[music] Welcome back to Calculus One, and welcome to Week 10 of our time together.
Now, for the last few weeks, we've been looking at applications of the derivative,
right? We looked at related rates, at
optimization problems and most recently, numerical applications of the derivative.
This week, in Week 10, we change gears. We look at anti-differentiation.
What is anti-differentiation? Well, it's really the opposite of
differentiation, right? When I ask for the derivative of a
function, right? I give you a function, you give me a
derivative. To anti-differentiate means I give you a
function, you give me another function whose derivative is the function I gave
you, right? To anti-differentiate means to
differentiate in reverse, right? To start with a function and find a new
function whose derivative is the given function.
Now, this turns out to be way harder than differentiating, right?
Differentiating is hard because it's, you know, a technical process and you've got
to apply the rules carefully. But there's not a lot of creativity in how
you apply the derivative rules. In contrast, anti-differentiating leaves a
ton of room for creativity and flashes of insight, which I think will make it a lot
more fun. Another question you might have is, why
we're doing this at all? Right?
Why is it worth our time trying to undo differentiation?
Anti-differentiation is really a bridge between two different parts in the course,
right? The first 2 3rd of this course has been
about derivatives and, and the last third of this course is about something called
integration. It turns out that anti-differentiation
connects differentiation and integration, which is what we're going to be spending
the last third of the course doing. So, maybe it doesn't seem super
well-motivated right now, but when we get to something called the Fundamental
Theorem of Calculus, all this anti-differentiation stuff is really going
to crystallize. This week, we're really just focusing on
the mechanics of how to undo differentiation.
I hope you have fun. If you're confused or, or really excited
about how things are going in the course, really however you're feeling, post
something to the forums, right? All of us on the teaching staff want to
hear from you. Good luck.