A few weeks ago, someone interested in my adventure asked me what Calculus is. I had to honestly reply that I had no clear idea, but that I thought it might have something to do with the rate of change in a curve. Well, one week into the class, I cannot precisely define the term, but I can begin to approach the answer from a few different directions.
From my textbook: “We have seen that the concept of a limit arises in trying to find the area of a region, the slope of a tangent to a curve, the velocity of a car, or the sum of an infinite series. In each case the common theme is the calculation of a quantity as the limit of other, easily calculated quantities. It is this basic idea of a limit that sets calculus apart from other areas of mathematics. In fact, we could define calculus the part of mathematics that deals with limits”.*
Today, while mowing the lawn and trying to avoid heat stroke, the door of understanding partially opened. In calculus, so far as I have learned, it is very difficult to precisely measure the value of a limit. We can try, by calculating values that are very close to that limit, and then assuming a value for the limit.
Just like my marriage. I can get very close to the line (limit), but I can’t completely get there. Why, or why not, is the unknowable in each unique marriage and is not a part of this discussion. In this case, the domain and range of the function are limited to me and her and our relationship. She knows exactly how far to go, or which button to press, to elicit a response from me; she knows exactly how far to go within the bounds of my known behavior. She carefully goes no further. What lies beyond is predictable, but not knowable. The same is true for me.
As I cut the grass this morning, I worked until I thought it was not safe to continue. I know my limits (a function of age, able to be determined with a relatively simple linear equation) and have no wish to go beyond the known (life on Earth). Calculus surrounds us, and plays a central role in our lives. Who knew?
*Calculus – Early Transcendtals, 4th Edition, James Stewart, 1999.