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The topic for week two is integrals.

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And what we're going to cover in this
series of videos, first integration.

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So this is just the definition of an
integral.

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It's the problem we're trying to solve.

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And it boils down to basically trying to
find the area in between a curve,

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in between the, a curve representing the
graph of a function and the x axis.

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The second topic, the fundamental theorem
of calculus, this gives us a mathematical

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tool that allows us to answer the question
we, we set up in, in part one.

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In part three, I just discuss some
applications of integration.

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So this is sort of showing the kind of

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problem you can interpret as an area and
then

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a couple of quick examples of how you can

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generalize that once I'm allowed to use an
integral.

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Then I'm going to switch to techniques of
integration.

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So,

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like the differentiation we did in the

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first week integration is a mathematical
operation.

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It's unfortunately a little bit trickier.

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So with differentiation, we had a set of
rules that

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you can apply to a function to find its
derivative.

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In integration we have to run that
backwards and it's

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not so clear cut exactly how that's going
to work,

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but there are a lot of sort of rules of

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thumb that can help you out and so that's
what

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I mean by techniques of integration.

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Integration by parts, integration by
substitution and

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completing the square are all techniques
of integration.

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So there are tricks that are going to help
you find the integral of a function.

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And then we'll start moving on to some
topics we'll need

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to be able to take derivatives of the
Black-Scholes pricing formula.

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So, in particular, we're going to need to
be able to take

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the derivative of an integral.

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So, that will be topic

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number seven, different, differentiating
definite integrals.

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We're also going to look at integrals that
have an unbounded region.

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So, that would be integrating from, say a
minus infinity up to a certain value x.

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We can also look at improper integrals
where the function

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takes an inter, sorry, where the function
takes an infinite

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value, and that will be what we talk about
in topic nine, improper integrals two.

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And then we'll put all of that together
and learn how to take

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the derivative of a function defined to be
the improper integral of another function.