I want to understand in the simplest terms why it is crucial for conputer science and if there is such a thing as a simple calculus exercise to be explained?
In: Mathematics
at its most basic, calculus is how to usefully multiply and divide by 0.
For example, how fast is the car moving RIGHT NOW? speed is [distance travled]/[time taken] so without calculus you can only say what your average speed over a time was, if you try to get the speed of right now (time taken is 0) that just doesnt work, division by 0. Calculus lets you say “Great, but what is it anyway?” and provides you the tools to figure out the answer by “approaching 0”. This is a derivative
Same for the area under a curve, area has a height and a width, you can divide up a shape into more smaller and smaller areas but with calculus we can say “but what if the width was 0, but we had an infinite number of areas? whats the area then?” and it works by approaching 0 and infinity.
There are a lot of applications of this, but for computer science it isnt really that important. There are a few things you NEED calculus for, but there are some things you NEED group theory for, none of those things are things the average programmer needs to worry about. What is more important is ways of thinking. Simply by learning calculus you learn some ways of thinking that absolutely lock in algebra (which you DO use) to an extent that just learning algebra doesnt. You also learn how to think about numbers approaching things instead of being things, which is useful for algorithm efficiency analysis (which EVERY programmer should be thinking about) where you need to consider how your algorithm scales as its inputs go to infinity.
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