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Vector and Tensor Analysis by Nawazish Ali Shah: A Review


Vector and Tensor Analysis by Nawazish Ali Shah: A Review




Vector and tensor analysis is a branch of mathematics that deals with the study of vectors, tensors, and their applications in physics, engineering, and other fields. Vectors are quantities that have both magnitude and direction, such as force, velocity, or displacement. Tensors are generalizations of vectors that can represent more complex phenomena, such as stress, strain, or curvature.




Vector And Tensor Analysis By Nawazish Ali Shah Pdf Free Download



One of the books that covers this topic in depth is Vector and Tensor Analysis by Nawazish Ali Shah, a professor of mathematics at the University of Engineering and Technology in Lahore, Pakistan. The book is intended for undergraduate and graduate students of science and engineering, as well as researchers and practitioners who need to use vector and tensor analysis in their work.


The book consists of 12 chapters, covering the following topics:


  • Algebra of vectors: basic definitions, operations, properties, and applications of vectors.



  • Geometry of vectors: vector equations of lines and planes, angles, distances, and projections.



  • Differentiation of vectors: limits, continuity, derivatives, gradients, directional derivatives, divergence, curl, and Laplacian operators.



  • Integration of vectors: line integrals, surface integrals, volume integrals, divergence theorem, Stokes' theorem, and Green's theorem.



  • Curvilinear coordinates: cylindrical, spherical, and general orthogonal curvilinear coordinates, transformation of coordinates, differential operators in curvilinear coordinates.



  • Tensors: definition, notation, types, operations, properties, and applications of tensors.



  • Algebra of tensors: addition, subtraction, multiplication, contraction, inner product, outer product, quotient rule, and symmetrization of tensors.



  • Calculus of tensors: differentiation and integration of tensors with respect to scalars and vectors.



  • Curvilinear tensors: covariant and contravariant components of tensors in curvilinear coordinates.



  • Affine tensors: affine transformation of tensors.



Metric tensors: definition, properties, examples,


  • and applications of metric tensors.



Riemannian geometry: Christoffel symbols,


covariant derivative,


geodesics,


curvature tensor,


Ricci tensor,


scalar curvature,


  • and Einstein's field equations.



The book is well-written and organized,


with clear explanations,


examples,


diagrams,


and exercises.