INTEGRAL AND VECTOR CALCULUS

Paper Code: 
MAT201
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
9.00
Reduction formulae:sin^n x,cos^n x,tan^n x and sin^m 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 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.

 

9.00

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

 

Essential Readings: 

1. A text book on Integral Calculus, Gorakh Prasad, Pothishala Pvt .Ltd , Allahabad, 1992.
2. Integral Calculus, Sharma & Jain Galgotia Publication, Dariyaganj, New Delhi, 2001.
3. Integral Calculus, Shanti Narayan, S.Chand and Co., New Delhi, 1996.
4. A text book of Vector Calculus, Shanti Narayan, S.Chand and Co.New Delhi, 1996.
5. Vector algebra &Calculus, Ray and Sharma, Students and Friends Co. Agra, 1998.

References: 

1. Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley and sons, 2005.
2. Vector Analysis, Muray R. Spiegel , Schaum Publishing Company , New York, 2007.
3. Introduction to Vector Analysis, Saran and Nigam , Pothisala Pvt. Ltd, Allahabad, 2001.           

Academic Year: 
2017-2018
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