Problem solving with hyperbolic functions

In summary, the conversation discusses the use of hyperbolic functions in solving problems beyond just the theory of hyperbolic trig functions. The speaker is looking for a tutorial to demonstrate clever uses of hyperbolic functions in solving problems, particularly in the context of conic sections and neural networks.
  • #1
Tahmeed
81
4
Mod note: Because his caps-lock key is stuck, it's OK for this post to be in all caps.
FIRSTLY, MY LAPTOP'S CAPS LOCK IS BEHAVING REALLY WEIRD AND I HAVE NO CONTROL ON IT WHATSOEVER. SO SORRY FOR POSTING IN ALL CAPS/ALL SMALL LETTERS

I HAVE RECENTLY LEARNED HYPERBOLIC FUNCTIONS. HOWEVER, I AM CURIOUS TO KNOW WHETHER I CAN USE IT TO solve problems of other topics AS WELL? IF YES, CAN SOMEONE FIND ME A TUTORIAL THAT SHOWS POSSIBLE CLEVER USES OF THIS IN SOLVING PROBLEMS? THERE IS A BUNCH OF TUTORIAL BUT MOST OF THOSE DEALS WITH THEORY OF HYPERBOLIC TRIG FUNCTION.
THANKS IN ADVANCE
 
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  • #2
Tahmeed said:
FIRSTLY, MY LAPTOP'S CAPS LOCK IS BEHAVING REALLY WEIRD AND I HAVE NO CONTROL ON IT WHATSOEVER. SO SORRY FOR POSTING IN ALL CAPS/ALL SMALL LETTERS

I HAVE RECENTLY LEARNED HYPERBOLIC FUNCTIONS. HOWEVER, I AM CURIOUS TO KNOW WHETHER I CAN USE IT TO solve problems of other topics AS WELL? IF YES, CAN SOMEONE FIND ME A TUTORIAL THAT SHOWS POSSIBLE CLEVER USES OF THIS IN SOLVING PROBLEMS? THERE IS A BUNCH OF TUTORIAL BUT MOST OF THOSE DEALS WITH THEORY OF HYPERBOLIC TRIG FUNCTION.
THANKS IN ADVANCE
When most people talk about hyperbolic functions, they are really talking about the hyperbolic trig functions, such as sinh() (hyperbolic sine), cosh() (hyperbolic cosine), etc.

Otherwise, I'm not sure I understand what you're asking -- if it's really about the equations of hyperbolas, such as ##\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1##, for example.
 
  • #3
It would also be helpful to know what you mean by "solving problems". In a more general form, we are talking about conic sections. These appear in various mathematical contexts and also in physics, as they describe surfaces defined by quadratic polynomials, like an electromagnetic potential. I don't know of anything like "What can I do with quadratic functions". They simply appear sometimes and are in itself a field that can be studied.
 
  • #4
Hyperbolic tangent (tanh) is one of the classic nonlinear transform functions used in neural nets and deep learning. Frequently people use piecewise linear functions instead, but I think tanh is still used -- in recurrent nets as I recall.

Not sure if this is what OP is getting at though
 

1. What are hyperbolic functions?

Hyperbolic functions are a group of mathematical functions that are closely related to exponential functions. They are used to describe the behavior of certain curves, such as the hyperbola, and are commonly used in physics, engineering, and other scientific fields.

2. How are hyperbolic functions different from trigonometric functions?

While trigonometric functions are based on circles and triangles, hyperbolic functions are based on hyperbolas. This means that they have different shapes and properties, and their values can be expressed in terms of exponential functions instead of circular functions.

3. What are some real-world applications of hyperbolic functions?

Hyperbolic functions are commonly used in fields such as physics, engineering, and economics to model and solve various problems. For example, they can be used to calculate the trajectory of a rocket, the shape of a suspension bridge, or the growth rate of a population.

4. How do I solve problems using hyperbolic functions?

To solve problems using hyperbolic functions, you will need to have a good understanding of their properties and how they relate to each other. It is also important to be familiar with basic algebraic manipulations and calculus techniques. Practice and familiarity with these concepts will help you to successfully solve problems involving hyperbolic functions.

5. Are there any common mistakes to avoid when working with hyperbolic functions?

One common mistake when working with hyperbolic functions is forgetting to convert between radians and degrees when using inverse hyperbolic functions. It is also important to keep track of the signs and arguments of the functions, as they can affect the final solution. It is always a good idea to double check your work and make sure you are using the correct formulas and properties.

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