Book of Quantum Mechanics
What Most Don't Get About Functions
Functions are the hidden infrastructure of the physical universe, yet most math classes treat them as rigid black boxes where numbers go in and numbers come out.
Problem Timestamps (6)▾
Mastering functions requires more than memorizing f(x) notation—you need to understand domain boundaries, coordinate system transformations, physical assumptions, and exponential growth models.
Why You Can't Master Physics Without Complex Numbers
We learn early on that i² = -1, but calling complex numbers "imaginary" is an accident of history that obscures their geometric reality.
Problem Timestamps (5)▾
Mastering complex numbers requires more than memorizing formulas—you need to understand their geometry, phase, and the time evolution of frequencies.
Why You Can't Master Science Without Calculus
Learning science and engineering without calculus is like going to culinary school to become a chef, but leaving with the skills of a cook who can only follow recipes.
Why Cartesian Makes Math Harder Than It Needs to Be
Doing math and calculus in Cartesian coordinates is like navigating an entire road trip solely from a satellite view—convenient on a flat map, but completely unnatural when the terrain curves.
Partial Derivatives and How Nature is Built on Them
Introductory calculus courses stop at single-variable slopes and tangent lines, but nature doesn't operate in one dimension.
Professor Justin Lorieau
Visual video essays, animated Manim derivations, and companion problem sets in thermodynamics, quantum mechanics, and physical chemistry. Created from university lectures to build deep mathematical intuition.