A Supplement to the Pictures

I apologize that I forgot to bring the camera today.

If you need any supplement to your notes, what we learned in class today was:

1. Vector fields are functions of multiple variables that return vectors, showing for instance how a fluid is flowing.
2. There are two types of derivatives for vector field functions:
3. The scalar (non-vector) derivative is called the divergence, and shows how much more or less fluid is flowing out of a point than flowed in. I think it could be thought of as linear acceleration of the fluid.
4. The vector derivative is called the curl, and shows the tendency of the fluid to rotate at a given point, the vector being the axis of greatest rotation. To visualize it, look at a graph of the vector field, and see what would happen if you put a paddle wheel into water flowing like that. Remember that longer vectors push harder on the paddle.
5. All gradient fields are vector fields, but not all vector fields are gradient fields. A vector field that is a gradient field is described as conservative, and is marked by the curl of the vector field being zero everywhere.

To use Maple for this, type with(plots) and use the functions

fieldplot([M(x,y), N(x,y)], x = min..max, y=min..max, arrows = SLIM, grid = [a, b]);

and/or
gradplot(f(x,y), x=min..max, y=min..max, arrows = SLIM, grid = [a, b]);
with M, N, and f being functions of x and y, min and max being the limits you desire for the domain, and a and b being the length and width of the field in terms of numbers of sample vectors.

If you need any help with Calc 1 or 2

In the past I have also made blogs for Calculus 1 and 2, which have links here:

http://newberry103s09.blogspot.com/ for Calculus 1 (this was pretty thoroughly done)

http://alikhanian5b.blogspot.com/ for Calculus 2 (this was done over a summer semester so it was not as thorough)

If you know anyone who needs help with single-variable calculus, especially calc 1, feel free to email them a link.

Introduction

This blog is created to help Calculus 3 students, primarily at LeTourneau University, with their class.

As the semester goes on, pictures of the markerboard will be added to a linked Picasa web album so that current and future students can have a supplement to their class notes.

There will also be occasional posts about the material, with the intent of clarifying things that might be hard to understand.