INTEGRAL AND VECTOR CALCULUS
Reduction formulae: Sinnx, Cosnx, tannx and SinmxCosnx, where m, n are positive integers. Definition and properties of Gamma and Beta functions, Relation between Gamma and Beta functions, Duplication formula and 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 (cartesian and polar forms).
Double integrals, Change of order of integration, Triple integrals, Dirichlet’s integral.
Scalar and vector point function, 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 Green’s theorems (without proof) their applications and related problems.
1.Gorakh Prasad, A Text Book on Integral Calculus, Pothishala Pvt.Ltd, Allahabad, 1992.
2. Shanti Narayan, Integral CalculusS. Chand & Co. Pvt. Ltd., New Delhi, 1996.
3. Shanti Narayan, A Text Book of Vector Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 1996.
4.M. Ray and H. S. Sharma, Vector Algebra and Calculus, Students and Friends Co. Agra, 1998.
- Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 2005.
- G. C. Sharma & Madhu Jain, Integral Calculus, Galgotia Publication, Dariyaganj,New Delhi, 1996.
- P.K. Mittal, Shanti Narayan, Integral Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 2005.
- Muray R. Spiegel, Vector Analysis, Schaum Publishing Company, New York, 2007.
- Saran and Nigam, Introduction to Vector Analysis, Pothisala Pvt. Ltd, Allahabad,2001.
- Paul C. Matthews, Vector Calculus, Springer London, 2005.
