Student's Guide to Vectors and Tensors

ISBN-10: 0521171903

ISBN-13: 9780521171908

Edition: 2011

Authors: Daniel Fleisch

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Book details

List price: $56.95
Copyright year: 2011
Publisher: Cambridge University Press
Publication date: 9/22/2011
Binding: Paperback
Pages: 206
Size: 6.25" wide x 9.00" long x 0.50" tall
Weight: 1.122
Language: English

Preface
Acknowledgments
Vectors
Definitions (basic)
Cartesian unit vectors
Vector components
Vector addition and multiplication by a scalar
Non-Cartesian unit vectors
Basis vectors
Chapter 1 problems
Vector operations
Scalar product
Cross product
Triple scalar product
Triple vector product
Partial derivatives
Vectors as derivatives
Nabla - the del operator
Gradient
Divergence
Curl
Laplacian
Chapter 2 problems
Vector applications
Mass on an inclined plane
Curvilinear motion
The electric field
The magnetic field
Chapter 3 problems
Covariant and contravariant vector components
Coordinate-system transformations
Basis-vector transformations
Basis-vector vs. component transformations
Non-orthogonal coordinate systems
Dual basis vectors
Finding covariant and contravariant components
Index notation
Quantities that transform contravariantly
Quantities that transform covariantly
Chapter 4 problems
Higher-rank tensors
Definitions (advanced)
Covariant, contravariant, and mixed tensors
Tensor addition and subtraction
Tensor multiplication
Metric tensor
Index raising and lowering
Tensor derivatives and Christoffel symbols
Covariant differentiation
Vectors and one-forms
Chapter 5 problems
Tensor applications
The inertia tensor
The electromagnetic field tensor
The Riemann curvature tensor
Chapter 6 problems
Further reading
Index
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