# Some basic practical applications of Calculus

I am currently studying Calculus on my own for fun. I enjoy different components of math and how they can be used to solve so many problems.

Many people, however, think I am crazy because I am studying mathematics in my spare time. Many people ask me "how will this ever be useful?" and many times I cannot think of an answer. Often, people do not understand the significance of certain things in math.

For example, I would explain to someone how the Gamma function is like an extension of the factorial. The usual response is "Okay, how is that useful?" When I attempt to explain, I then need to go into many other details about other concepts.

What are some basic uses for Calculus and its functions? I know that this is really vague, but I was hoping someone may help.

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Math doesn't have to be useful. You said it yourself: You study calculus because you just enjoy it. –  Javier Badia Apr 8 '12 at 23:48
But then, of course mathematics were probably initially used because it has a practical application. –  Argon Apr 9 '12 at 0:02
When they said "How it that useful?" and you answered "Who cares?", what did they say? –  Michael Hardy Apr 9 '12 at 1:25
I wonder how they'd respond if you asked in return how art is useful. –  KCd Apr 9 '12 at 2:20
That math happens to be useful is a nice side effect. That math actually works for modeling what we see in real life is a miracle in itself. –  Ｊ. Ｍ. Apr 14 '12 at 4:49
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Here is a very general but broad class of applications: Suppose you have some quantity $q(t)$ that you want to model with respect to time, like maybe a population, or a chemical concentration, or an object's speed, or whatever. Quite often there will be a natural way to describe the quantity you're interested in by using a differential equation, i.e. an equation which relates the rate of change $\frac{dq}{dt}$ of the quantity to $q(t)$ itself.