Back in MA101 in college, back in my first calculus class, the subject was taught very badly.

In retrospect, just a few minutes of insightful commentary would have made things a whole lot easier, at least for a simpleton like me. Now that I have reached the (ahem) revered status of septuagenarian, I would like to offer a few remarks from which some of my successor simpletons might hopefully reap some benefit.

The basic calculus concept is called the "first derivative", but what does that phrase mean? The first derivative describes the rate at which the value of one variable changes in response to a change of some other variable. The value of the "dependent" variable, __depends__ on how the value of the "independent" variable is made to change.

Imagine a toddler running unfettered around a playground. Where that __toddler__ runs to at any time is very much an independent variable, but where the __parent__ runs to while chasing that toddler is very much a dependent variable. (Now where did that child go?? Oh!! Over there.)

The ratio of the two variables' incremental changes is expressed as a fraction, "dy/dx", which is what we mean by the phrase "first derivative". We call this fraction "dy/dx" where "y" is the dependent variable and "x" is the independent variable. The "dx" is some teeny, tiny, teensy-weensy, little itty bitty change in the value of "x" for which there dependently arises the "dy" which is also a teeny, tiny, teensy-weensy, little itty bitty change in the value of "y". We look at this "y versus x" relationship as that itty bitty change goes smaller and smaller and smaller in the limit to zero. Easy huh??

Treating "dy" and "dx" as two new variables in themselves where the "dy" as the dependent variable and "dx" is the independent variable, we can do the same thing again to get the second derivative which we denote as d²y/dx². We can keep on doing this over and over to find the third derivative, the fourth derivative and so on and so on. Still easy, huh??

This whole process so far described is called "differentiation". Doing differentiation isn't usually too hard and as the MA101 course unfolded, this concept should have been presented clearly. It is fairly easily grasped so that even someone like me can manage to deal with it.

The process of going the other way is called "integration".

The less readily evident process is in doing integration. Quite frankly, most cases of doing integration require a bit more intellectual prowess than this writer can muster. The thing that I failed to realize in my first encounter with integration was that my professor couldn't do it either!!!

That being so, various geniuses of this world have striven over the durations of their lifetimes to tabulate their answers to integration examples. We (meaning you, me and my professor) can find their results, the products of their work efforts, in books we often call a "Table of Integrals".

My mother (a math major) gave me a Pierce's Table of Integrals that had been published in 1910. It's a very thin, very graceful little hardcover book. By comparison, when I attended New York University in the early 1970s, I found Table of Integral books in the NYU library which were so large that they required two hands to keep from dropping them to the floor while trying to pick them up from a bookshelf.

It was impressive.

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