Tweets on ordinary and partial differential equations from @JohnDCook
Joined March 2013
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'The partial differential equation entered theoretical physics as a handmaid, but has gradually become mistress.' -- Einstein
The Wronskian of two functions is the numerator when using the quotient rule to differentiate their ratio.
Closed-form solutions to nonlinear PDEs johndcook.com/blog/2024/04/2…
We regard Butcher's work on the classification of numerical integration methods as an impressive example that concrete problem-oriented work can lead to far-reaching conceptual results. -- Alain Connes (Fields medal 1982)
Ten life lessons from differential equations johndcook.com/blog/2015/07/2…
'The more I teach differential equations, the less I understand the mystery of differential equations.' -- Gian-Carlo Rota
Numerical solution of differential-algebraic equations web.mscsoftware.com/support/… (DASSL)
'Classical mathematics concentrated on linear equations for a sound pragmatic reason: it could not solve anything else.' -- Ian Stewart
The differential equation implicit in The Pit and the Pendulum by Edgar Allan Poe.
johndcook.com/blog/2026/10/1…
2x2 grid giving an overview of numerical differential equation solvers johndcook.com/blog/2020/06/1…
Discretized wave equations terrytao.wordpress.com/2014/…
I got an email just now from PDF Expert, an inexpensive alternative to Adobe software.
At first glance I thought it said PDE expert, a flashback to an earlier career.
Difference equations and differential equations johndcook.com/blog/2022/06/1…