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Results tagged with ca.classical-analysis-and-odes
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user 12400
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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A global implicit function theorem
The following result can be found in the paper "Natural operations on
differential forms" by Richard S. Palais:
Corollary 4.3: "Let $f_{1}, \ldots , f_{n}$ be $n$ real valued functions of $n$
real va …
- 78
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Routh-Hurwitz for eigenvalues
From Gershgorin's circle theorem (see Wikipedia) I believe it follows that a matrix $A = [A_{ij}]$ with real entries has eigenvalues with negative real part if
\begin{equation}
A_{ii} + \sum_{j\neq i …
- 78
4
votes
Accepted
mechanics: convergence to an equilibrium point
Consider the total energy
\begin{equation}
E = x'^2/2 + V(x)
\end{equation}
and assume that $V$ is bounded below and $V(x) \rightarrow \infty$ as $||x||\rightarrow \infty$
(i.e., V is radially unboun …
- 78