Our calculus studies began with encountering a hungry bear. He looked up at us, licked his lips, and charged at us with the fury of a steam-powered locomotive. Being the smart people we are, we ran. What else is there to do? We're not confronting a ravenous bear with nothing but a piece of paper, a pencil, and a graphing calculator.
Despite running, we couldn't outrun the hungry bear. We encountered limits, derivatives, integrals, and even some weird things about counting to infinity. We've managed to wrestle our way free a couple times, and the bear decided to leave us alone. As far as we've come, there's no turning back. But we can take a break for a second and enjoy the scenery.
Now that we've seen the worst calculus has to dole out, there are a couple more concepts we need to understand before we can declare ourselves masters of the calculus circus. The first we already know from second grade. No, we're not talking about delicious peanut butter and potato chip sandwiches. We are talking about patterns.
In calculus, we're going to practice our pattern-finding on lists of numbers, also known as sequences. We will see that we already know a good deal about sequences, and we will learn some neat tricks to impress our friends with, sort of like balancing a baseball bat on our chin while singing our ABC's. We can also look for patterns in sets, functions, and the real world, but sequences of numbers are a nice place to start.