Reduction Formulae: Sinnx, Cosnx,Tannx, SinmxCosnx 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.
Rectification: length of Cartesian and polar curves. Quadrature : Area of Cartesian and polar curves, Volumes and Surfaces of solids of revolution.
Double integrals, Change of order of integration, Triple integrals, Drichlet’s Integral .
Scalar and vector point functions, Differentiation and Integration of vector point function, Gradient, directional derivatives, Divergence and Curl of a vector point function.
Identities involving differential vector operators, Gauss divergence, Stokes and Greens theorems ( without proofs ) and their applications.
1. Gorakh Prasad, A text book on Integral Calculus , Pothishala Pvt .Ltd , Allahabad, 1992.
2. Sharma & Jain, Integral Calculus, Galgotia Publication, Dariyaganj, New Delhi, 2001.
3. Shanti Narayan , Integral Calculus , S.Chand and Co., New Delhi, 1996.
4. Shanti Narayan , A text book of Vector Calculus, S.Chand and Co.New Delhi, 1996.
5. Ray and Sharma, Vector algebra &Calculus, Students and Friends Co. Agra, 1998
1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and sons, 2005.
2. Muray R. Spiegel ,Vector Analysis, Schaum Publishing Company , New York, 2007.
3. Saran and Nigam , Introduction to Vector Analysis, Pothisala Pvt. Ltd, Allahabad, 2001.
Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/integral-and-vector-calculus-2
[2] https://maths.iisuniv.ac.in/academic-year/2016-2017