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Vector and tensor analysis is a branch of mathematics that deals with the study of vectors, tensors, and their applications 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 popular books on vector and tensor analysis is written by Prof. Dr. Nawazish Ali Shah, who is a professor of mathematics at the University of Engineering and Technology, Lahore, Pakistan. The book is titled Vector & Tensor Analysis for Scientists and Engineers and it covers the basic concepts and techniques of vector and tensor algebra, calculus, and analysis in a clear and rigorous manner. The book also includes many examples and exercises to illustrate the theory and applications of vector and tensor analysis.

The book is divided into two parts: Part I deals with the algebra of vectors and tensors, while Part II deals with the calculus and analysis of vector and tensor fields. Some of the topics covered in the book are:

• Curvilinear coordinates

• Transformation of coordinates

• Coordinate surfaces and coordinate curves

• Unit vectors in curvilinear coordinate system

• Rectangular Cartesian coordinates

• Cylindrical polar coordinates

• Spherical polar coordinates

• Line, surface, and volume integrals

• Gauss's divergence theorem

• Stokes's theorem

• Green's theorem

• Laplacian operator

• Gradient, divergence, and curl operators

• Differentiation of vectors and tensors

• Integration of vectors and tensors

• Divergence theorem for tensors

• Stokes's theorem for tensors

• Tensors of rank zero, one, two, and higher

• Tensor product, contraction, inner product, outer product, and mixed product

• Tensor notation and index notation

• Kronecker delta symbol and Levi-Civita symbol

• Metric tensor and Christoffel symbols

• Covariant, contravariant, and mixed tensors

• Raising and lowering of indices

• Tensors in Euclidean space

• Tensors on manifolds

• Tensors on hypersurfaces

• Riemannian geometry

• Affine connection and parallel transport

• Covariant derivative and Lie derivative

• Geodesics and curvature

• Ricci tensor and scalar curvature

• Einstein tensor and Einstein field equations

The book is suitable for undergraduate and graduate students of mathematics, physics, engineering, and other related disciplines who want to learn the fundamentals of vector and tensor analysis. The book can also be used as a reference for researchers and practitioners who work with vector and tensor quantities in their fields.

The book is available in PDF format for free download from the website of MathCity.org, which is a non-profit organization that provides online resources for mathematics education in Pakistan. The PDF file contains the solutions of the exercises of the book as well. The solutions are provided by Prof. Fazal Abbas Sajid, who is also a professor of mathematics at the University of Engineering and Technology, Lahore. The solutions of Chapter 5 are written by Ms. Javeria Abbas Ahmand and Chapter 6 are written by Ms. Shaniza Ghafoor. The PDF file is about 16 MB in size.

If you want to learn more about vector and tensor analysis, you can also check out other books on the subject, such as Introduction to Vectors and Tensors Volume 1: Linear and Multilinear Algebra by Ray M. Bowen and C.-C. Wang, which is also available in PDF format for free download from the website of Texas A&M University. You can also watch online lectures on vector and tensor analysis by Dr Nawazish Ali on YouTube, which are based on his book.

• You can also compare and contrast the book by Dr Nawazish Ali with other books on vector and tensor analysis, such as Vector and Tensor Analysis with Applications by A. I. Borisenko and I. E. Tarapov, which is a classic text on the subject that covers both the theory and applications of vector and tensor analysis in physics and engineering.

• You can also mention some of the benefits of learning vector and tensor analysis, such as developing your mathematical skills, enhancing your understanding of physical phenomena, and expanding your knowledge of various fields of science and engineering that use vector and tensor quantities, such as mechanics, fluid dynamics, electromagnetism, relativity, quantum mechanics, cosmology, etc.

• You can also provide some tips and suggestions for the readers who want to learn vector and tensor analysis, such as reviewing the prerequisites of linear algebra, calculus, and differential geometry, following the examples and exercises in the book, checking their solutions with the PDF file or online resources, watching the online lectures by Dr Nawazish Ali or other instructors, and practicing their skills by solving problems from other sources or creating their own problems.

Vector and tensor analysis is a branch of mathematics that deals with the study of vectors, tensors, and their applications 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 popular books on vector and tensor analysis is written by Prof. Dr. Nawazish Ali Shah, who is a professor of mathematics at the University of Engineering and Technology, Lahore, Pakistan. The book is titled Vector & Tensor Analysis for Scientists and Engineers and it covers the basic concepts and techniques of vector and tensor algebra, calculus, and analysis in a clear and rigorous manner. The book also includes many examples and exercises to illustrate the theory and applications of vector and tensor analysis.

The book is divided into two parts: Part I deals with the algebra of vectors and tensors, while Part II deals with the calculus and analysis of vector and tensor fields. Some of the topics covered in the book are:

• Curvilinear coordinates

• Transformation of coordinates

• Coordinate surfaces and coordinate curves

• Unit vectors in curvilinear coordinate system

• Rectangular Cartesian coordinates

• Cylindrical polar coordinates

• Spherical polar coordinates

• Line, surface, and volume integrals

• Gauss's divergence theorem

• Stokes's theorem

• Green's theorem

• Laplacian operator

• Gradient, divergence, and curl operators

• Differentiation of vectors and tensors

• Integration of vectors and tensors

• Divergence theorem for tensors

• Stokes's theorem for tensors

• Tensors of rank zero, one, two, and higher

• Tensor product, contraction, inner product, outer product, and mixed product

• Tensor notation and index notation

• Kronecker delta symbol and Levi-Civita symbol

• Metric tensor and Christoffel symbols

• Covariant, contravariant, and mixed tensors

• Raising and lowering of indices

• Tensors in Euclidean space

• Tensors on manifolds

• Tensors on hypersurfaces

• Riemannian geometry

• Affine connection and parallel transport

• Covariant derivative and Lie derivative

• Geodesics and curvature

• Ricci tensor and scalar curvature

• Einstein tensor and Einstein field equations

The book is suitable for undergraduate and graduate students of mathematics, physics, engineering, and other related disciplines who want to learn the fundamentals of vector and tensor analysis. The book can also be used as a reference for researchers and practitioners who work with vector and tensor quantities in their fields.

The book is available in PDF format for free download from the website of MathCity.org, which is a non-profit organization that provides online resources for mathematics education in Pakistan. The PDF file contains the solutions of the exercises of the book as well. The solutions are provided by Prof. Fazal Abbas Sajid, who is also a professor of mathematics at the University of Engineering and Technology, Lahore. The solutions of Chapter 5 are written by Ms. Javeria Abbas Ahmand and Chapter 6 are written by Ms. Shaniza Ghafoor. The PDF file is about 16 MB in size.

If you want to learn more about vector and tensor analysis, you can also check out other books on the subject, such as Introduction to Vectors and Tensors Volume 1: Linear and Multilinear Algebra by Ray M. Bowen and C.-C. Wang, which is also available in PDF format for free download from the website of Texas A&M University. You can also watch online lectures on vector an

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