DIFFERENTIAL CALCULUS
Paper Code:
MAT102
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Unit I:
I
9.00
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
9.00
Derivative of an arc, Intrinsic equation of the curve, Pedal equation (Cartesian and Polar Curves), Curvature.
Unit III:
III
9.00
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
Envelopes, Asymptotes(Cartesian and Polar curves).
Unit V:
V
9.00
Multiple points, Classification of double points – Node, cusp, point of inflexion.
Tracing of curves: Cartesian and Polar form.
Essential Readings:
- Shanti Narayan, Differential Calculus , S.Chand and Co., New Delhi.,1996
- M. Ray & G.C. Sharma, Differential Calculus, Shivlal agarwal & Co. Agra, 1998.
- Gorakh Prasad , Text Book on Diff.Calculus , Pothishala Pvt.Ltd, Allahabad,1992.
- Chaurasia, Goyal , Agarwal , Jain ;Diff. Calculus, RBD, Jaipur,2006.
References:
- Theory and problems of Advanced Cal. - Schaum’s outline series New York, 2011.
- H.S.Dhami,Differential Calculus,New Age Int. Ltd.,New Delhi, 2012.
- Akhtar&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.
Academic Year:
