Vector and Tensor Analysis by Dr. Nawazish Ali Shah: A Review
Vector and tensor analysis is a branch of mathematics that deals with the properties and applications of vectors and tensors in various fields of science and engineering. 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.
One of the books that covers this topic in depth is Vector and Tensor Analysis by Dr. Nawazish Ali Shah, a professor and former chairman of the Department of Mathematics at the University of Engineering and Technology, Lahore. The book is intended for students and engineers who want to learn the fundamentals and applications of vector and tensor analysis in a clear and concise manner.
The book consists of 12 chapters, covering topics such as algebra and geometry of vectors, differentiation and integration of vectors, curvilinear coordinates, gradient, divergence, curl, Laplacian, line integrals, surface integrals, volume integrals, Green's theorem, Stokes' theorem, Gauss' divergence theorem, scalar and vector fields, scalar and vector potentials, conservative fields, irrotational fields, solenoidal fields, orthogonal curvilinear coordinates, cylindrical coordinates, spherical coordinates, Cartesian tensors, Kronecker delta symbol, Levi-Civita symbol, summation convention, transformation of coordinates, contravariant and covariant tensors, mixed tensors, symmetric and antisymmetric tensors, addition and subtraction of tensors, multiplication of tensors by scalars and vectors, inner product of tensors, outer product of tensors, contraction of tensors, quotient rule for tensors, differentiation of tensors with respect to scalars and vectors,divergence and curl of tensors, Laplacian of tensors, line integrals of tensors, surface integrals of tensors, volume integrals of tensors, Green's theorem for tensors, Stokes' theorem for tensors, Gauss' divergence theorem for tensors, applications of vector and tensor analysis to mechanics, fluid dynamics, electromagnetism, relativity, and differential geometry.
The book is well-written and organized, with clear definitions, theorems, proofs, examples, exercises, and diagrams. The book also provides historical notes and references to the original sources of some of the concepts and results. The book is suitable for undergraduate and graduate students who have a basic knowledge of calculus and linear algebra. The book can also serve as a reference for engineers and scientists who need to use vector and tensor analysis in their work.
In conclusion, Vector and Tensor Analysis by Dr. Nawazish Ali Shah is a comprehensive and rigorous introduction to the subject that covers both the theory and the applications. The book is a valuable resource for anyone who wants to learn more about the mathematical tools that are essential for understanding and solving problems in various domains of science and engineering. 061ffe29dd