I've researched this topic a lot, but couldn't find a proper answer to this, and I can't wait a year to learn it at school, so my question is:
What exactly is calculus?
I know who invented it, the Leibniz controversy, etc., but I'm not exactly sure what it is. I think I heard it was used to calculate the area under a curve on a graph. If anyone can help me with this, I'd much appreciate it.
Answer
In a nutshell, Calculus (as seen in most basic undergraduate courses) is the study of change and behaviour of functions and sequences. The three main points are:
- Limits: How sequences and functions behave when getting closer and closer to a desired point (geometrically, what happens when you "zoom in" near a point)
- Derivatives: How functions change over a parameter (geometrically, the "slope of a graph at a given point")
- Integrals: What's the cumulative effect of a function (geometrically, the "area under a graph")
And obviously (and maybe especially), how these relate to one another; the crowning jewel of Calculus is probably the Fundamental Theorem of Calculus, which truly lives up to its name and was developed by none other than Leibniz and Newton.
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