NapkinCalc

the curriculum / 39 courses / 162 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.

Getting Started

1 courses
  1. 01 Start Here — A Complete Tour Start here. One live worksheet that shows every feature — variables, units, plots, diagrams, sums, matrices, and the solvers — and how to use each. 14 lessons

Mathematics

23 courses
  1. 01 Pre-Algebra — Numbers & First Variables The on-ramp: order of operations, signed numbers, fractions/decimals/percents, ratios & proportions, and a first look at variables. 5 lessons
  2. 02 Algebra 1A — Equations & Lines Part 1 of 2. Solving linear equations, inequalities (and the sign-flip trap), and the slope–intercept story of straight lines. 3 lessons
  3. 03 Algebra 1B — Systems, Exponents & Factoring Part 2 of 2. Systems of equations by elimination, the three exponent rules, and factoring with the zero-product rule. 3 lessons
  4. 04 Algebra 2A — Functions & Quadratics Part 1 of 2. Functions as machines (and composition), the quadratic formula & discriminant, and the parabola's vertex. 3 lessons
  5. 05 Algebra 2B — Exponentials, Logs & Sequences Part 2 of 2. Exponential growth & decay, the logarithm as its inverse (and the log laws), and arithmetic & geometric series. 3 lessons
  6. 06 Trigonometry A — Triangles & the Unit Circle Part 1 of 2. Right-triangle ratios (SOH-CAH-TOA), the Pythagorean theorem, and the unit circle that extends sine & cosine to every angle. 2 lessons
  7. 07 Trigonometry B — Waves & the Triangle Laws Part 2 of 2. Sine waves (amplitude, frequency, period), the Pythagorean identity, and the laws of cosines & sines for any triangle. 3 lessons
  8. 08 Precalculus A — Functions & Transformations Part 1 of 2. Function notation, composition, graph transformations (shifts & stretches), and inverse functions. 4 lessons
  9. 09 Precalculus B — Polynomials & Rational Functions Part 2 of 2. Polynomial zeros & end behaviour, rational functions and their asymptotes, and a first taste of the limit. 3 lessons
  10. 10 Calculus 1A — Limits & Continuity Part 1 of 3. What a limit really is, limits at infinity & asymptotes, continuity, and the Intermediate Value Theorem — every idea computed live. 3 lessons
  11. 11 Calculus 1B — The Derivative Part 2 of 3. The derivative as a limit of slopes, tangent lines, the power/product/quotient rules, the chain rule, and implicit differentiation — with live Steps. 5 lessons
  12. 12 Calculus 1C — Applications of the Derivative Part 3 of 3. Related rates, linear approximation, finding maxima & minima, optimization word problems, and Newton's method — the derivative earning its keep. 5 lessons
  13. 13 Calculus 2A — Integrals Part 1 of 2. The Riemann sum, the Fundamental Theorem of Calculus, and symbolic integration with live Steps. 2 lessons
  14. 14 Calculus 2B — Series & Taylor Part 2 of 2. Geometric series that converge, the harmonic series that doesn't, and Taylor polynomials impersonating functions. 3 lessons
  15. 15 Linear Algebra A — Matrices & Determinants Part 1 of 2. Matrices as machines that transform space, the determinant as an area-scaling factor (ad − bc), and the transpose. 2 lessons
  16. 16 Linear Algebra B — Inverses & Solving Systems Part 2 of 2. The matrix inverse (and when it exists), and solving linear systems with Cramer's rule — systems as matrix equations. 2 lessons
  17. 17 Differential Equations A — Modeling Change & Decay Part 1 of 2. What a differential equation is, the exponential-decay law y′ = −k·y (verified numerically), and Newton's law of cooling. 2 lessons
  18. 18 Differential Equations B — Oscillation & Damping Part 2 of 2. The harmonic oscillator y″ = −ω²·y, natural frequency √(k/m), and damped oscillation — decay enveloping a wave. 2 lessons
  19. 19 Probability — Chance & Counting What probability means, counting with permutations & combinations, independent events, and the binomial distribution. 3 lessons
  20. 20 Statistics — Describing & Inferring Describing data (mean, median, standard deviation), the normal curve and the 68–95–99.7 rule, and z-scores. 3 lessons
  21. 21 Discrete Mathematics — Logic & Number Theory Logic (and/or), set counting by inclusion–exclusion, modular arithmetic & GCD, and proof by patterns (induction). 4 lessons
  22. 22 Multivariable Calculus — Vectors & Gradients Vectors (dot, cross, length), functions of two variables, partial derivatives, and the gradient that points uphill. 4 lessons
  23. 23 Proofs & Logic — How We Know Logical statements, implication & contrapositive, direct proof, counterexamples, and proof by induction. 4 lessons

Physics

5 courses
  1. 01 Physics 1 — Motion & Energy Kinematics, free fall, projectiles, Newton’s laws, friction, and energy conservation — all with units. 5 lessons
  2. 02 Physics 2 — Momentum & Waves Collisions & conservation of momentum, circular motion, and waves — frequency, wavelength, and harmonics. 4 lessons
  3. 03 Physics 3 — Electricity & Magnetism Coulomb’s law, fields, magnetic force on moving charge, the solenoid, and the electromagnetic wave. 5 lessons
  4. 04 Physics 4 — Thermo & Fluids The ideal gas law, heat & specific heat, Carnot’s limit, pressure with depth, buoyancy, and Bernoulli. 5 lessons
  5. 05 Physics 5 — Modern Physics Photons, the photoelectric effect, matter waves, special relativity’s γ, E = mc², and half-life dating. 5 lessons

Electrical

5 courses
  1. 01 Electricity 1 — DC Circuits Ohm’s law, series & parallel circuits, the voltage divider, real energy costs, and RC charging. 5 lessons
  2. 02 Electricity 2 — AC Circuits RMS voltage, reactance, series RLC impedance, and resonance — with the impedance dip plotted live. 4 lessons
  3. 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. 4 lessons
  4. 04 AC Motors Induction motors: synchronous speed, slip, full-load current, shaft torque, and power-factor correction. 5 lessons
  5. 05 Power Systems — Distribution Three-phase power, transformers, why transmission is high-voltage, feeder voltage drop, and PF penalties. 5 lessons

Engineering

5 courses
  1. 01 Statics — Forces & Equilibrium Resolve forces, balance moments, read a free-body diagram, solve a truss joint, and decide whether the crate slides — every number live and unit-checked. 6 lessons
  2. 02 Mechanics of Materials — Stress & Strain Stress, strain, Hooke's law and Young's modulus, factor of safety, shear, thermal stress, and pressure-vessel hoop stress — the math that decides if a part survives. 6 lessons
  3. 03 Beams & Columns — Bending & Buckling Second moment of area, bending stress, beam deflection, and Euler column buckling — with the cross-section drawn live and the moment diagram plotted. 4 lessons
  4. 04 Thermodynamics — Energy & Cycles The first law, specific heat, the ideal gas law, heat-engine and Carnot efficiency, the fridge COP, and heat conduction — energy bookkeeping with units enforced. 6 lessons
  5. 05 Fluid Mechanics — Flow & Pressure Hydrostatic pressure, buoyancy, continuity, Bernoulli, the Reynolds number, and pump power — the physics of anything that flows, every term unit-checked. 6 lessons

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