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. Differential Calculus, Shanti Narayan, S. Chand and Co., New Delhi., 1996
2. Differential Calculus, M. Ray & G.C. Sharma, Shivlal agarwal & Co. Agra, 1998.
3. Text Book on Diff.Calculus, Gorakh Prasad, Pothishala Pvt.Ltd, Allahabad, 1992.
4. Differential Calculus, Chaurasia, Goyal , Agarwal , Jain, RBD, Jaipur,2006.
1. Theory and problems of Advanced Cal. Schaum’s outline series New York, 2011.
2. Differential Calculus, H.S. Dhami, New Age Int. Ltd., New Delhi, 2012.
3. A text Book of Differential Calculus, Akhtar & Ahsan, PHI Ltd. New Delhi, 2002.
4. A Problem book in Mathematical Analysis, G.N. Berman, Mir Publishers, Moscow, 2004.
Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/differential-calculus-4
[2] https://maths.iisuniv.ac.in/academic-year/2017-2018