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.
Unit II:
II
12.00
Derivative of an arc, Intrinsic equation of the curve, Pedal equation (Cartesian & Polar Curves) Curvature
Unit III:
III
12.00
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.
Unit IV:
IV
12.00
Envelopes, Asymptotes. (Cartesian and Polar curves).
Unit V:
V
12.00
Multiple points, Classification of double points –Node, cusp, points of inflexion.
Tracing of curves: Cartesian and Polar form.
Essential Readings:
Shanti Narayan, Differential Calculus, S.Chand and Co., New Delhi.
M. Ray & G.C. Sharma, Differential Calculus, Shivlal agarwal & Co. Agra.
Gorakh Prasad, Text Book on Diff.Calculus, Pothishala Pvt.Ltd, Allahabad.
