the curriculum / 18 courses / 79 lessons / free
Learn it by changing the numbers.
A college-style path through mathematics, physics and electrical engineering — taught in live NapkinCalc worksheets. Every result on these pages was computed by the real engine, and every worksheet opens in the app where you can edit any number and watch the whole page re-derive.
Mathematics
- 01 Algebra 1 Solving equations, lines & slope, systems, and the exponent rules — the foundation everything else builds on.
- 02 Algebra 2 Quadratics & the discriminant, exponentials & logarithms, and the sums of sequences — verified live.
- 03 Trigonometry Right triangles, the unit circle, sine waves, and the laws of sines & cosines — with live diagrams.
- 04 Precalculus — Functions Functions as machines: notation, composition, transformations, inverses, and rational functions with asymptotes.
- 05 Calculus 1 — Limits & Derivatives Limits computed numerically, the difference quotient becoming the derivative, and tangent lines — watch h shrink.
- 06 Calculus 2 — Integrals & Series Riemann sums ground out by the engine vs the exact integral, the fundamental theorem, and series that converge (or don’t).
- 07 Linear Algebra — Matrices Matrices as machines, the determinant as a volume factor, inverses, and Cramer’s rule solving real systems.
- 08 Differential Equations Equations about change: exponential decay verified numerically, Newton’s cooling, and the harmonic oscillator.
Physics
- 01 Physics 1 — Motion & Energy Kinematics, free fall, projectiles, Newton’s laws, friction, and energy conservation — all with units.
- 02 Physics 2 — Momentum & Waves Collisions & conservation of momentum, circular motion, and waves — frequency, wavelength, and harmonics.
- 03 Physics 3 — Electricity & Magnetism Coulomb’s law, fields, magnetic force on moving charge, the solenoid, and the electromagnetic wave.
- 04 Physics 4 — Thermo & Fluids The ideal gas law, heat & specific heat, Carnot’s limit, pressure with depth, buoyancy, and Bernoulli.
- 05 Physics 5 — Modern Physics Photons, the photoelectric effect, matter waves, special relativity’s γ, E = mc², and half-life dating.
Electrical
- 01 Electricity 1 — DC Circuits Ohm’s law, series & parallel circuits, the voltage divider, real energy costs, and RC charging.
- 02 Electricity 2 — AC Circuits RMS voltage, reactance, series RLC impedance, and resonance — with the impedance dip plotted live.
- 03 Electronics 1 — Filters & Op-Amps Decibels, RC filters with the rolloff plotted live, op-amp gain you can dial, and sizing an LED resistor.
- 04 AC Motors Induction motors: synchronous speed, slip, full-load current, shaft torque, and power-factor correction.
- 05 Power Systems — Distribution Three-phase power, transformers, why transmission is high-voltage, feeder voltage drop, and PF penalties.
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