Introduction

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Welcome…

…to Math 223 (calculus 3)

I’m Doug Baldwin.

Introductions

Me: I’ve been in the math department for about 9 years now, although I came to Geneseo 30+ years ago. I started in the computer science department, but when the college closed that I moved to math. My computer science interests tend to be pretty mathematical (for instance, computer graphics, more of which in a minute), so the move actually worked very well for me. Now I teach a mixture of traditional math courses (e.g., calculus, proofs) and specialized ones at the intersection of math and computer science (e.g., Math 230, computer graphics, computability, etc.)

You: Find someone you don’t already know, introduce yourself to that person, and share a bit about why you’re taking this class and what you hope to get out of it. You’ll have an opportunity, but not a requirement, to share some of those ideas with me too, so I know a bit more about why you’re here and what you might find interesting.

(This is more than just a nice social thing: I devote lots of class time to small-group problem-solving, and having at least one person here who you kind of know will smooth the way for that.)

Who are you and what are your interests? The class is mostly math, math/adolescence education, and physics majors. No out-of-class interests people are hoping to tie to calculus, although there’s one animator who might find connections.

What Is Calculus 3?

Could calculus 3 be all about computer-generated animals?

Well, not completely, but computer-generated animals do bring up a surprising amount of what we’ll do:

• Everything you see in this video is basically a surface described by an equation, analogous to curves on an xy graph, except that instead of curves in a 2-dimensional space, these are surfaces in 3 dimensions. Functions and their graphs in 3 (or more) dimensions underlie just about everything we’ll do in this course.
• The shading of colors to capture lighting effects is based on physics models of how light reflects from surfaces. Those models depend very much on planes that are tangent to surfaces, and on the so-called “normals” to those planes, i.e., lines perpendicular to them. So very much like curves in 2 dimensions have tangent lines, whose slopes are given by derivatives, surfaces in 3 dimensions have tangents, and derivatives to describe them. We’ll spend a good deal of time studying those derivatives.

• Notice how some of the shadows in the video are “soft shadows,” i.e., shadows that fade from fully shadowed to no shadow rather than ending on sharp lines. One way to calculate soft shadows is to think of the light source as an extended set of points, each of which emits some light. Then add up the light emitted by each point “visible” from a possibly shadowed location, multiplying each point’s light by some measure of the area or angle subtended by that point. And that’s an integral, except instead of integrating a function along some part of the x axis, we need to integrate over some part of a surface.

Next

Detailed course policies and plans, as described in the syllabus.

Please read the syllabus by tomorrow, and come to class ready to mention either something from it that seems particularly important or something that needs more explanation.

This will be a model for how lots of class meetings will work, i.e., I’ll give you something to read or otherwise do before class, and then in class I’ll collect your discoveries and questions, as a starting point for discussion or other in-class activities.

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