# A Brief on Tensor Analysis

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xiv
2. James G. Simmonds
Pages 1-24
3. James G. Simmonds
Pages 25-44
4. James G. Simmonds
Pages 45-69
5. James G. Simmonds
Pages 71-105
6. Back Matter
Pages 107-114

### Introduction

There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri­ can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec­ tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple­ looking integrals called the components of the moment of inertia tensor.

### Keywords

Analysis Brief Derivative Eigenvalue Tensoranalysis calculus differential equation

#### Authors and affiliations

1. 1.Department of Applied MathematicsUniversity of VirginiaCharlottesvilleUSA

### Bibliographic information

• Book Title A Brief on Tensor Analysis
• Authors James G. Simmonds
• Series Title Undergraduate Texts in Mathematics
• DOI https://doi.org/10.1007/978-1-4419-8522-4
• Copyright Information Springer-Verlag New York, Inc. 1994
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-94088-5
• Softcover ISBN 978-1-4612-6424-8
• eBook ISBN 978-1-4419-8522-4
• Series ISSN 0172-6056
• Edition Number 2
• Number of Pages XIV, 114
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site