Hyperbolic Definition and 336 Threads

I am using the book Elementary Partial Differential Equations by Berg and McGregor. However, the book neglected to discuss problems of the this form, uu_{xy}-u_xu_y=0. How do I approach this problem? Thanks.

Hi! I'm trying to derive the hyperbolic distance formula for the upper-half plane model. It is given here: http://en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model" I have the first formula, (ds)2= ... But I can't figure out how they got the distance formula below it. I understand...

Homework Statement Two recording devices are set 2400 feet apart, with the device at Point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound...

Homework Statement 6x^2-6xy+14y^2-45=0 Two recording devices are set 2400 feet apart, with the device at Point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record...

Homework Statement edit* It says Verify the formulas in problems arcsin(z) = -iln(iz ±sqrt(1-z^2)) arccos(z) = iln(z ±sqrt(1-z^2))tanh-1z = (1/2)ln((1+z)/(1-z)) The Attempt at a Solutionyeah, my prof just threw it at us, all i have is nothing... absolutely nothing. I don't know why he does...

Hello, how do symmetry groups in the Euclidean space differ from the symmetry groups in the hyperbolic space (in the Poincaré disk) ? I've been told that in the hyperbolic case one has at disposal a richer "vocabulary" to describe symmetries, but I don't see how, and maybe I misunderstood...

This is a carryover from a previous thread: https://www.physicsforums.com/showpost.php?p=2875138&postcount=68 Sports Fans: I am familiar with the Minkowski equations and the Lorentz transformations in one or two dimensions: A) In algebraic form (1) t2 - x2 = t'2 - x'2 (2) t' =...

Homework Statement \int cosh(2x)sinh^{2}(2x)dx Homework Equations Not sure The Attempt at a Solution This was an example problem in the book and was curious how they got to the following answer: \int cosh(2x)sinh^{2}(2x)dx = \frac{1}{2}\int sinh^{2}(2x)2cosh(2x) dx =...

I'm currently reading through Roger Penrose's book The Road to Reality and in his Hyperbolic Geometry discussion he introduces the concept of how to define the distance between two points. He defines a Conformal Representation of a Hyperbolic Space bounded by a circle and then he states there...

I have always been curious as to where the definition of cosh(x) and sinh(x) come from and how they are related to the natural exponential. I know it has something to do with Euler's formula but I don't know the details of the derivation. Could anyone shed some light on this? I haven't yet...

Hello, Consider x \in (0,1) , that is x between 0 and 1. Can someone explain why the following is true: \frac{x-1}{x+1} = \tanh \left( \ln \left( \frac{x}{2} \right) \right)

Homework Statement Now, I decided for no real reason to derive a formula for the hyperbolic tangent using only what I know about the derivative of the inverse hyperbolic tangent. However, what I have looks wrong, and I'd like to check it here. Homework Equations \frac{d...

Homework Statement z = 2y^2 - x^2 Homework Equations The Attempt at a Solution I kind of know how to do it. z = y^2/b^2 - x^2/a^2 the first power is the axis of paraboloid. let x = k thus z = 2y^2 - k^2 and the vertex of this parabola (if x = 0 we see it is a...

Homework Statement The area bounded by y=2 coshx, the x-axis, the y-axis, and the line x=4 is revolved about the x-axis. Find the volume of the solid generated. Homework Equations I sliced the area along the axis of revolution. That is the strip is dx. So the equation necessary is...

Hi, please find attached the problem and the short and sweet Answer. I can't understand the last step of the answer.

Homework Statement In space-time when one "travels" a distance x from a point (within the light cone) this, in effect, comes off the time it takes. This is a hyperbolic relationship Homework Equations tau = SQRT[t2 - x2] We'll stay with one dimension (x) The Attempt at a...

I was thinking that if i have for example a boost in the direction of x, then the boost should be equivalent to an hyperbolic rotation of the y and z axes in the other direction. I don't know if it's true or not. Then I want to know if somebody knows this result or why is false? I was...

This is driving me crazy. Consider a two-dimensional spacetime, with coordinates (t,x). If this is a flat spacetime, we can just imagine a regular-old two-dimensional plane. On that plane I could just as easily map a Cartesian/Euclidean coordinate system as a hyperbolic system of coordinates...

Homework Statement I need to fit a curve using cosh to a hyperbola with a vertex of (0,0) and a point at (4,7). The scanned worksheet can be found here http://img519.imageshack.us/i/scan0001gu.jpg/" http://img192.imageshack.us/i/scan0002uz.jpg/" Homework Equations y=a cosh...

I need to do a project where i hang a chain from two points and find the hyperbolic function for it. The problem is, its a complete do it yourself project and i we never learned hyperbolic functions in class. That means i need to learn how to find hyperbolic fuctions from a set of data that i...

Hyperbolic functions :((( Homework Statement Question is: and Homework Equations Now from what i can recall the formula for sin(A+B) = sinAcosB+sinbcosA so same goes for hyperbolic function i suppose? sinh(2x+x) = sinh2xcoshx+cosh2xsinx (2sinhxcoshx)coshx +...

1. Differentiate cosh(x) using first principles 2. cosh(x) = (e^x+e^-x)/2 From previous exercises, I know the answer will be sinh(x)= (e^x-e^-x)/2 but I cannot get to the answer. I seem to be left with the equation: lim h ---> 0 (e^2x*e^2h +1-e^h*2e^x +e^h)/(2h*e^x*e^h) But when...

"Identifying" tiles in hyperbolic space? So I have a software project I've been working on on and off that involves the hyperbolic plane. There is something I am stuck on: So let's say I have filled the hyperbolic plane with one of the tilings of regular n-gons. I now would like to "label"...

Greetings PF, I do very much love lurking these forums for countless hours of leisure brain twisting. Infinite thanks for that. A very simple question for you all. I believe the answer is 'true', however, I'm not formally educated in mathematics, so I feel a bit like I'm grabbing at...

Homework Statement How to show that there exists a triangle whose defect is greater than 14 degrees Homework Equations The Attempt at a Solution No idea what to do here... something about the angle of parallelism

cosh x= e^x+e^-x/2 sinh x= e^x-e^-x/2 Can someone explain why the hyperbolic trigonometric functions are defined in terms of the natural exponential function, e^x ?

Homework Statement Find the limit of e^(2x) / sinh(2x), as x approaches infinity. Homework Equations The Attempt at a Solution Changed equation to e^(2x) / [(e^(2x) - e^(-2x)) / 2]. Based of the sinh identity. found limit of e^(2x) = ∞ ... e^(-2x) = 0 ... 2 = 2...

I read the wiki on hyperbolic functions but i don't really understand. I also plotted cosht,sinht on wolfram it made sideways v lying on the x axis. Can anyone explain why people made hyperbolic functions. I still don't really understand what it means apart from cosht being the x coordinate...

Hi everybody I've been lately a little bit concerned over the hyperbolic motions that have the following equations in (ct,x)-space: \frac{x^2}{(c^2/a)^2}-\frac{(ct)^2}{(c^2/a)^2}=1. We know that events horizons are the lines that form a 45-degree angle by both ct- and x-axis. So what...

Hello dear friends, I have this PDE Can anyone help me in finding what type PDE is it. So that I can try to solve this . As per my knowledge, I think this is second order and Nonlinear Is my guess is correct? Is it parabolic or hyperbolic, or is Elliptic and what method can...

Hello All, Am studying GR using a text by Hartle. From time to time need a better intuitive understanding of hyperbolic functions than I currently have. Never learned them for my physics undergrad. Any short sweet highly understandable primer, etc, that anyone knows of (preferably free of...

Hello friends, I am now interested in Einstein scalar field equations with a very little knowledge about Physics. I would like to ask why vacuum Einstein equations are hyperbolic equations? As far as I know that for 3+1-dimensional manifold V, we can convert the vacuum Einstein equations as a...

In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?

Please tell me how to find the orbital energy of ellipse and hyperbolic trajectory. Thank you.

Homework Statement Solve ln(sinh-1(x)) = 1 (Just give the formula for x, no calculator is necessary) sinh-1(x) = asinh Homework Equations The Attempt at a Solution When I did this, I knew sinh-1(x) = ln(x + sqrt.(x^2 +1), but the equation would look like ln(ln(x +...

Homework Statement find f-1(t) and compute f-1(0) where f(t) = sinh(t)Homework Equations sinh(t)=( et- e-t)/2The Attempt at a Solution t= (ey- e-y)/2 ln2t = y - - y y = (ln2t)/2 but wikipedia says http://upload.wikimedia.org/math/8/e/d/8edd21edb4cd413e462fe82ef4ac249b.png" what silly...

Homework Statement Hi all. I have to solve the differential equation \frac{dv}{dt} = g(1 - \frac{\rho}{g}v^2). The Attempt at a Solution Apparently the solution should involve the inverse hyperbolic tangent function - with the equation in this form it should just be separable, correct...

Homework Statement I need to solve: 1/4tanh(θ) + c Homework Equations x=2sinh(θ) θ = arcsinh(x/2) The Attempt at a Solution I worked out that since tanh(θ) = sin(θ)/cosh(θ) then 1/4tanh(θ) + c = x/8cosh(θ) + c But i don't know how to work out cosh(θ) or cosh(arcsinh(x/2))...

Homework Statement find all other hyperbolic function at x for tanhx=12/13 Homework Equations tanhx = sinhx/coshx cothx=1/tanhx etc... The Attempt at a Solution the only thing i got is cothx=13/12 all i need to know is how to find sinhx and i will be fine.

I've posted on this before and have now realized I was doing it completely wrong before but's still bugging me. I have to find the area of the hyperbolic paraboloid z=xy contained within the cylinder x^{2}+y^{2}=1. I've parametrized x^{2}+y^{2}=1 into polar coordinates to give that...

I need to find the area of the hyperbolic paraboloid z=xy contained within the cylinder x^2+y^2=1. I know I need to take a double integral but am having real difficulty finding the correct limits, so far I've got that; \int dx\int dy With the x limits being 1 and -1 and the upper y limit...

Homework Statement $\displaystyle \Large y = \ln (x + \sqrt{x^2 - 1})$ Homework Equations The Attempt at a Solution i used my graphing calc.. but that's not the point. how do i do this question? i mean, how do i find the graph of that function?

Homework Statement Find the real part, the imaginary part, and the absolute value of: cosh(2-3i) Homework Equations The Attempt at a Solution I know how to write this using exponentials, but when I looked up the answer the book expanded cosh(2-3i) to cosh 2 cos 3 − i sinh 2...

Delete please.

Homework Statement On July 1, 2004, the Cassini spacecraft approached Saturn with hyperbolic excess velocity 5.5 km/s to swing by the planet at the closest approach distance rp = 80,680 km. Compute the impulsive ΔV required for a maneuver performed at the closest approach to Saturn to...

uxx - x2 uyy = 0 (assume x>0) Is there any systematic method (e.g. change of variables) to solve this hyperbolic equation? dy/dx = [B + sqrt(B2 - AC)]/A => dy/dx = x => 2y -x2 = c dy/dx = [B - sqrt(B2 - AC)]/A => dy/dx = -x => 2y + x2 = k So the characteristic curves are 2y -x2 =...

y=km(ln(cosh(gt/km)^(1/2))) constants k and m dy/dx=gtanh((gt/km)^(1/2))/(2(gt/km)^(1/2))...?

Find the points on the graph of y=sinhx at which the tangent line has slope 2 dy/dx=coshx=2 (e^x+e^(-x))=4 x-x=ln4

Hello! A book on calculus was introducing hyperbolic functions and pointed out that the identities such as cosh x and sinh x, etc. for hyperbolic functions were analogous to cos x and sin x for circular functions. I tried finding some internet sources explaining why this is so, but they tend to...

Kind of an odd question, but here goes: can anyone offer any examples of physical systems that include the use of the hyperbolic tangent function in their mathematical solution?