Letter to Students

Why study calculus? Is it because you want to be a doctor, an engineer, a forensic scientist, a biologist, or a mathematician? Or is it because someone told you that it would be "good for you"? Well, all of those are certainly legitimate reasons. But if you aren't quite sure "Why calculus?" here is another reason: It is one of the greatest intellectual achievements of humankind, and, even more to the point, it is easily accessible to anyone who already has studied algebra, trigonometry, and geometry.

Gottfried Leibniz and Isaac Newton independently invented Calculus. Although the notation, terminology, and rigor may have changed or been standardized over the years, the concepts that we will study have not changed fundamentally since the work of the co-inventors in the 17th century.

We will begin Calculus with the study of Rates of Change and what are called derivatives. Rates of Change are all around us. For example, velocity is the rate of change of distance with respect to time; and acceleration is the rate of change of velocity with respect to time. So, we experience derivatives every time we ride in a car, or fly in an airplane. Calculus can also be used to compute areas and volumes of odd shapes with what are known as integrals. Thus, calculus has a place in architecture too.

That calculus is important in real-world applications is not in dispute. In fact, there are so many applications of calculus that studying it really is "good for you." Besides engaging in a worthwhile intellectual endeavor, you will be helping to keep your future career options open. That, from a practical point of view, is not a bad reason at all.

Moreover, studying calculus can be a lot of fun, but we will let you be the judge of that.

How to study calculus. Calculus has a lot of rules. We admit it! Find the derivative of this function, or the integral of that. However, you should train yourself to keep the rules in perspective: Always put the concepts first. When you study a given calculus concept, ask yourself three questions:

The above is what we might call "high-level thinking." It provides a way for you to stay oriented, to know what you are learning, and for what purpose. The rest is in the details, important though they are. The combined process is a lot like using a map to hike through the woods. Yes, you have to look at individual trees and their proximity to local landmarks to find your way, but you always want to keep the map and a compass handy to give an overview of the whole trip. So it goes with the study of calculus concepts. Always know where you are going, the direction to take to get there, and how to accomplish the task. The proof, though, is in getting there!

Practice, practice, practice. In the end, there is no other way. You cannot learn calculus by reading about it. You have to take a pencil and paper and work problems. Learning calculus, or mathematics in general, is a participatory activity. You have to do it to learn it, to make it your own.

Using Calculus on Demand to study calculus.

What do you do if you have a problem? If you are studying calculus in a classroom setting, you can talk to other students or to the teacher. However, if you are studying on your own, you can Post a Comment using the bottom link on the green sidebar of a lecture-page. There you can communicate with other students who also are studying calculus on-line. You could either state your problem and ask for help, or you may find that someone has already answered that or a similar question. You may even find questions that you can answer for other students. We encourage you to look at the Post a Comment section of COD on a regular basis.



Back to Index page