Apr 30, 2020 · 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 …

Jul 30, 2013 · How were Hyperbolic functions derived/discovered? Note that the above is an explanation of how you can interpret these functions, and how you can see the relation to the exponential function.

Jan 27, 2017 · I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful. Is there any good examples …

Feb 17, 2022 · 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 …

Oct 2, 2018 · The hyperbolic functions are defined as the even and odd parts of $\exp x$ so $\exp\pm x=\cosh x\pm\sinh x$, in analogy with $\exp\pm ix=\cos x\pm i\sin x$. Rearranging gives the desired …

Oct 28, 2017 · 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

Jul 28, 2014 · 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, …

Dec 20, 2014 · Hyperbolic functions describe the same thing but can also be used to solve problem that can't be solved by Euclidean Geometry (where circular functions are sufficient).They can be used to …

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 …

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 …