- 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,
- 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
- 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
- Circumference of hyperbolic circle is $2\\pi \\sinh r$
A hyperbolic circle turns out to be a Euclidean circle after it is flattened out in the Poincare half-plane model The only difference is that, since distances are larger nearer to the edge, the center of the hyperbolic circle is not the same as the Euclidean center, but is offset toward the edge of the half-plane
- Relationship Between Hyperbolas and Hyperbolic Spaces
2) When searching for images of "Hyperbolic Spaces", the following types of images always come up: What is the relationship between the above diagrams and hyperbolic spaces? Are these pictures trying to illustrate some concept in particular (e g the projection of some shape from Euclidean Space to Hyperbolic Space, e g dodecahedral tessellation)?
- Parabolic, Hyperbolic, Elliptic - Mathematics Stack Exchange
The terms "parabolic," "hyperbolic" and "elliptic" are used to classify certain differential equations The terms "hyperbolic" and "elliptic" are also used to describe certain geometries Is there a
- 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
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