Bibliography

The first published table of logarithms, conceived to replace multiplication by addition. The product-becomes-sum property dates from here.

Recast Napier's logarithms to base 10, the form that dominated practical calculation through printed tables and the slide rule for three centuries.

First published the general solution f(x − ct) + g(x + ct) of the 1-D wave equation.

Recast trigonometry and the exponential as functions of a real (and complex) variable and unified them through e^{iθ} = cos θ + i sin θ. Names the constant e.

First statement of the fluid equations of motion in their modern form — what we now call the Euler equations.

Introduced the decomposition of arbitrary functions into trigonometric series, motivated by the heat equation. The mathematical foundation of frequency-domain analysis.

Introduced the potential due to a point source and the integral identities now called Green's theorem — the origin of the Green's function used to solve forced wave and radiation problems.

The memoir, written for King Oscar II's prize, in which Poincaré found that the three-body problem admits trajectories of bewildering complexity — the first recognition of what we now call sensitive dependence. The origin of dynamical-systems theory.

A three-equation truncation of atmospheric convection that never settles and never repeats. The paper that introduced the strange attractor and the popular image of the butterfly effect.

May's review showing that the one-line logistic map x → rx(1−x) — a population model a schoolchild can iterate — already contains the full period-doubling route to chaos. The manifesto that brought chaos to a wide scientific audience.

Discovers that the period-doubling cascade approaches its accumulation point at a universal geometric rate δ ≈ 4.6692, the same for every smooth unimodal map. Universality made chaos a quantitative science.

Available free online. The most physics-friendly introductory calculus text.

The standard British mathematical-methods reference. Covers everything in the Foundations book at greater depth.

The rigorous-undergraduate calculus reference. Pace and exposition match the Foundations book's posture.

The standard modern textbook on nonlinear dynamics — flows, bifurcations, the Lorenz system, fractals, and Lyapunov exponents. The exposition this chapter is built to match.