A student’s guide to vectors and tensors 1st Edition by Daniel Fleisch 0521193699 9780521193696

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Product details:

ISBN 10: 0521193699 

ISBN 13: 9780521193696

Author: Daniel Fleisch

Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student’s Guide to Maxwell’s Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book’s supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.

Table of contents:

1 Vectors

1.1 Definitions (basic)

1.2 Cartesian unit vectors

1.3 Vector components

1.4 Vector addition and multiplication by a scalar

1.5 Non-Cartesian unit vectors

1.6 Basis vectors

1.7 Chapter 1 problems

2 Vector operations

2.1 Scalar product25

2.2 Cross product

2.3 Triple scalar product

2.4 Triple vector product

2.5 Partial derivatives

2.6 Vectors as derivatives

2.7 Nabla – the del operator

2.8 Gradient

2.9 Divergence

2.10 Curl

2.11 Laplacian

2.12 Chapter 2 problems

3 Vector applications

3.1 Mass on an inclined plane

3.2 Curvilinear motion

3.3 The electric field

3.4 The magnetic field

3.5 Chapter 3 problems

4 Covariant and contravariant vector components

4.1 Coordinate-system transformations

4.2 Basis-vector transformations

4.3 Basis-vector vs. component transformations

4.4 Non-orthogonal coordinate systems

4.5 Dual basis vectors

4.6 Finding covariant and contravariant components

4.7 Index notation

4.8 Quantities that transform contravariantly

4.9 Quantities that transform covariantly

4.10 Chapter 4 problems

5 Higher-rank tensors

5.1 Definitions (advanced)

5.2 Covariant, contravariant, and mixed tensors

5.3 Tensor addition and subtraction

5.4 Tensor multiplication

5.5 Metric tensor

5.6 Index raising and lowering

5.7 Tensor derivatives and Christoffel symbols

5.8 Covariant differentiation

5.9 Vectors and one-forms

5.10 Chapter 5 problems

6 Tensor applications

6.1 The inertia tensor

6.2 The electromagnetic field tensor

6.3 The Riemann curvature tensor

6.4 Chapter 6 problems

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