Explaining Calculus (Intro)

In our day and age, this word strikes fear into many hearts. Much like ‘rocket science,’ it is used in our culture to represent anything that is extremely difficult or even something incomprehensible. I am talking about calculus. Those who have taken a course in this topic will have a good idea of what kinds of problem calculus can answer – although in my experience those who have not taken a course in calculus don’t really know what it means. Or perhaps they do know what it is about, but are too intimidated by the word ‘calculus’ to trust themselves. Or – and I suspect most people are in this position – perhaps they actually do understand the core concepts behind calculus, but just don’t realize that they do.

Because I am convinced that most people understand at least parts of all the basic concepts that go into calculus, I am convinced that it shouldn’t be so scary. In fairness, mastering all of the computational details can be quite difficult. Just like mastering a sport, this requires a lot of practice and repetition. But, this doesn’t mean learning about what calculus is has to be difficult. Just like a person can understand the strategy and details of a sport without being a professional athlete, I also believe that we can all understand what is ‘going on’ with calculus without mastering the more difficult calculations.

I write this post at the beginning of the Fall 2020 academic semester. This semester, I am teaching a course called “Survey of Calculus 1” – which is the first calculus course a student takes. To be clear, this isn’t some sort of ‘easy’ version of calculus. The fact of the matter is that there is a natural way to split up the subject of calculus into two segments. For now, let’s just call them (A) and (B). The two segments are very closely related. In fact, if you already know (A), you can use (A) to teach people (B). And if you already know (B), you can use (B) to teach people (A). Even more, (A) and (B) both arise out of a common origin using the concept of limits. For those who already know this, I am talking about differential calculus and integral calculus. If you don’t know what these are, that doesn’t matter. When we talk about “Calculus 1” courses, we basically mean differential calculus, and “Calculus 2” is integral calculus (and a related third topic called infinite series). So, I will be teaching a semester-long course focusing on differential calculus.

Ever since taking my first course in calculus, I have found it fascinating and have been saddened by the fear others experience towards calculus. I don’t think we should have that fear. Because I have this conviction, I want to write about the course as I teach it. My goal right now is to write about this topic using the same line of thoughts and topics that I’ll be using in my actual course

I know that I have some people reading this who know calculus already, and some who know a little bit about it, and some who have no idea what it is, and I plan to write this series in such a way that I hope it will be interesting and informative for anyone. In order to do this, I will try to place emphasis on both the intuitive framework that gives calculus its intrigue as well as some of the mathematical details and how these details work to tell us not just about the world of numbers, but about the world in which we live every day.

This is my goal. I will be doing lots of writing on this subject, and hopefully it will be interesting!

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