January 29

Theoretically, Euler's Method approximates a curve by using line segments. The smaller the delta x, the shorter the segments, and thus usually the more accurate the approximation.

You do need to know how to do Euler's Method by hand, but it can get tedious so it is appropriate to use the calculator program (regularly). Don't forget to put the differential equation in Y1.

for Peter (and 4th period...)

Peter wanted to know how to do something so I'm typing...

.....

This seems like it should work well.

January 28

I introduced slope fields today. Here are my notes for class.



This is what a slope field looks like when generated on a computer:




There really isn't going to be anything complicated associated with this topic. There's this thing called Euler's Method that we'll do tomorrow, but it is really just applied arithmetic. Really.

Tuesday, January 27

Here are notes from class today. Mostly a revisiting of solving differential equations.



The algebra step of going from ln y = x + C to y = Ce^x is a key concept.

a communist society...

So this is not _my_ blog, this is _our_ blog.

I guess I'm in charge, but what I find appealing about this setup is that all of you are enabled to be authors and so can add your thoughts at any time. I think that ultimately the structure here will be exactly what I envisioned, both in form and creation.

This is new territory for me though, so I expect it will evolve as I (we) gain in experience and wisdom.