Reduction Formulae: Sin^n(x) , Cos^n(x) , Tan^n(x) , Sin^n(x)Cos^n(x) where m, n are positive integers. Definition and properties of Gamma and Beta functions, Relation between Gamma and Beta functions, Duplication formula and simple problems related to these functions.
Unit II:
II
12.00
Rectification: length of Cartesian and polar curves. Quadrature: Area of cartesian and polar curves, Volumes and Surfaces of solids of revolution.
Unit III:
III
15.00
Double integrals, Change of order of integration, Triple integrals, Drichlet’s Integral
Unit IV:
IV
8.00
Scalar and vector point functions, Differentiation and Integration of vector point function, Gradient, directional derivatives.
Unit V:
V
15.00
Divergence , Curl and identities involving differential vector operators, Gauss divergence theorem , Stokes and Greens theorems (without proof ) and their applications.
Essential Readings:
Gorakh Prasad, A text book on Integral Calculus , Pothishala Pvt .Ltd , Allahabad.
Sharma & Jain, Integral Calculus, Galgotia Publication, Dariyaganj ,New Delhi.
Shanti Narayan , Integral Calculus , S.Chand and Co., New Delhi.
Shanti Narayan , A text book of Vector Calculus, S.Chand and Co. New Delhi
Ray and Sharma, Vector algebra &Calculus, Students and Friends Co. Agra
References:
Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and sons.
Muray R. Spiegel ,Vector Analysis, Schaum Publishing Company , New York.
Saran and Nigam , Introduction to Vector Analysis, Pothisala Pvt. Ltd, Allahabad.
