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7 articles on university: the maths or physics explained, ready-to-teach lesson plans, and how to build each slide in Tracé.

A square wave built from 12 odd harmonics, next to a bar chart of their amplitudes: 1, 1/3, 1/5, 1/7, 1/9calculus · signals · waves · universityFourier Series: How Sine Waves Build a Square WaveAdd sin x, sin 3x / 3, sin 5x / 5… and a square wave appears. The formula, why only odd harmonics, the 9% Gibbs overshoot, and a click-by-click slide.The Taylor polynomial 1 + x + x²/2 + x³/6 + x⁴/24 closing in on the curve of eˣcalculus · university · explainerTaylor Series: Approximating Functions with PolynomialsHow Taylor series build eˣ and sin x from polynomials term by term, how accurate a few terms are, the small-angle approximation, and a click-by-click slide.Newton's method on x² − 2: tangents from x₀ = 3 down to the root √2, with the values in a tablecalculus · numerical methods · university · explainerNewton's Method, Animated: One Tangent per ClickTeach Newton's method visually: follow each tangent down to the x-axis, compare it with bisection, and see why it converges so fast, or fails.Euler's method with step 0.5 for y′ = y, below the exact curve eˣ, over the direction fielddifferential equations · calculus · university · explainerEuler's Method and Direction Fields, VisuallyA visual lesson on differential equations: draw the direction field, follow solution curves, then watch Euler’s method step away from the exact solution.A 16-QAM constellation in noise with decision boundaries and Gray-coded bit labelssignals · engineering · university · explainerQAM Constellation Diagrams, Explained (BPSK to 256-QAM)What a constellation diagram shows, why 256-QAM needs a cleaner channel than QPSK, Gray coding, noise and phase errors, with animated examples.Sequence diagram of the TCP three-way handshake: SYN, SYN-ACK and ACK between client and servernetworking · engineering · university · explainerHow to Explain the TCP Three-Way HandshakeTeach the TCP handshake with a sequence diagram that plays one message per click: SYN, SYN-ACK, ACK, sequence numbers, and what happens when a packet is lost.Bifurcation diagram of the logistic map from r = 2.5 to 4, with a line at r = 3.56sequences · dynamical systems · university · explainerThe Logistic Map: Teaching the Road to ChaosOne simple rule, x → r x (1 − x), goes from a steady state to cycles to chaos as r grows. Cobweb diagrams and the bifurcation diagram, explained.