College of Technology, Pantnagar

The sign of the first derivative, concavity and point of inflection, asymptotes and symmetry, Rolle’s Theorem, mean value theorem, extended mean value theorems, Taylor’s formula, estimating approximation errors, Taylor’s theorem with remainder and estimating the remainder, Newton’s method for approximating solution of equation, inverse functions and Picard’s method convergence and divergence of infinite series of non-negative terms with the help of comparison test, integral test, Limit comparison test, ratio test and root’s test limit and continuity of functions of two or more variables, partial derivatives, chain rules for functions of two or more variables, linear approximation of two and more variables and their increment estimation. Maxima, minima and saddle points for functions of two or more variables, Lagrange multipliers method, the first and second fundamental theorems of integral calculus. Leibnitz’s rule, approximating finite sums with integrals, rules for approximating definite integrals with the help of trapezoidal and Simpson’s rules and their error estimation. Convergence and divergence of improper integrals, calculating volume by slicing, volume modeled with shells and washers, length of a plane curve, area of a surface of revolution, polar coordinates, polar equations of conics and other curves, area of plane curves, are length and surface are Multiple integrals, double integrals, area bounded by curves, first and second moments, polar moment of inertia, radius of gyration, changing double integrals from Cartesian to polar coordinates, evaluation of triple integrals, physical applications in three dimensions and idea of spherical and cylindrical coordinates, hyperbolic functions: definitions and identities, derivatives and integrals, inverse hyperbolic functions.