Asymptotes, Test for concavity and convexity, Points of inflexion, Multiple Points, Curvature, Tracing of Curves (Cartesian and Parametric coordinates only). Integration of hyperbolic functions. Reduction formule. Definite integrals. Fundamental theorem of integral calculus. Quadrature, rectification.
Exact differential equations. First order and higher degree equations solvable for x, y, p. Clairaut’s form and singular solutions. Geometrical meaning of a differential equation. Orthogonal trajectories. Linear differential equations with constant and variable coefficients. Variation of Parameters method, reduction method, series solutions of differential equations. Power series method, Bessel and Legendre equations.