The movement of a Slinky can be modeled as an n-body problem consisting of n coupled masses connected by a springs that obey Hooke’s Law. This crude model can be further refined by taking the continuum limit where n goes to infinity becomes the wave equation dy²/dt² = b dy² /dx².
Coupled Oscillators:
Generalization to n coupled harmonic oscillators:
The Continuum Limit:
The Youtube videos of 3blue1brown. Particularly the videos on Linear Algebra and Fourier Series/Transforms.
The books of Paul Nahin. Particularly An Imaginary Tale, Hot Molecules Cold Electrons, Dueling Idiots and The Logician and the Engineer.
The Princeton Companion to Mathematics. Particularly Tao’s article on differential forms.
Proofs from The Book.
Charles Pinter’s Abstract Algebra.
Halmos’ Naive Set Theory.
Real Analysis and Applications by Frank Morgan.
Riley. Mathematical Methods.
Geometrical Methods of Physics by Schutz (And his other book on General Relativity).
Differential Forms for Scientists and Engineers by Harley Flanders.
