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.
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 FieldFree Open →
- Electric Field of Continuous Charge DistributionsFree Open →
- Electric Flux & Gauss's Law Open →
- Applications of Gauss's Law — Symmetric Charge Distributions Open →
- Electric Potential & Potential Energy Open →
- Poisson's & Laplace's Equations — Boundary-Value Problems Open →
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.
Magnetic Forces, Materials & Inductance
Forces and torques from magnetic fields, magnetic materials, boundary conditions, and inductance.
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 ImpedanceFree Open →
- Wave Polarization & the Poynting VectorFree Open →
- Reflection & Transmission at Normal Incidence Open →
- Transmission Lines — Telegrapher's Equations, Reflection Coefficient & Input Impedance Open →
- Standing Waves, SWR & Reading a Smith ChartOptional Open →
Signals: Continuous & Discrete-Time
What a signal is, elementary signal building blocks, and a first look at sampling.
LTI Systems & Convolution
Linearity, time-invariance, and convolution — the flagship module of the signals half.
- Systems: Linearity, Time-Invariance, Causality, StabilityFree Open →
- The Impulse Response & ConvolutionFree Open →
- Convolution Properties & Graphical Convolution Open →
- Discrete-Time Convolution & Difference Equations Open →
- Differential Equations for CT LTI Systems & Complex Exponentials as Eigenfunctions Open →
- LTI System Response to Standard Inputs Open →
Fourier Analysis
Fourier series and transforms — the frequency-domain view of signals, and where aliasing comes from.
- Fourier Series — Trigonometric & Exponential FormFree Open →
- Fourier Series Properties & Parseval's TheoremFree Open →
- The Fourier Transform, Its Inverse & Properties Open →
- Frequency Response of LTI Systems — Filters Revisited from the Signals Side Open →
- Sampling Revisited — Aliasing in the Frequency Domain & Reconstruction Open →
- The Discrete-Time Fourier TransformOptional Open →
Laplace & Z-Transforms, Capstone
Laplace and Z-transforms, transfer functions, and a capstone signal-processing chain.
- The Laplace Transform, Its Properties & Region of ConvergenceFree Open →
- Solving Linear LTI Systems with Laplace — Partial-Fraction InversionFree Open →
- Transfer Functions, Poles & Zeros, Stability via the ROC Open →
- The Z-Transform, Its ROC & the Relationship to the DTFT Open →
- Capstone: Designing & Analyzing a Signal-Processing ChainOptional Open →
New lessons are added continuously. Prefer to test yourself? Try the Electrical Aptitude test.