Mathematics
- To explain the concepts of mathematical logic methods.
- To illustrate the idea of sets, set operations and functions.
- To analyze the properties of relations.
- To solve polynomial equations using numerical methods.
||Analytic Geometry , Trigonometry and Differential Calculus
- To interpret the ideas of conic sections, tangents and normal to a conic and their properties.
- To determine the parametric forms of conic sections.
- To apply the concepts of trigonometric functions, their properties and summation of trigonometric series.
- To solve problems involving successive differentiation and indeterminate forms.
- To determine the Taylor and Maclaurin series expansions of given functions.
- To compute curvature and related parameters of a given curve or curves.
- To calculate the partial derivatives, maxima and minima of functions and Lagrange multipliers for extremum problems.
- To solve the area and volume problems using multiple integrals.
||Vector Calculus, Theory of Numbers and Laplace transform
- To determine the arc length, unit tangent vector, unit normal vector, gradient vector and directional derivatives of vector functions.
- To examine the applications of vector integration.
- To apply the concept of congruence, Fermat’s theorem, Wilson’s theorem and Euler’s phi function.
- To determine the Laplace transform of a given function.
- To use the ideas of finite and infinite sets and the properties of set of real numbers.
- To explain the idea of sequences and their convergence.
- To detect the convergence and divergence of sequences.
- To interpret the concepts of series, alternating series their convergence and absolute convergence.
- To solve problems involving the convergence and absolute convergence of series.
- To apply the concept of limit of functions.
- To explain the concepts of nature of solutions of differential equations, exact equations and homogeneous equations
- To solve second order linear differential equations using different methods.
- To compute the solutions of second order linear differential equations using power series method.
- To determine the solutions of first order partial differential equations.
- To explain the concepts of binary structures, groups and subgroups.
- To demonstrate different finite group structures using permutation groups.
- To analyse the concepts of homomorphism of groups and factor groups using theorems and examples.
- To illustrate the idea of normal subgroups through theorems.
- To categorize different binary structures into groups, rings, integral domains and fields.
- To deduce the concepts of ideals and factor rings from the concepts of normal subgroups and factor groups.
||Human Right and Mathematics for Environmental Studies
- To discuss the basic knowledge about environment.
- To explain different kinds of environmental pollution and its causes.
- To identify the need of environmental protection.
- To apply knowledge about Fibonacci numbers.
- To estimate the value of Golden ratio.
- To describe various rules protecting human rights.
- To explain various bodies of UNO constituted for the protection of human rights.
||Open Course-Applicable Mathematics
- To develop mathematical skills.
- To apply shortcut methods for solving problems.
- To explain the basic operations in Mathematics.
- To describe the definitions of trigonometric ratios.
- To acquire the basic arithmetic skills involving percentage, average, time and distance and elementary algebra.
- To explain continuity and discontinuity of various functions.
- To explain the meaning of derivative of a function.
- To describe theorems associated with differentiability.
- To acquire knowledge about L’ Hospital rule and limits.
- To acquire the idea about Riemann integrability and Riemann integration.
- To explain uniform convergence of a series.
- Distinguish between pointwise convergence and uniform convergence.
||Graph Theory and Metric Spaces
- To explain basic concepts of graphs, directed graphs and weighted graphs.
- To describe the properties of trees, spanning trees, cut vertices and connectivity.
- To examine Eulerian and Hamiltonian graphs.
- To explain the basic concepts of metric spaces.
- To discuss open sets, closed sets and Cantor set.
- To establish the concepts of convergence, completeness and continuous mapping in metric spaces.
- To explain the concepts of limit, continuity of complex functions and analytic functions.
- To use elementary complex functions.
- To integrate
- To examine the convergence of complex sequence and series.
- To detect singular points and residues.
- To evaluate improper integrals.
- To deduce the given matrix using the process of Gaussian elimination.
- To compute the rank of a matrix.
- To explain the concepts of vector spaces and subspaces.
- To detect linear independent sets and basis.
- To explain linear mapping and linear transformation.
- To find kernel and range of a transformation.
- To explain theorems associated with linear transformations.
- To compute eigen values and eigen vectors of transformation.
||Choice Based Operations Research
- To translate the real world problems into corresponding linear programming problem.
- To apply the concepts of duality in solving linear programming problem.
- To solve transportation and assignment problems.
- To describe the concept of Game theory.
- To demonstrate their own work.
- To produce a mature oral presentation of a non- trivial mathematical topic.
- To investigate their awareness in relation to the wider research field.
||Partial Differentiation, Matrices, Trigonometry and Numerical Methods.
- To draw graphs, level curves and contours.
- To discuss about partial derivatives.
- To practice questions to find the rank of a matrix using elementary transformations and solve linear equations.
- To apply Cayley-Hamilton theorem.
- To discuss about hyperbolic and circular functions.
- To compute summation of infinite series.
- To use numerical methods to find solutions of algebraic and transcendental equations.
||Integral Calculus and Differential Equations
- To apply definite integrals to find volumes, length of plane curves and area of surfaces of revolution.
- To use multiple integrals to find volume of a solid and area of bounded regions.
- To discuss about first order ordinary differential equations and partial differential equations.
- To solve first order differential equation and partial differential equation.
||Vector Calculus, Analytic Geometry and Abstract Algebra
- To solve problems involving vector valued functions
- To use Green’s theorem, Stoke’s theorem to integrate in vector fields.
- To illustrate the idea about conic sections, polar coordinates and conics in polar coordinates.
- To discuss about groups, cyclic groups and homomorphism of groups.
||Fourier Series, Laplace Transform and Complex Analysis
- To discuss about periodic functions, trigonometric series and Fourier series.
- To solve differential equations using power series method.
- To explain Laplace transforms.
- To apply Laplace transforms to solve differential equations.
- To discuss about complex numbers and analytic functions.
- To use Cauchy-Riemann equations to
- To implement Cauchy integral theorem for complex integration.