Why are certain PDE called "elliptic", "hyperbolic", or "parabolic"?
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 …
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 …
trigonometry - How were hyperbolic functions derived/discovered ...
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.
Why are the hyperbolic functions defined the way they are?
Feb 7, 2020 · How is hyperbolic function related to trigonometry ? The followings are the graphical representation between geometric and hyperbolic functions (especially for sin x, cos x, tan x, sinh x, …
Relationship Between Hyperbolas and Hyperbolic Spaces
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 …
Parabolic, Hyperbolic, Elliptic - Mathematics Stack Exchange
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
Distance in hyperbolic geometry - Mathematics Stack Exchange
Feb 20, 2017 · 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, …
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 …
trigonometry - Proof for hyperbolic trigonometric identities ...
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 …
Real world uses of hyperbolic trigonometric functions
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 …