Calculus

I actually took Calculus in University; I passed it with minimal effort and a C to show for it. Post university, my Calculus education was firmly in the "Plug and Pray" camp of development. Whilst taking an exam, I would see a pattern, think I recognize it from something I have seen before, and attempt to work the formula based on some other formula.

At no point did I really understand anything that was going on. Most people use addition, subtraction, multiplication, and division without understanding number theory. You CAN do Calculus without understanding it at all (I did).

However, there is a big disadvantage to learning in this fashion; retention is awful. In order to build up a higher understanding, you need "footholds" of comprehension. Often, as you gain higher understanding of a subject matter, the footholds that you built upon to get at your current elevation are forgotten (internalized might be a better word). I think this is the reason that it is often so difficult for experts to explain their expertise to a laymen.

Anyway, getting distracted. The point is that without these footholds I had a basically flat knowledge of Calculus. I had a number of formulas memorized that were each disparate flat structures of knowledge. Nothing was associated. Nothing reinforced anything else. Naturally, I forgot these formulas. Because there is no association to spark memory, once I had forgotten the formulas, I had effectively lost them.

But, this time is going to be different. I am doing it on my own. I am doing it at my own pace. If desired, I can spend days on a single concept. My simple goal for this year is to understand Calculus at a fundamental level. Such that I can naturally express problems I see in the world in terms of Calculus. I wish to have a layman's mastery of The Calculus.

Tools

• Calculus 4th Ed. , Michael Spivak
  I picked this book as I liked the fact that it seemed to be an attempt to teach Calculus from first principles. I am not going for "can do/use calc" I am going for "understands calc". It has been so long and my knowledge was so shallow that Calculus is effectively new to me. I want a book that is going to assume I don't know anything about Calculus before picking it up.
  
• This Blog:
  On this blog, I am basically just going to outline interesting problems I worked through from the book, using this blog as a sort of notebook of my progress. I succeeded in installing a really neat library called mathjax that allows you to display Tex formulas online. Bit excited by that actually.
  
• Time:
  I am going at my own pace, I am not skipping when I don't understand. This is for me. I have no class I need to pass. I have no test I need to prepare for. This is for me (although you are welcome to follow along). Until I get it, the procession does not move forward!
  
• You:
  I don't know if anyone will follow along, but sometimes my pace may be crawling. If you see that, and you have the time, maybe you want to leave a comment about the current problems I am having? Maybe just a word of encouragement, that helps as well. Thanks.