DIFFERENTIAL CALCULUS
Taylor’s and Maclaurins theorems with different remainders, Expansion of sin(x), cos(x), ex, log(1+x), (1+x)m, Derivative of an arc, Pedal equation (Cartesian and Polar Curves).
Infinite series of non-negative terms, Convergences (definition), Test for Convergence (Without Proof): Comparison test, Cauchy’s nth root test, D’Alembert’s ratio test, Raabe’s test, D’Morgan’s test, Cauchy’s condensation test, Logarithm ratio test, Gauss test. Alternating Series – Leibnitz Test, Absolute and conditional convergence.
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 related problems.
Radius, center and chord of curvature, Envelopes (Cartesian curves), Asymptotes (Cartesian and Polar curves).
Multiple points, Classification of double points: Node, cusp, point of inflexion, Tracing of cartesian and polar curves.
1. Shanti Narayan, Differential Calculus, S.Chand & Co. Pvt. Ltd. New Delhi, 1996
2. M. Ray & G.C. Sharma, Differential Calculus, Shivlal Agarwal & Co. Agra, 1998.
3. Gorakh Prasad, Text Book on Differential Calculus, Pothishala Pvt. Ltd, Allahabad,1992.
4. H.S. Dhami, Differential Calculus, New Age International (P) Ltd., New Delhi, 2012.
1. Schaum’s, Theory and Problems of Advanced Calculus, Schaum’s outline series New York, 2011.
2. Ahsan Akhtar, Sabiha Ahsan, A Text Book of Differential Calculus, PHI Ltd. New Delhi, 2002.
3. G.N. Berman, A Problem Book in Mathematical Analysis, Mir Publishers, Moscow, 2004.
4. G.C.Sharma & Madhu Jain, Calculus, Galgotia Publication, Dariyaganj, New Delhi, 1996.
5. Chaurasia, Goyal, Agarwal, Jain, Differential Calculus, RBD, Jaipur, 2006.
6. Ulrich L. Rohde, G.C. Jain, Ajay K. Poddar, A.K. Ghosh, Introduction to Differential Calculus, Wiley Publications, USA, 2012.
