The Levi-Civita Tensor and Identities in Vector Analysis (UMAP)
Author: Chang-li Yiu and Carrol O. Wilde
A unit that involves applications of vector field identities. This module allows students to gain the ability to derive vector identities and vector field identities using the Levi-Civita tensor.
Table of Contents:
1. INTRODUCTION
2. THE KRONECKER-DELTA
3. PERMUTATIONS
4. THE LEVI-CIVITA TENSOR
5. A USEFUL NOTATIONAL CONVENTION
6. RELATION BETWEEN THE KRONECKER-DELTA AND THE LEVI-CIVITA TENSOR
7. IDENTITIES IN VECTOR ALGEBRA
8. IDENTITIES IN VECTOR FIELDS
9. THE LEVI-CIVITA TENSOR IN FOUR DIMENSIONS
10. MODEL EXAM
11. ANSWERS AND SOLUTIONS TO EXERCISES
12. ANSWERS TO MODEL EXAM
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