This becomes an exercise in bookkeeping at some point.

In Algebra, if you miss an i, a two becomes a three or

these magic identities don't cancel, okay.

So, start carefully.

I'll get right to you.

My tips and tricks here are really be systematic.

I would really go after how do I extract this.

That means I need the diagonal components of this.

So I can figure out which of this rows and columns contribute to that and

I just record one at a time.

If I record the whole thing, it's going to take pages and

pages just to write everything out and don't even need all the terms.

So just be smart use only the ones that you need and then you can derive it.

And then you eventually reduce it down to this form.

But to get to this form, you will also have to use the unit identity.

At some point you can have beta double prime one, beta double prime two, squared,

squared, squared, all added up.

And you recognize all these things are just one.

Well that's going to get rid of all of those, all right?

And then you apply it.

If you think you get here without ever applying the unit constraints,

you did some magic in your math.

I'd love to see that.

But, so this is kind of one thing.

So Jordan, you had a question?

>> Yeah, I don't know if this is indicated in the homework when we do this problem.

But how much are you okay with us doing Mathematica for this?

>> So, you're welcome to use Mathematica as well or MATLAB.

Both of those tools do symbolic manipulation.

It's not going to do everything for you.

Is not that smart yet.

Unfortunately I love it to do that, but it's going to get you there and then

probably have to manipulate and saying hey these terms apply this constraints.

So you're welcome to use symbolic manipulators as well.

Many in the class do.

Many in class have not used them before and this is typically the problem that

goes you know what this might be worth learning.

[LAUGH] Which is good.

These are fantastic,

this class has lots of algebra and I'm not grading on the algebra.

I'm grading on doing the right algebra, right, and that's where you come in.

So you're welcome to turn in mathematical code that you've developed and did it this

way and this is where I manipulated and this is how I get to the answer.

Or for many of you, it'll be purely done by hand, which works, it's just We need,

the key is don't do everything at once.

Figure out, I'm going after this one.

Which terms do I need?

If I'm going after this one, I needed two off diagonal terms differenced.

Go after only those two terms, and that's going to keep your algebra manageable.

Then it works pretty readily.

You can't drop any I's and J's and so forth, Katie.

>> And along that same note,

how much of our code are you wanting us to turn in for homework.

So if you're doing this as a derivation just show me everything.

It won't be that much.

I mean, you'll have some steps, then I take this, maybe you did it by hand,

you can handwrite over it, that's fine.

If it's a longer programming assignment like integrate these differential

equations just put the code at the back or

right there with the assignment, then we can see it.

Just include the code include the primary code.

Later on when I've done sub problems already that I can use as sub routines.

You don't have to turn in 60 pages of sub routines that you happen to use.

I'm really looking for the main integration parts like that so.

So for most it sends a being easy, if there's a question, and

this is really a lot, ping me.

If you've written in a way that's very verbose, and

you'd rather turn it in online, that part instead of printing everything out,

we've done that before as well.

Yes, Nathaniel?

>> Just a question, while we're on the topic.

You said in this class you'd like us to

develop sort of one program or one sort of set of programs.

>> Yes. >> When we have an assignment that you

sort of intend on us making something would you say explicitly code this up,

it will be used later or should we just be coding things?

>> Yeah I generally give some general guidelines.

Like for this integrator my suggestion is do it in a general way.

Lets make one program that computes these angle sets, but make it as a state vector.

And the integration we do it by hand in terms of the state vector set.

So now it's three coordinates, later on it might six coordinates or eight.

You could use the integrator and that's all you need at this stage.