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Differential Eqns
@diff_eq
Tweets on ordinary and partial differential equations from @JohnDCook
Ikut March 2013
17
Mengikuti
75.8K
Pengikut
4.6K
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Differential Eqns
@diff_eq
5 bulan yang lalu
Differential equation modeling https://t.co/ePqOKgEpiL
Differential Eqns
@diff_eq
1 hari yang lalu
Third order ODEs https://t.co/5RKnPzot4F
Differential Eqns
@diff_eq
3 hari yang lalu
Third-order ODEs are uncommon, and usually nonlinear, such as the Blasius equation. https://t.co/8JjZmrukx0
Differential Eqns
@diff_eq
4 hari yang lalu
Bernoulli's equation: y' + p(x) y = q(x) y^n. Can be turned into a linear equation by the substitution u = y^(1-n).
Siapa yang Harus Diikuti
Algebra Etc.
@AlgebraFact
Tweets about algebra, number theory, and miscellaneous math by @JohnDCook.
Analysis Fact
@AnalysisFact
Daily tweets about real and complex analysis and related topics. From @JohnDCook.
Probability Fact
@ProbFact
Daily tweets on probability from @JohnDCook.
Differential Eqns
@diff_eq
4 hari yang lalu
Delay differential equations https://t.co/CagdhjKG8v
Differential Eqns
@diff_eq
5 hari yang lalu
Dirichlet boundary conditions specify solution values on boundary. Neumann boundary conditions specify normal derivatives of solution.
Differential Eqns
@diff_eq
6 hari yang lalu
There are important non-linear PDEs with closed-form solutions https://t.co/ejGjRodMyj
Differential Eqns
@diff_eq
9 hari yang lalu
The canonical example of elliptical PDEs is Laplace's equation.
Differential Eqns
@diff_eq
10 hari yang lalu
“Good theory is (almost) as useful as exact formulas.” — Lawrence Evans re PDEs
Differential Eqns
@diff_eq
11 hari yang lalu
Conservative vector fields and exact ODEs https://t.co/jIQms6h8KJ
Differential Eqns
@diff_eq
12 hari yang lalu
A solution corresponding to an eigenvalue with positive real part grows exponentially.
Differential Eqns
@diff_eq
13 hari yang lalu
If a linear ODE has complex eigenvalues, solutions oscillate. If real parts are negative, oscillations decay exponentially.
Differential Eqns
@diff_eq
16 hari yang lalu
Blow up in finite time https://t.co/uYyooli9Yc
Differential Eqns
@diff_eq
17 hari yang lalu
'Knowing what is big and what is small is more important than being able to solve partial differential equations.' -- Stan Ulam
Differential Eqns
@diff_eq
18 hari yang lalu
Laplace transforms turn differential equations into algebraic equations.
Differential Eqns
@diff_eq
19 hari yang lalu
Math developed for going to the moon https://t.co/32RZVlBGdT
Differential Eqns
@diff_eq
20 hari yang lalu
To solve y'' + p(x) y' + q(x) y = 0, assume a power series for y, plug it in, and solve recurrence for coefficients.
Differential Eqns
@diff_eq
20 hari yang lalu
We usually start with a DE and then look for solutions. But it can be useful to find a DE that a function of interest satisfies. If it’s a nice DE some properties of the solutions follow easily.
Differential Eqns
@diff_eq
23 hari yang lalu
Laguerre polynomials satisfy x y'' + (n+1-x) y' + k y = 0. These polynomials come up on quantum mechanics.
Differential Eqns
@diff_eq
24 hari yang lalu
'The central problem of ... modern mathematics is the study of ... functions defined by differential equations.' -- Felix Klein
Differential Eqns
@diff_eq
25 hari yang lalu
A cautionary tale about numerical solutions to differential equations: https://t.co/U9Ag4ytS3r
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