A Brief on Tensor Analysis

1. Front Matter

   Pages i-xiv

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2. Introduction: Vectors and Tensors

   • James G. Simmonds

   Pages 1-24

3. General Bases and Tensor Notation

   • James G. Simmonds

   Pages 25-44

4. Newton’s Law and Tensor Calculus

   • James G. Simmonds

   Pages 45-69

5. The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem

   • James G. Simmonds

   Pages 71-105

6. Back Matter

   Pages 107-114

   PDF

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.

• Analysis
• Brief
• Derivative
• Eigenvalue
• Tensoranalysis
• calculus
• differential equation

• Department of Applied Mathematics, University of Virginia, Charlottesville, USA

  James G. Simmonds

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