Calculus-I

Course Code:6374, Course Title: Calculus-I Marks 50, 2 Credits, 30 Lectures Functions & their graphs : Polynomial and rational functions, logarithmic and exponential functions, trigonometric functions & their inverses, hyperbolic functions & their inverses, combinations of such functions.Limit and continuity: Definitions and basic theorems on limit and continuity. Limit at infinity & infinite limits, Computation of limits. Differentiation: Tangent lines and rates of change. Definition of derivative. One-sided derivatives. Rules of differentiation . Successive differentiation. Leibnitz's theorem. Related rates. Linear approximations and differentials. Applications of Differentiation: Mean value theorem. Maximum and minimum values of functions. Concavity and points of inflection. Optimization problems. Integration: Antiderivatives and indefinite integrals. Techniques of integration. Definite integration using antiderivatives. Fundamental theorems of calculus. Basic properties of integration. Integration by reduction. Applications of Integration: Arc length. Plane areas. Surfaces of revolution. Volumes of solids of revolution. Volumes by cylindrical shells. Volumes by cross sections. Approximation and Series: Taylor polynomials and series. Convergence of series. Taylor's series. Taylor's theorem and remainders. Differentiation and integration of series. Evaluation: Final exam (Theory, 3 hours): 50 marks. Six questions will be set, of which any four are to be answered. Books Recommended: 1.Howard Anton -Calculus (7th and forward editions).2.E.W. Swokowski - Calculus with Analytic Geometry. 3.Md. A Matin & B Chakraboty, - DifferentialCalculus