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Title-Calculus (Code-09010102)

 Unit Content Learning objects Teaching Guidelines Methodology Time (Hrs) one ·         Definition of the limit of a function. Basic properties of limits ·         Continuous function and classification of discontinuities, ·         Differentiability, Successive differentiation. Leibnitz theorem ·         Maclaurin and Taylor series expansions. ·         Jacobians Students will be able to 1.    Understand the limit of a function. Leibnitz theorem and its application. 2.    Expansion of function by Maclaurin and Taylor series. Lecture should be effective so that student can grasp the topics easily. 1. Lecture. 2.  Seminar. 3. Assignment. 4.  Discussion on Assignment. 5. Evaluation of Assignment. 15 Two ·         Asymptotes in Cartesian coordinates, intersection of curve and its asymptotes ·         Asymptotes  in polar coordinates ·         Curvature, radius of curvature for Cartesian Curves, Parametric curves, polar curves ·         Newton’s method. Radius of Curvature for pedal curves. Tangential polar equation ·         Center of curvature. Circle of curvature. Chord of curvature, evolutes ·         Points of inflexion. Multiple points, Cusps, nodes & conjugate points, types of cusps and Tracing of Curves Students will be able to 1.   To find the asymptotes of the curves in Cartesian & polar, parametric coordinates. 2.   Radius of curvature ,centre of curvature of various curves 3.   Points of inflexion, Cusp, node and conjugate points. Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.     Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15 Three ·         Reduction formulae., ·         Beta and Gama functions, ·         Double and Triple integrals ·         Dirichlets integrals, ·         Change of order of integration in double integrals. ·         Rectification, intrinsic equation of curves ·         Quardrature( area ) Sectorial area, Area bounded by closed curves ·         Volumes and surfaces of solids through revolution. 1.    To make students familiar with Reduction formulae, 2.    Beta and Gama functions 3.    Dritchlets integrals, 4.    Rectification of intrivsic function ,Quadrature 5.    Volume and surface area of the solids. Lecture should be effective sothat student can grasp the topics easily. 1.    Lecture. 2.    Seminar. 3.    Discussion/Interaction with Students. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15