- Introduction
- A Quick Tour of Geometric Algebra
- The Basic Rules of a Geometric Algebra
- 3D Geometric Algebra
- Developing the Rules
- General Rules
- 3D
- The Geometric Interpretation of Inner and Outer Products
- Comparison with Traditional 3D Tools 24
- New Possibilities 24
- Exercises
- Applying the Abstraction
- Space and Time
- Electromagnetics
- The Electromagnetic Field
- Electric and Magnetic Dipoles
- The Vector Derivative
- The Integral Equations
- The Role of the Dual
- Exercises
- Generalization
- (3+1)D Electromagnetics
- ╇ Review of (3+1)D
- Introducing Spacetime
- Background and Key Concepts
- Time as a Vector
- The Spacetime Basis Elements
- Spatial and Temporal Vectors
- Basic Operations
- Velocity
- Different Basis Vectors and Frames
- Events and Histories
- Events
- Histories
- Straight-Line Histories and Their Time Vectors
- Arbitrary Histories
- The Spacetime Form of ∇
- Working with Vector Differentiation
- Working without Basis Vectors
- Classification of Spacetime Vectors and Bivectors
- Exercises
- Relating Spacetime to (3+1)D
- Change of Basis Vectors
- Further Spacetime Concepts
- Application of the Spacetime Geometric Algebra to Basic Electromagnetics
- The Electromagnetic Field of a Point Charge Undergoing Acceleration
- Appendices
- Axial versus True Vectors
- Complex Numbers and the 2D Geometric Algebra
- The Structure of Vector Spaces and Geometric Algebras
- A Vector Space
- A Geometric Algebra
- Quaternions Compared
- Evaluation of an Integral in Equation (5.14)
- Formal Derivation of the Spacetime Vector Derivative