You are probably already familiar with some mathematical functions, for example there are 1st-level notebooks on trigonometric functions, exponential functions, logarithmic functions and power functions.
In this notebook you will get to know about another set of functions, the hyperbolic functions. In learning about these you'll need to use those other functions.
One main use for the hyperbolic functions is that they allow us to integrate some simple and common functions that we otherwise couldn't integrate.
Hyperbolic functions also often occur in models of real-life problems.
The two main hyperbolic functions are called the "hyperbolic sine" function and the "hyperbolic cosine" function.
You will notice straightaway that there seems to be some link between these hyperbolic functions and the trig functions, sine and cosine. This connection involves complex variables and is therefore discussed in detail in the later MathHelp notebook on Complex Numbers. However we will note the very strong similarities between the hyperbolic and trigonometric functions in a later section of this notebook.
I'll introduce you first to these two functions through their definitions in terms of another known function, the exponential function.