A Gentle Introduction to Tensors: From Linear Algebra to Tensor Calculus, Geometry, and Physics
Original PDF نویسندگان: Dr. Xingzhuang Zhao
جزئیات
فرمت: Original PDF صفحات: 656 pages تاریخ انتشار نسخه الکترونیکی : May 26, 2026
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لینک: https://www.amazon.com/dp/B0H31MV938
2,126,000 تومان
زمان تحویل: حداکثر 24 ساعت
توضیحات
A Gentle Introduction to Tensors is a clear, example-driven guide to tensor analysis and tensor calculus. It is written for readers who want to understand not only the formulas, but also the geometric meaning behind them.The book begins with the foundations: vectors, covectors, bases, dual spaces, metrics, tensor products, tensor types, and index notation. It then develops tensor fields, coordinate transformations, manifolds, pullbacks, pushforwards, covariant derivatives, curvature, Lie derivatives, embedded curves and surfaces, differential forms, integration, and applications in mechanics and physics.Designed for self-study, the book emphasizes step-by-step derivations, consistent notation, carefully placed examples, and remarks that address common sources of confusion. Vectors and vector-like objects are written in bold, upper and lower indices are used consistently, and geometric ideas are connected to their coordinate formulas throughout.Topics include:Vector spaces, dual spaces, covectors, and metricsTensor products, tensor types, and transformation lawsScalar, vector, covector, and tensor fieldsManifolds, tangent spaces, and tensor bundlesPullbacks, pushforwards, and coordinate transformationsConnections, Christoffel symbols, covariant derivatives, and geodesicsCurvature, torsion, Lie derivatives, and differential formsSurface geometry, stress, strain, elasticity, fluids, relativity, and gravitationWhether you are studying mathematics, physics, engineering, continuum mechanics, relativity, or differential geometry, this book provides a gentle but systematic path from linear algebra to modern tensor calculus.
2,126,000 تومان
زمان تحویل: حداکثر 24 ساعت