Mean Value theorems (Lagrange’s, Cauchy, Taylor’s and Maclaurins with different remainders). Expansion of sin(x), cos(x), e^x, log(1+x), (1+x)^m.

Derivative of an arc, Intrinsic equation of the curve, Pedal equation (Cartesian and  Polar Curves), Curvature.

Partial differentiation, Total derivative , Euler’s theorem for homogeneous functions, Maxima and Minima of functions of  two independent variables – necessary and sufficient conditions ( without proof) , Lagrange’s undetermined multipliers ( without proof ) and simple problems.

Envelopes, Asymptotes(Cartesian and Polar curves).

Multiple points, Classification of double points – Node, cusp, point of inflexion.
Tracing of curves: Cartesian and Polar form.