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.
- Uses plain language to explain vectors and tensors – some of the most powerful problem-solving tools available
- Supported by a host of online materials, including interactive solutions to the problems and audio podcasts
- Written by Daniel Fleisch, author of the highly popular A Student's Guide to Maxwell's Equations
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Reviews & endorsements
'This is both helpful and innovative … Fleisch's book is an excellent and challenging resource for students in this subject area.' Optics and Photonics News
'In the reviewer's experience it takes students a long time to get a feeling for what vectors and especially tensors are, and in this respect this book is very useful: it helps them become confident in using and applying these concepts … Each chapter concludes with a section of problems and, moreover, the author supplies an interactive website and a series of audio podcasts. In the reviewer's opinion this book will certainly become as popular as the author's book A Student's Guide to Maxwell's Equations which uses the same approach.' Rabe von Randow, Zentralblatt MATH
'This highly readable introductory book will be of great assistance to those taking undergraduate or graduate courses and meeting tensors for the first time.' George Matthews, Institute of Mathematics and its Applications (ima.org.uk)
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Customer reviews

17th Oct 2024 by UName-267604
Amazing . I am a non physicist and found this book very useful
17th Oct 2024 by UName-285100
Great step by step introduction to a rather heavy subject. However I still miss some practical examples of vectors with both co and contravariant coordinates, but neither have I found them in other books on the subject.
17th Oct 2024 by UName-432211
Astronomy, mathematics, and physics use different coordinate systems and vector representations. When a vector system or problem includes others' work, tacit assumptions in material can lead to confusion over even the simplest things. This book is the best resource I have found for clearing the fog and re-establishing coherence in transformations and vector speak. Clearly and concisely written. Portable.
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Product details
- Date Published: September 2011
- format: Paperback
- isbn: 9780521171908
- length: 206 pages
- dimensions: 228 x 151 x 10 mm
- weight: 0.34kg
- contains: 80 b/w illus. 50 exercises
- availability: Available
Table of Contents
1. Vectors
2. Vector operations
3. Vector applications
4. Covariant and contravariant vector components
5. Higher-rank tensors
6. Tensor applications
Index.
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Author
Daniel A. Fleisch, Wittenberg University, Ohio
Daniel Fleisch is an Associate Professor in the Department of Physics at Wittenberg University, where he specializes in electromagnetics and space physics. He is the author of A Student's Guide to Maxwell's Equations (Cambridge University Press, 2008).