Loading

Instructions

These slides should work with any modern browser: IE 9+, Safari 5+, Firefox 9+, Chrome 16+.

Navigate with arrow keys; you may need to give the window focus by clicking outside the lecture frame (the pig) for key commands described throughout this slide to work properly.
Press M to see a menu of slides. Press G to go to a specific slide. Press W to toggle scaling of the deck with the window. If scaling is off, slides will be 800 by 600; it is off by default.
Use left click, middle click, right click or hold A, S, D on the keyboard and move the mouse to rotate, scale, or pan the object.

If your browser or hardware does not support WebGL, interacting with models will be very slow (and in general models can get CPU-intensive). Navigate to a slide away from any running model to stop model animation.

Math 126

Syllabus

Highlights

Professor: Max Lieblich, lieblich@uw.edu
Course website: enjoy.
Homework: webassign, due every Tuesday and Thursday
Midterms: 2/5 and 3/5 in section.
Final: TBA 1:30 PM-4:20 PM.
Grading: 25% for homework, each midterm, final. Simple!
What can we expect from one another?

Math Study Center

Open to anyone, with questions or without, confused or clear, loving math or not.
Communications B-014
Hours:
- M-Th: 9:30AM to 9:30PM
- Fri: 9:30AM to 1:30PM
- Sun: 2PM to 6PM
You will need to make your own private Math Study Center on Saturday.

Questions?

Am I ready for this course?
What will the median grade be?
How will I ever stop loving calculus?

You have seen

Derivatives...
Integrals...
Differential equations...
In one variable only
(with a smidgen of parametric motion).

We have really only equipped you to understand life on a string.

That sucks

How can we understand a situation closer to reality?

How can we

model three-dimensional space?
describe shapes in that space?
describe physical properties of objects in space (center of mass, density, etc.)?

Questions we might ask:

Question

How does it feel to fly along this spiral trefoil path?

Question

How do we find lines perpendicular to a surface (even a weird one)?

Question

What makes this shape...

Question

...different from this one?

Properties we might examine

We could try to characterize shapes and objects using things like

Curvature (what is this?)
Surface area (I think I know what this is)
Volume (OK, whatever)
Anything else?

What is reality?

Three dimensional space

What is it?
Here's a picture:

No, really, that's a picture. Is it missing something?

What is reality?

How can we describe this space so that we can calculate things? Get a handle on it? Use it for something?

Predict future positions or motions
Quantify mass, volume, stress
Tell the supplier how much cheese we need for the giant wheel

René Descartes

⟨⟨Je pense, donc je suis.⟩⟩
"I think, therefore I am."

Descartes thought of something brilliant, something that shook the world.

Does anyone know what I am talking about?
(The pineal gland??)

René Descartes

Descartes discovered coordinates

The 3D space of human experience is the set of ordered triples of numbers:
$$\mathbf{R^3}=\{(x,y,z) | x,y,z\in\mathbf{R}\}$$
Here's a picture you probably recognize.

Numbers breed numbers

We can now calculate distance!

Distance between two points $(a,b,c)$ and $(a',b',c')$ is

$$\sqrt{(a'-a)^2+(b'-b)^2+(c'-c)^2}.$$

This generalizes the Pythagorean theorem. The book has a good explanation of why it's true. See if you can figure it out (using the Pythagorean theorem) before you read it! If you have already read it, try before reading it again. (You read each section of the book several times, right?)

Numbers breed equations

We can now describe shapes!

What is the set of points at distance 1 from $(0,0,0)$?
What shape is the set of points $(x,y,z)$ such that $x+y=z$?
...such that $x^2+y^2=z^2$?
...such that $x^2+y^2=z$? (How does it differ from the previous one?)
...such that $y=x^2$?
...such that $z=4$?

Next time: vectors!

← →