The topic for week two is integrals.
And what we're going to cover in this
series of videos, first integration.
So this is just the definition of an
integral.
It's the problem we're trying to solve.
And it boils down to basically trying to
find the area in between a curve,
in between the, a curve representing the
graph of a function and the x axis.
The second topic, the fundamental theorem
of calculus, this gives us a mathematical
tool that allows us to answer the question
we, we set up in, in part one.
In part three, I just discuss some
applications of integration.
So this is sort of showing the kind of
problem you can interpret as an area and
then
a couple of quick examples of how you can
generalize that once I'm allowed to use an
integral.
Then I'm going to switch to techniques of
integration.
So,
like the differentiation we did in the
first week integration is a mathematical
operation.
It's unfortunately a little bit trickier.
So with differentiation, we had a set of
rules that
you can apply to a function to find its
derivative.
In integration we have to run that
backwards and it's
not so clear cut exactly how that's going
to work,
but there are a lot of sort of rules of
thumb that can help you out and so that's
what
I mean by techniques of integration.
Integration by parts, integration by
substitution and
completing the square are all techniques
of integration.
So there are tricks that are going to help
you find the integral of a function.
And then we'll start moving on to some
topics we'll need
to be able to take derivatives of the
Black-Scholes pricing formula.
So, in particular, we're going to need to
be able to take
the derivative of an integral.
So, that will be topic
number seven, different, differentiating
definite integrals.
We're also going to look at integrals that
have an unbounded region.
So, that would be integrating from, say a
minus infinity up to a certain value x.
We can also look at improper integrals
where the function
takes an inter, sorry, where the function
takes an infinite
value, and that will be what we talk about
in topic nine, improper integrals two.
And then we'll put all of that together
and learn how to take
the derivative of a function defined to be
the improper integral of another function.