Tag
Differential Equations
A differential equation relates a function to its rates of change, and solving one means finding the functions that satisfy that relation. The linear case is the one that yields completely: the solution set of a linear system is the kernel of a linear operator, its dimension is the order of the equation, and the matrix exponential writes every solution down at once. Writing here treats an ordinary differential equation as a statement about an operator on a function space, which is what makes superposition a theorem rather than a convenience. Partial differential equations are filed separately.
Blog
July 5, 2026
Mathematical Pharmacology
Pharmacokinetics, pharmacodynamics, and quantitative systems pharmacology reconstructed as one state-space object: controllability, observability, BIBO stability, and Metzler positivity built once at arbitrary compartment count, specialised to the reversible/dissipative (GENERIC) structure of compartmental kinetics, generalised to tensor QSP networks, and closed by a computable answer to when adding a compartment buys real structure versus an unidentifiable direction.
July 3, 2026
Classical Mechanics from Zero, in Two Languages
Classical mechanics constructed from nothing but an inertial frame, in matrix and linear algebra and in geometric algebra side by side: rotations and rigid-body dynamics without Euler angles, one vector derivative replacing grad, div, and curl, and the Lagrangian and Hamiltonian formalisms in both languages.
April 4, 2026
Numerical Analysis via Discrete Exterior Calculus
A self-contained reconstruction of numerical analysis through discrete exterior calculus: simplicial complexes, cochains, the discrete Hodge star, and the Hodge Laplacian, applied to quantum mechanics, computational electromagnetics, and fluid dynamics.
March 10, 2026
Kuramoto: How Order Emerges from Chaos
Fireflies, neurons, power grids: all governed by the same equation. A tour through the Kuramoto model, its order parameter, and the phase transition that turns noise into rhythm.