The Levi-Civita Tensor and Identities in Vector Analysis (UMAP)

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