Calculus
Calculus and the Legend of the Founding of Carthage
How modern calculus of variations solved an ancient math problem.
Panda the Red
Optimization
The Method of Lagrange Multipliers
How to solve constrained optimization problems.
Geometry
Why Trisecting the Angle is Impossible
An accidental introduction to field theory.
PDE
Laplace’s Equation
Flows and fields
Relativity
Thinking Relativistically
Problem-solving in special relativity.
Astrophysics
Kepler’s Laws of Planetary Motion
The laws of planetary motion.
Quantum Physics
Schrödinger’s Equation
“So do any of you guys know quantum physics?” Paul Rudd in Avengers: Endgame
Analysis
Root-Finding Algorithms
Ways of determining when an equation is equal to zero
Mathematics
The Arithmetic-Geometric Mean Inequality
Suppose that x and y are non-negative real numbers, not necessarily distinct. The famous arithmetic-geometric mean inequality says that:
Quantum Mechanics
What is Wave-Particle Duality?
Why we need quantum physics.
Physics
Einstein’s Theory of Relativity
Explained as simply as possible, but no simpler.
Physics
The Wave Equation
Bonus: Separation of Variables
Physics
The Heat Equation: Inhomogeneous Boundary Conditions
This is the third article in my series on partial differential equations. Before reading further you might want to read part one (9…
Physics
The Heat Equation: Forcing
The inhomogeneous heat equation
Physics
The Heat Equation, explained
Your first PDE. Bonus: Fourier series.
Mathematics
Taylor’s Theorem
Approximating functions near points. It’s cooler than it sounds, trust me.