Differential Calculus
Mean Value theorems (Lagrange’s, Cauchy, Taylor’s and Maclaurins with different remainders). Expansion of sin(x), cos(x), ex, 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.
1. Shanti Narayan, Differential Calculus , S.Chand and Co., New Delhi.,1996
2. M. Ray & G.C. Sharma, Differential Calculus, Shivlal agarwal & Co. Agra, 1998.
3. Gorakh Prasad , Text Book on Diff.Calculus , Pothishala Pvt.Ltd, Allahabad,1992.
4. Chaurasia, Goyal , Agarwal , Jain ;Diff. Calculus, RBD, Jaipur,2006.
1. Theory and problems of Advanced Cal. - Schaum’s outline series New York, 2011.
2. H.S.Dhami,Differential Calculus,New Age Int. Ltd.,New Delhi, 2012.
3. Akhtar&Ahsan, A text Book of Differential Calculus ,PHI Ltd.New Delhi, 2002.
4. G.N.Berman, A Problem book in Mathematical Analysis, Mir Publishers, Moscow, 2004.
