The final three chapters function independently of each other and cover Euclidean three-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. Tensor Calculus An Introduction to Differential Geometry with Use of the Tensor Calculus By Prof. As treatments of tensor calculus directed towards relativity are comparatively numerous, relativity has been excluded almost. x tf.constant( 1, 2, 3) y tf.constant(2) z tf.constant( 2, 2, 2) All of these are the same computation. This book is intended as a general brief introduction to tensor calculus.
of the mathematical concepts associated with tensor calculus and (ii) develop. In that case, the scalar is broadcast to be the same shape as the other argument. areas of tensor calculus, differential geometry and continuum mechanics. The first five chapters-comprising tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor-develop their subjects without undue rigor. The simplest and most common case is when you attempt to multiply or add a tensor to a scalar. A geometrically oriented introduction to the calculus of vector and tensor fields on three-dimensional Euclidean point space, with applications to the. "This book will prove to be a good introduction, both for the physicist who wishes to make applications and for the mathematician who prefers to have a short survey before taking up one of the more voluminous textbooks on differential geometry." - MathSciNet (Mathematical Reviews on the Web), American Mathematical SocietyĪ compact exposition of the fundamental results in the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity.
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