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Why are certain PDE called elliptic, hyperbolic, or parabolic? Why are the Partial Differential Equations so named? i e, elliptical, hyperbolic, and parabolic I do know the condition at which a general second order partial differential equation becomes these,
If we know a system of PDEs is hyperbolic or elliptic or parabolic . . . First, I argue that words like elliptic, parabolic, and hyperbolic are used in common discourse by analysts to describe equations or phenomena via implicit analogy, and that analogy is how we think about PDE most of the time
How to determine where a non-linear PDE is elliptic, hyperbolic, or . . . 8 I'm trying to understand the classification of PDEs into the categories elliptic, hyperbolic, and parabolic Frustratingly, most of the discussions I've found are "definition by examples '' I think I more or less understand this classification in the case of quasi-linear second-order PDE, which is what's described on Wikipedia
Distance in hyperbolic geometry - Mathematics Stack Exchange Is there any formula like this for distance between points in hyperbolic geometry? I know that for example in the Poincaré disc model we have a certain formula, another in the Klein model, and so on, but I was wondering if we can have some distance formula that exists independent of the model
Hyperbolic curve and hyperbola? - Mathematics Stack Exchange Def: A hyperbolic curve is an algebraic curve obtained by removing r r points from a smooth, proper curve of genus g, g, where g g and r r are nonnegative integers such that 2g − 2 + r> 0 2 g 2 + r> 0 How does this relate to a hyperbola, which is an algebraic curve? I don't understand the "removing points" part Why would you remove points? Thanks for clearing up my confusion
What are the interesting applications of hyperbolic geometry? By contrast, in hyperbolic space, a circle of a fixed radius packs in more surface area than its flat or positively-curved counterpart; you can see this explicitly, for example, by putting a hyperbolic metric on the unit disk or the upper half-plane, where you will compute that a hyperbolic circle has area that grows exponentially with the radius