# A Brief on Tensor Analysis

• James G. Simmonds
Textbook

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

1. Front Matter
Pages i-xi
2. James G. Simmonds
Pages 1-24
3. James G. Simmonds
Pages 25-42
4. James G. Simmonds
Pages 43-67
5. James G. Simmonds
Pages 68-88
6. Back Matter
Pages 89-94

### Introduction

When I was an undergraduate, working as a co-op student at North American Aviation, I tried to learn something about tensors. In the Aeronautical En­ gineering 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 tum-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. Tensor-what power those two syllables seemed to resonate. I had heard the word once before, in an aside by a graduate instructor to the cognoscenti in the front row of a course in strength of materials. "What the book calls stress is actually a tensor. . . ." With my interest twice piqued and with time off from fighting the brush­ fires of a demanding curriculum, I was ready for my first serious effort at self­ instruction. In Los Angeles, after several tries, I found a store with a book on tensor analysis. In my mind I had rehearsed the scene in which a graduate stu­ dent or professor, spying me there, would shout, "You're an undergraduate.

### Keywords

Analysis Brief Eigenvalue Impress Tensoranalysis derivative differential equation integral mechanics operator tensor analysis time

#### Authors and affiliations

• James G. Simmonds
• 1
1. 1.Department of Applied Mathematics and Computer Science Thornton HallUniversity of VirginiaCharlottesvilleUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-0141-7
• Copyright Information Springer-Verlag New York 1982
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4684-0143-1
• Online ISBN 978-1-4684-0141-7
• Series Print ISSN 0172-6056
• Buy this book on publisher's site
Industry Sectors