Differential Eqns @diff_eq
Tweets on ordinary and partial differential equations from @JohnDCook johndcook.com/PDE Joined March 2013-
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Cauchy–Kowalevski theorem for analytic PDEs en.wikipedia.org/wiki/Cauchy%E2…
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The Yang-Mills equations are the Euler-Lagrange equations of the Yang-Mills Lagrangian.
Heat equation and the normal distribution johndcook.com/blog/2023/01/2…
What are the differences between finite element methods and finite volume methods? scicomp.stackexchange.com/questions/8217…
What good is a DE once you have the solution? johndcook.com/blog/2023/07/0…
'Separation of variables is of very limited utility but when it works it is very informative.' -- Jeffrey Rauch
Existence theorems for nonlinear PDEs often boil down to fixed-point theorems.
New post: The biggest math symbol johndcook.com/blog/2025/08/2…
Classical beam equations en.wikipedia.org/wiki/Euler%E2%…
Justifying separation of variables for PDEs johndcook.com/blog/2021/06/1…
Weyl's lemma: Every weak solution of Laplace's equation is in fact a smooth solution.
Differential Eqns retweeted
if you're taking/teaching applied dynamical systems this term & want to peek at a book-in-progress, i've updated the draft on my website... see below
"I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it." -- Paul Dirac
Mathieu functions came from using separation of variables to solve the PDEs describing the motion of a vibrating elliptical membrane.
The Dispersive PDE Wiki kvm16.pims.math.ca/DispersiveWiki…
When does y'' + ay' + by = 0 have a solution in terms of elementary functions? johndcook.com/blog/2019/03/2…
Relating convergence and stability for finite difference methods en.wikipedia.org/wiki/Lax_equiv…
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