In my last post, I talked about how I want to do research on how to build better calculators. However, I was being a bit misleading. Your basic hand-held calculator can solve all the math problems that most people encounter in their daily lives, so that problem has already been well solved. When I say I want to build better calculators, I mean that I want to build computers that solve harder math problems.

Here's where I come to a dilemma. My research usually tries to solve problems written in the language of calculus, and just the word "calculus" scares most people. Calculus seems to have this mystique of difficulty. For 85% of the population, calculus means "hard math that you never had because you chose a non-calc path in high school." For the other 14.9% of the population, calculus means "The highest (and hardest) math I know." My high school physics teacher never took calculus. Whenever he talked about it, his voice was filled with equal parts fear and awe, as if calculus were some black art that could rip the physical planes asunder if used improperly.

I want to dispel this myth. Today, I'll try to explain the notation of calculus and how it helps us. Then, I'll explain half of the results of calculus in 5 minutes. The target for this posts is the absolute lay person-- an amateur. I sometimes expect simple geometry, simple high school algebra, and that's about it. So if you don't understand these posts, please let me know in the comments.


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This, in a nutshell, is the first 3 months of calculus. You spend all your time calculating "slopes", or "derivatives" of many different functions. You learn some tricks that allow you to quickly calculate the "slope" of arbitrary functions. Then, you drill solving 100 maximization problems until you can do it in your sleep. The reason that you had to learn all those complicated simplification procedures in Algebra II was because calculating the "slope" can sometimes involve some tricky simplifications. From a conceptual standpoint though, you can sum up the first three months of calculus with the following ideas:

• The "slope of a graph at a point" is called the derivative at that point.
  
• If you zoom into any function, it becomes a straight line.
  
• Once you zoom in, you can just measure slope at that point.
  
• Whenever you are at a maximum or minimum, the slope of the graph is zero.
  
• Calculus is the language of physics. If there is a Heaven where you can learn the mysteries and wonders of the universe, then you can be sure that everyone in Heaven knows calculus.
  

Next post, I'll talk about the other half of calculus: integration. I'll show you why the "slope of" aka derivative operation is magically related to the area under a curve.

(Edit, fixed the statistics as per this this graph from the NSF.)

Tags: calculus, math, whatido