Introduction to Vectors and Tensors: Linear and Multilinear AlgebraTo Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further. |
Contents
Selected Reading for Part III | 244 |
VECTOR AND TENSOR | 266 |
CHAPTER 3 | 284 |
Copyright | |
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Other editions - View all
Introduction to Vectors and Tensors: Linear and Multilinear Algebra Ray M. Bowen,Chao-cheng Wang No preview available - 1976 |
Common terms and phrases
Abelian anholonomic arbitrary arc length called Cartan parallelism Cartesian coordinate system chart Christoffel symbols commute component form condition constant continuous subgroup coordinate curve covariant derivative curl curvature denotes differential form domain dt dt du² equation equivalent Euclidean manifold Euclidean parallelism exp(At exterior derivative formula Frobenius theorem function g₁ geodesic grad f gradient h₁ h₂ hypersurface identity inner product space integral curve isomorphism left-invariant field lemma Lie algebra Lie bracket Lie derivative linear mapping natural basis open set orthogonal prove r-form relative representation result right-hand side scalar fields skew-symmetric SL(V smooth curve subgroup of GL(V subset surface area surface coordinate system surface covariant derivative surface metric tangent space tangent vector tangential tensor field tensor field transformation rule U₁ vanishes ΧΟ ди ду дул дхі