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/ |
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