Why Should I Study Calculus?

Date: 03/04/2001 at 18:13:12
From: Aaron 
Subject: Why should I study calculus?

Dear Dr. Math,

I am starting an AP calculus class next year and I would like to 
understand why I should study calculus. What is its importance? Also, 
I am in Precalculus now and I would like to know what topics that I am 
studying are beneficial in studying calculus.

Thank You
Aaron

Date: 03/05/2001 at 09:34:54
From: Doctor Ian
Subject: Re: Why should I study calculus?

Hi Aaron,

Thanks for writing to Dr. Math.  

The _best_ reason to study calculus is because it's beautiful, and 
learning about it is fun. However, most people never figure that out, 
so they need some _other_ motivation to learn it.

If you want to learn about physics - which is a prerequisite for just 
about any kind of career in science or engineering - then you'll need 
to understand calculus for two reasons: First, because many of the 
laws you'll be learning about were derived using calculus; and second, 
because many of the problems you'll be asked to solve will require you 
to use calculus. 

The fact that you're asking the question suggests that no one has told 
you what the _point_ of calculus is, in which case you might be 
viewing it as just another set of tricks for pushing symbols around.  

Here is one way to think about it: The history of math is full of the
discovery of special formulas to deal with special situations, e.g.,
formulas to compute the area of a circle, the volume of a pyramid, the
surface area of a torus, and so on.  

Calculus is a _general_ way of computing these kinds of quantities,  
for situations in which the boundaries can be described by arbitrary 
functions, or collections of functions.  

Special case formulas are like interstate highways - they take you to 
a lot of important places very quickly, but there are a lot of places 
that they can't take you at all. Calculus, on the other hand, can take 
you to any place that has a street address.  

Since calculus deals with functions, studying calculus will be easier 
if you really understand, in a visceral way, what functions are and 
how they work. And since a large part of calculus involves extending a 
few standard techniques to new classes of functions - polynomials, 
trigonometric functions, conic sections, etc. - the more kinds of 
functions you can become familiar with, the easier calculus will be 
for you. 

I hope this helps. Let me know if you'd like to talk about this some
more, or if you have any other questions.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/