Math Foundations

Refreshers for everything the other books lean on.

A shared companion. Short, focused chapters on the mathematical machinery the other books invoke — calculus, vector calculus, complex exponentials, ODEs, PDEs, Fourier, linear algebra, dimensional analysis. Each chapter is a single page: link in from anywhere, scan, return.

Chapters

1. Chapter 0Pre-calculus: trigonometry and logarithmsRadians, the unit circle, identities; logs, exponentials, and decibel thinking
2. Chapter 1Single-variable calculusDerivatives, integrals, Taylor expansion — the working subset
3. Chapter 2Partial derivatives and vector calculusGradient, divergence, curl, the Laplacian
4. Chapter 3Complex exponentials and phasorsEuler's formula and why we use it for oscillations
5. Chapter 4Linear algebraVectors, matrices, eigenvalues, inner products, the spectral theorem
6. Chapter 5Linear ordinary differential equationsFirst- and second-order, homogeneous and forced
7. Chapter 6Linear partial differential equationsSeparation of variables and characteristics
8. Chapter 7Fourier series and the Fourier transformSinusoids as a basis, frequency as a dual coordinate
9. Chapter 8Dimensional analysisUnits, scaling, order-of-magnitude estimation
10. Chapter 9Numerical methodsHow the simulations on this site actually work
11. Chapter 10Statistics and probabilityRandom variables, the Gaussian, Brownian motion, Poisson, Bayes
12. Chapter 11Chaos and nonlinear dynamicsSensitive dependence, bifurcations, strange attractors, Lyapunov exponents
13. GlossaryGlossaryTerms used in this book
14. Chapter HHistoryA chronological narrative
15. Chapter SStudySpaced-repetition review
16. BibliographyBibliographySources and further reading