DiBeos

Hi it’s Luca,

Here is a list of the TOP 23 differential equations in mathematical physics, together with the areas they belong to:

Classical Mechanics

(1) Newtons Second Law

(2) Simple Harmonic Oscillator

(3) Euler–Lagrange Equation

(4) Hamilton Equations

(5) Hamilton–Jacobi Equation

Basic ODE Models

(6) Radioactive Decay Law

(7) Logistic Growth Equation

Diffusion and Wave-related Equations

(8) Heat / Diffusion Equation

(9) Wave Equation

(10) Helmholtz Equation

Dynamical Systems

(11) Lorenz Equations

Classical Fields

(12) Laplace’s Equation

(13) Poisson Equation

(14) Continuity Equation

(15) Maxwell’s Equations

Fluid Mechanics

(16) Navier–Stokes Equations

Statistical Mechanics

(17) Boltzmann Transport Equation

General Relativity-related Equations

(18) Einstein Field Equations

(19) Friedmann Equation

Quantum Mechanics-related Equations

(20) Schrödinger Equation

(21) Klein–Gordon Equation

(22) Dirac Equation

Bonus: Gauge Fields

(23) Yang–Mills Equations

We just published a video, together with a PDF guide, where we go in depth into each one of them. This will give you a lot of knowledge about the big picture behind mathematical physics as a whole.

Just click here to get the guide.

Otherwise, just keep being curious.

Best wishes,

Luca & Sophia Di Beo

P.S. When studying differential equations in mathematical physics, always start with this question: “What is the quantity, or what are the quantities, that are changing in space or in time?” 🤔