DIFFERENTIAL CALCULUS
Taylor’s and Maclaurins theorems with different remainders, Expansion of sinx, cosx, 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.
- Shanti Narayan, Differential Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 1996.
- M. Ray & G.C. Sharma, Differential Calculus, Shivlal Agarwal & Co. Agra, 1998.
- Gorakh Prasad, Text Book on Differential Calculus, Pothishala Pvt.Ltd, Allahabad, 1992.
- H.S. Dhami, Differential Calculus, New Age International (P) Ltd., New Delhi, 2012.
- Schaum’s, Theory and Problems of Advanced Calculus, Schaum’s outline series New York, 2011.
- Ahsan Akhtar, Sabiha Ahsan, A Text Book of Differential Calculus, PHI Ltd. New Delhi, 2002.
- G.N. Berman, A Problem Book in Mathematical Analysis, Mir Publishers, Moscow, 2004.
- G.C.Sharma & Madhu Jain, Calculus, Galgotia Publication, Dariyaganj, New Delhi, 1996.
- Chaurasia, Goyal, Agarwal, Jain, Differential Calculus, RBD, Jaipur, 2006.
- Ulrich L. Rohde, G.C. Jain, Ajay K. Poddar, A.K. Ghosh Introduction to Differential Calculus, Wiley Publications USA, 2012.
