Acknowledgments -- Introduction -- 1 Foundations of Maxwell's Equations -- 1.1 Historical Overview -- 1.2 Role of Electromagnetic Field Theory -- 1.3 Electromagnetic Field Quantities -- 1.4 Units and Universal Constants -- 1.5 Precision of Measured Quantities -- 1.6 Introduction to Complex Variables -- 1.7 Phasor Notation -- 1.8 Quaternions -- 1.9 Original Form of Maxell's Equations -- 2 Vector Analysis -- Introduction -- 2.1 Addition and Subtraction -- 2.2 Multiplication -- 2.3 Triple Products -- 2.4 Coordinate Systems -- 2.5 Coordinate Transformations -- 2.6 Vector Differentiation -- 2.7 Divergence Theorem -- 2.8 Stokes's Theorem -- 2.9 Laplacian of a Vector Field -- 3 Static Electric Fields -- Introduction -- 3.1 Properties of Electrostatic Fields -- 3.2 Gauss's Law -- 3.3 Conservation Law -- 3.4 Electric Potential -- 3.5 Electric Field for a System of Charges -- 3.6 Electric Potential for a System of Charges -- 3.7 Electric Field for a Continuous Distribution -- 3.8 Conductor in a Static Electric Field -- 3.9 Capacitance -- 3.10 Dielectrics -- 3.11 Electric Flux Density -- 3.12 Dielectric Boundary Conditions -- 3.13 Electrostatic Energy -- 3.14 Electrostatic Field in a Dielectric -- Endnotes -- 4 Solution of Electrostatic Problems -- Introduction -- 4.1 Poisson's and Laplace's Equations -- 4.2 Solutions to Poisson's and Laplace's Equations -- 4.3 Green's Functions -- 4.4 Uniqueness of the Electrostatic Solution -- 4.5 Method of Images -- 5 Steady Electric Currents -- 5.1 Current Density and Ohm's Law -- 5.2 Relation to Circuit Parameters -- 5.3 Superconductivity -- 5.4 Free Electron Gas Theory -- 5.5 Band Theory -- 5.6 Equation of Continuity -- 5.7 Microscopic View of Ohm's Law -- 5.8 Power Dissipation and Joule's Law -- 5.9 Boundary Condition for Current Density -- 5.10 Resistance/Capacitance Calculations -- Endnotes -- 6 Static Magnetic Fields -- Introduction -- 6.1 Magnetic Force -- 6.2 Magnetostatics in Free Space -- 6.3 Magnetic Vector Potential -- 6.4 The Biot-Savart Law.

6.5 Historical Conclusions -- 6.6 Atomic Magnetism -- 6.7 Magnetization -- 6.8 Equivalent Surface Current Density -- 6.9 Equivalent Magnetic Monopole Charge Density -- 6.10 Magnetic Field Intensity and Permeability -- 6.11 Ferromagnetism -- 6.12 Boundary Conditions for Magnetic Fields -- 6.13 Inductance and Inductors -- 6.14 Torque and Energy -- Endnotes -- 7 Time-Varrying Fields -- 7.1 Faraday's Law of Induction -- 7.2 E&M Equations before Maxwell -- 7.3 Maxwell's Displacement Current -- 7.4 Integral Form of Maxwell's Equations -- 7.5 Magnetic Vector Potential -- 7.6 Solution of the Time-Dependent Inhomogeneous Potential Wave Equations -- 7.7 Electric and Magnetic Field Equations for Source-Free Problems -- 7.8 Solutions for the Homogeneous Wave Equation -- 7.9 Particular Solution for the Inhomogeneous Wave Equation -- 7.10 Time Harmonic Fields -- 7.11 Electromagnetic Spectrum -- 7.12 Electromagnetic Boundary Conditions -- 7.13 Particular Solution for the Wave Equation with Inhomogeneous Boundary Conditions -- 7.14 Memristors -- 7.15 Electric Vector Potential -- APPENDIX A: MEASUREMENT ERRORS -- APPENDIX B: GRAPHICS AND CONFORMAL MAPPING -- APPENDIX C: VECTORS, MATRICEES, ORTHOGONAL FUNCTIONS -- BIBLIOGRAPHY -- Index.