Electromagnetics & Signals
An intuitive, interactive Electromagnetics and Signals & Systems course covering the topics typical of the first two years of an electrical engineering degree. Every lesson pairs plain-language explanations with precise field/wave diagrams, worked examples, hands-on simulations, and practice you can check yourself.
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Vector Calculus Foundations for EM
Vector fields, gradient, divergence, curl, and the two integral theorems every EM law relies on.
- Vector Algebra & Coordinate Systems 14 min · soon
- Vector Fields, Gradient, Divergence & Curl 18 min · soon
- Line, Surface & Volume Integrals 16 min · soon
- The Divergence Theorem & Stokes' Theorem 18 min · soon
Electrostatics I: Coulomb's Law, Gauss's Law & Potential
The electric field from first principles — Coulomb's law, Gauss's law, and electric potential.
- Coulomb's Law & the Electric Field 14 min · soon
- Electric Field of Continuous Charge Distributions 18 min · soon
- Electric Flux & Gauss's Law 16 min · soon
- Applications of Gauss's Law — Symmetric Charge Distributions 18 min · soon
- Electric Potential & Potential Energy 16 min · soon
- Poisson's & Laplace's Equations — Boundary-Value Problems 18 min · soon
Electrostatics II: Conductors, Dielectrics & Capacitance
Conductors, the method of images, dielectrics, and capacitance derived from field theory.
Steady Currents & Magnetostatics
Charge conservation, the Biot-Savart law, and Ampere's circuital law for steady currents.
- Current Density, the Continuity Equation & Ohm's Law in Point Form 16 min · soon
- The Biot-Savart Law 18 min · soon
- Ampere's Circuital Law 16 min · soon
- Applications of Ampere's Law — Solenoid, Toroid, Infinite Sheet 18 min · soon
- Magnetic Flux Density & the Vector Potential 16 min · soon
Magnetic Forces, Materials & Inductance
Forces and torques from magnetic fields, magnetic materials, boundary conditions, and inductance.
- Force on a Moving Charge & on a Current-Carrying Conductor 16 min · soon
- Torque on a Current Loop & the Magnetic Dipole Moment 16 min · soon
- Magnetic Materials & Boundary Conditions for B and H 18 min · soon
- Inductance & Mutual Inductance — from Flux Linkage 18 min · soon
- Energy Stored in Magnetic Fields 14 min · soon
Time-Varying Fields & Maxwell's Equations
Faraday's law, displacement current, and Maxwell's equations — the flagship module of the EM half.
Electromagnetic Waves, Reflection & Transmission Lines
Plane waves, reflection at boundaries, and transmission lines — where fields meet circuits.
- Plane Waves in Free Space & Lossy Media — Intrinsic Impedance 18 min · soon
- Wave Polarization & the Poynting Vector 16 min · soon
- Reflection & Transmission at Normal Incidence 18 min · soon
- Transmission Lines — Telegrapher's Equations, Reflection Coefficient & Input Impedance 20 min · soon
- Standing Waves, SWR & Reading a Smith ChartOptional 18 min · soon
Signals: Continuous & Discrete-Time
What a signal is, elementary signal building blocks, and a first look at sampling.
- What Is a Signal? Continuous vs Discrete-Time 14 min · soon
- Signal Operations: Shifting, Scaling, Reflection 14 min · soon
- Elementary Signals: Step, Impulse, Ramp, Exponential, Sinusoid 16 min · soon
- Periodic Signals & Signal Energy/Power 14 min · soon
- Sampling — A First Look at the Nyquist Rate 14 min · soon
LTI Systems & Convolution
Linearity, time-invariance, and convolution — the flagship module of the signals half.
- Systems: Linearity, Time-Invariance, Causality, Stability 16 min · soon
- The Impulse Response & Convolution 18 min · soon
- Convolution Properties & Graphical Convolution 18 min · soon
- Discrete-Time Convolution & Difference Equations 16 min · soon
- Differential Equations for CT LTI Systems & Complex Exponentials as Eigenfunctions 18 min · soon
- LTI System Response to Standard Inputs 16 min · soon
Fourier Analysis
Fourier series and transforms — the frequency-domain view of signals, and where aliasing comes from.
- Fourier Series — Trigonometric & Exponential Form 18 min · soon
- Fourier Series Properties & Parseval's Theorem 16 min · soon
- The Fourier Transform, Its Inverse & Properties 18 min · soon
- Frequency Response of LTI Systems — Filters Revisited from the Signals Side 18 min · soon
- Sampling Revisited — Aliasing in the Frequency Domain & Reconstruction 18 min · soon
- The Discrete-Time Fourier TransformOptional 16 min · soon
Laplace & Z-Transforms, Capstone
Laplace and Z-transforms, transfer functions, and a capstone signal-processing chain.
- The Laplace Transform, Its Properties & Region of Convergence 18 min · soon
- Solving Linear LTI Systems with Laplace — Partial-Fraction Inversion 18 min · soon
- Transfer Functions, Poles & Zeros, Stability via the ROC 18 min · soon
- The Z-Transform, Its ROC & the Relationship to the DTFT 18 min · soon
- Capstone: Designing & Analyzing a Signal-Processing ChainOptional 24 min · soon
New lessons are added continuously. Prefer to test yourself? Try the Electrical Aptitude test.