Understanding Geometric Algebra for Electromagnetic Theory [Hardcover]

This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison.

Professors can request a solutions manual by email: pressbooks@ieee.org

Preface xi

Reading Guide xv

1. Introduction 1

2. A Quick Tour of Geometric Algebra 7

2.1 The Basic Rules of a Geometric Algebra 16

2.2 3D Geometric Algebra 17

2.3 Developing the Rules 19

2.3.1 General Rules 20

2.3.2 3D 21

2.3.3 The Geometric Interpretation of Inner and Outer Products 22

2.4 Comparison with Traditional 3D Tools 24

2.5 New Possibilities 24

2.6 Exercises 26

3. Applying the Abstraction 27

3.1 Space and Time 27

3.2 Electromagnetics 28

3.2.1 The Electromagnetic Field 28

3.2.2 Electric and Magnetic Dipoles 30

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