Author's Note: You will understand this if you have taken a Calculus course. If you have not, you should not bother reading. I turned this in for our final assignment, which was to write a brief paper on "what have I learned in Calc I."
Another Author's Note (this is the last, I promise): for my latest updates and writings, follow me on Twitter: bryesk.
A Brief, Yet Concise Explanation on the Purpose of Calculus.
Calculus is a very effective form of anesthesia. It is based on the principle of pain distribution, kind of like when a person complains of a headache and another "friend" kicks them in the leg so they forget about the pain in their head. Calculus works the same way. No longer do we students have to worry about discomforting things such as car payments or our failure of finding a life-mate, instead we integrate using the chain rule. Same pain, different area.
Another definition of calculus is manipulating equations using the concept of the limit, which is approaching something with out ever getting to it (like trying to get to my graduation date.) Of course, trying to get near a point by approaching it using an infinite number of small steps can take a lot of time, which is why class is 50 min long.
Differentiation is full of rules: the constant multiple rule, the sum or difference rule, the power rule, and the I'm-not-going-to-tell-the-students- any-of-these-rules-until-I-make-them-work-at-least-five-hundred-and-seventy- three-problems-the-hard-way rule. The last one is also referred to as the Fundamental Theorem of Calculus Teachers.
Integration is a lot of fun, in a twisted, sick, sadistic way. One way to integrate is by using u-substitution, which steps I have listed below.
1) Take out your brain. Call it 'u'
2) Differentiate your brain using only a pen, a calculator, and a blender.
3) Throw away brains. Fill head with favorite type of fondue.
4) Drool excessively.
Calculus also has something to do with tangent lines, concavity, surfaces of revolution, the length of an arc, and fluid force, but all of that was just 'extra'. All in all, I found that taking calculus was one of the most rewarding experiences of my life (yeah, not really, but I'm trying to get a good grade here.) Ha ha, just joking. Please don't fail me.