Need Short Easy Primer on Hyperbolic Functions

[glamotte7]

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 course)?

glamotte7

 

[Nabeshin]

I'm not sure what it is exactly you want to know.. this is rather like asking for a book solely dedicated to the sine, cosine, and tangent functions (overkill, certainly!). Having already studied Hartle, I would say a look at various wikipedia articles should inform you of their properties, identities, integrals and derivatives, which is really all one needs for that level of discussion.

 

[glamotte7]

Thanks Nabeshin

Any other suggestions anyone?

 

[Pinu7]

There really is not too much to learn. You can always go to wikipedia: http://en.wikipedia.org/wiki/Hyperbolic_function

There is also something known as "hyperbolic geometry" which is somewhat useful to GR.

 

[rezeew]

,

Hyperbolic functions are a set of mathematical functions that are closely related to trigonometric functions, but are based on the hyperbola instead of the circle. They are commonly used in many areas of mathematics and physics, including general relativity.

One way to think about hyperbolic functions is to consider them as the "cousins" of trigonometric functions. Just as trigonometric functions are based on the unit circle, hyperbolic functions are based on the hyperbola. This means that they have similar properties and relationships, but their formulas and graphs look slightly different.

One of the most commonly used hyperbolic functions is the hyperbolic sine (sinh), which is defined as (e^x - e^-x)/2, where e is the base of the natural logarithm. This function is closely related to the regular sine function, but it has a much faster growth rate.

Another important hyperbolic function is the hyperbolic cosine (cosh), which is defined as (e^x + e^-x)/2. This function is similar to the regular cosine function, but it has a more gradual growth rate.

Hyperbolic functions also have inverse functions, just like trigonometric functions. The inverse of the hyperbolic sine is called the hyperbolic arc sine (arcsinh), and the inverse of the hyperbolic cosine is called the hyperbolic arc cosine (arccosh). These functions are useful for solving equations involving hyperbolic functions.

In terms of applications, hyperbolic functions are commonly used in physics to model and solve problems related to waves, such as sound waves, electromagnetic waves, and even gravitational waves in general relativity. They are also used in engineering and other fields to describe and analyze various physical phenomena.

I hope this short primer has helped to provide a better understanding of hyperbolic functions. There are many free online resources and tutorials available that can provide more in-depth explanations and examples. I would also recommend consulting a math or physics textbook for further study. Best of luck in your studies!