This book explores the fundamental but often overlooked connection between Maxwell's equations, as they are taught in undergraduate electrical engineering courses, and special relativity. Written for an audience of practical engineers instead of theoretical physicists, it exposes the underlying contradictions brought about by the emergence of electromagnetic theory, one of the greatest triumphs in mathematical physics of all time that unified the phenomena of electricity, magnetism, and light, into a world in which the classical Galilean principle of relativity was considered incontrovertible. It explains how Einstein redefined the concepts of space and time and what it means to measure them, while altogether disbanding the notion of global simultaneity.

A manifestly relativistic formulation of electromagnetic laws is first presented and then applied to common engineering problems, like the interaction of electromagnetic fields at dynamic interfaces, the derivation of propagating modes in closed metal waveguides, and the foundations of microwave network theory. Mathematical toolkits for relativistic analysis, such as tensor notation and spacetime algebra, are explained. These tools are then used to analyze the consequences of motion at relativistic speeds upon otherwise well-known electromagnetic circuit behaviors.

Well-drawn and insightful diagrams along with articulate explanations help the reader to gain an intuitive understanding of four-dimensional spacetime and the nature of the electromagnetic field in that context, while summary tables and comprehensive appendices serve as a resource for further selfdirected exploration. Readers trained in microwave engineering will learn to see their field from a new perspective, and shall gain from that new insight the ability to conceive of unexpected solutions to practical engineering problems that might otherwise defy one's intuition.

**Chapter 1 Classical Electromagnetics**

1.1 Early Concepts in Electricity and Magnetism

1.2 Advancement Through Experimentation

1.3 Mathematical Refinement

1.4 Matter and Energy

**Chapter 2 Reference Frame Transformation**

2.1 Galilean Transformation

2.2 Spacetime

2.3 Lorentz Transformation

2.4 Poincare’s Coordinate Time and Other Variants

2.5 Resolution of Apparent Paradoxes

**Chapter 3 Waves in Spacetime**

3.1 Partial Boosts

3.2 Doppler Effects

3.3 Global Navigation Satellite Systems

3.4 Dispersion in Minkowski Space

**Chapter 4 Covariant Electrodynamics**

4.1 Kinematics of Moving Charges

4.2 Ricci Calculus

4.3 Relativistic Representations of the EM Field

4.4 Maxwell’s Equations in Tensor Form

4.5 Lorentz Force Law in Tensor Form

4.6 Covariant Wave Equations

**Chapter 5 The Calculus of Spacetime**

5.1 Geometric Algebra

5.2 Electromagnetic Laws in Spacetime Algebra

5.3 Transformations

5.4 Subalgebras

**Chapter 6 Interactions with Matter**

6.1 Macroscopic Field Equations

6.2 Waves in Matter

6.3 Material Interfaces

6.4 Wave Reflection and Refraction

**Chapter 7 Guided Waves**

7.1 Rectangular Waveguide

7.2 Circular Waveguide

7.3 Dispersion

7.4 Coaxial Line

**Chapter 8 Network Analysis**

8.1 Integral Forms

8.2 Compact Ports

8.3 A New Language for Network Analysis

8.4 Rotors for Network Analysis