Active Geophysical Monitoring

CHAPTER 17

MAXWELL’S EQUATIONS AND NUMERICAL ELECTROMAGNETIC MODELING IN THE CONTEXT OF THE THEORY OF DIFFERENTIAL FORMS

Michael S. Zhdanov^a

Contents

1. Introduction

2. Differential Forms in Vector Field Theory

2.1. Concept of the differential form

2.2. Exterior (wedge) product of the differential forms

2.3. Canonical representations of the differential forms in three-dimensional Euclidean space

2.4. The exterior derivative operation

3. Nonstationary Field Equations and Differential Forms

3.1. Nonstationary vector fields and differential forms in four-dimensional space E₄

3.2. Differential form equations

3.3. Exterior derivative of a scalar field and a generalized source 1-form

3.4. Exterior derivative of a four-potential and a generalized source ...