INTEGRAL AND VECTOR CALCULUS
Paper Code:
MAT201
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Unit I:
I
9.00
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 simple problems related to these functions.
Unit II:
II
9.00
Rectification: length of Cartesian and polar curves. Quadrature: Area of Cartesian and polar curves, Volumes and Surfaces of solids of revolution.
Unit III:
III
9.00
Double integrals, Change of order of integration, Triple integrals, Drichlet’s Integral .
Unit IV:
IV
9.00
Scalar and vector point functions, Differentiation and Integration of vector point function, Gradient, directional derivatives, Divergence and Curl of a vector point function.
Unit V:
V
9.00
Identities involving differential vector operators, Gauss divergence, Stokes and Greens theorems ( without proofs ) and their applications.
Essential Readings:
- Gorakh Prasad, A text book on Integral Calculus , Pothishala Pvt .Ltd , Allahabad, 1992.
- Sharma & Jain, Integral Calculus, Galgotia Publication, Dariyaganj, New Delhi, 2001.
- Shanti Narayan , Integral Calculus , S.Chand and Co., New Delhi, 1996.
- Shanti Narayan , A text book of Vector Calculus, S.Chand and Co.New Delhi, 1996.
- Ray and Sharma, Vector algebra &Calculus, Students and Friends Co. Agra, 1998
References:
- Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and sons, 2005.
- Muray R. Spiegel ,Vector Analysis, Schaum Publishing Company , New York, 2007.
- Saran and Nigam , Introduction to Vector Analysis, Pothisala Pvt. Ltd, Allahabad, 2001.
Academic Year:
