INTEGRAL AND VECTOR CALCULUS

Paper Code: 
MAT201
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
9.00

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.

9.00

Rectification: length of Cartesian and polar curves. Quadrature: Area of Cartesian and polar curves, Volumes and Surfaces of solids of revolution.

9.00

Double integrals, Change of order of integration, Triple integrals, Drichlet’s Integral .

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.

Identities involving differential vector operators, Gauss divergence, Stokes  and Greens theorems ( without proofs ) and their applications.

Essential Readings: 

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

References: 

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.          

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