Differentiation of vector functions, Directional derivatives, Gradient, divergence and curl of a point function. Expansion formulas, curvilinear coordinates. Orthogonal curvilinear. Arc length ,volume element ,Gradient ,divergence and curl in term of curvilinear coodinate. Line, surface and volume integrals, Gauss’s divergence theorem, Green’s theorem and Stokes’s theorem. With examples. Coordinate transformations and their equations, Algebra of Cartesian tensors, Tensors of different ranks, inner and outer products, contraction, contraction theorem, Quotient theorem, Kronecker tensor, Levi-civita tensor. Applications to vector analysis, Differential of Cartesian tensors. Christofell symbols. Contravariant, covariant and mixed tensor. The line element and metric tensor.

This course is designed to enable the students to understand and use the techniques and basic Principles of vector analysis , use of indices , transformation equations for basis vectors, components ,coordinates. Curvilinear coordinate, important theorems’ on line and surface integrals. which are used in mechanics.

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Book Title : Vector Analysis and Cartesian Tensor

Author : D.E Bourne and P.C.Kendull

Edition : 2nd

Publisher : stanley thornes

Book Title : Vector & Tensor Analysis for Scientists and Engineers

Author : Dr Nawazish Ali Shah

Edition : third

Publisher : A-one

Book Title : An Introduction to Vector Analysis with Application to Geometry and Mechanics

Author : K.L. Mir

Edition :

Publisher : Ilmi Kitab Khana

Book Title : Vector and Tensor Analysis for Scientist and Engineers

Author : N. A. Shah

Edition :

Publisher : 3rd Edition, A-ONE Publishers, Lahore

Book Title : Vector and Tensor Methods

Author : F. Chorlton

Edition :

Publisher : Ellis Horwood Publisher, Chichester

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