Differential Equations
The “Well-Posedness” of Differential Equations: the Sense of Hadamard
An overwhelmingly large portion of our modeling of the universe is accomplished by posing and solving differential equations..
Physics
Physics
Inverse-Square Law of Gravitation: The Role of the Apple and the Moon
How Newton confirmed the inverse-square law
Geometry
To 3D and Beyond
How many spatial dimensions do we live in? How many can we directly perceive? Are the two answers the same? If they are different, what effect, if any, do any higher dimensions have on us?
Physics
The Breakup of a Liquid Droplet
The Science of Liquid Droplets
Physics
The Fascinating Mystery of Systems with Many Length Scales
An Introduction to Critical Phenomena in Physics
Physics
A No-Nonsense Introduction to the Physics of the Big Bang
An Introduction to Cosmology and the Birth of the Universe
Chemistry
Let’s Derive the Ideal Gas Law from Scratch!
With nothing but a good model, a few definitions, and some math, we’ll derive a fundamental relationship of chemistry.
Symmetry
Emmy Noether and One of the Deepest Observations in All of Physics
The Correspondence Between Symmetry and Conservation Laws
Analysis
Distributions: What Exactly is the Dirac Delta “Function”?
The theory of distributions , also known as generalized functions, often remains something of an enigma…
Classical Mechanics
The Navier-Stokes Equations
A simple introduction to a million dollar problem
Classical Mechanics
A Geometric Intuition for Energy Conservation
In a sense, Conservation of Energy is just Conservation of Area.
Physics
Approaches to Solving Problems in Physics
Becoming a master at physics requires a lot of work, but learning the techniques and guidelines in this article is taking the first step.