Day 2 in Mat329

Last time: Welcome

Next time: Limits and Continuity

Today:

Announcements
- Reminder: stow those rectangles....
- Reminder: quiz tomorrow.
- Roll
Last time we began with a brief overview of Multivariate Functions. Some comments:
- Definition of a function (p. 10):
  
  A function is a rule that assigns to each element x in a set D exactly one element (called f(x)) in a set E.
  The difference between multivariate and univariate functions is in that domain D.
- While we are moving from univariate to multivariate functions, we will tend to focus on functions of two variables. These are obviously the simplest non-univariates cases. KISS!
Just a comment: with each section, I'll produce a section summary, which highlights some of the things I think most important. In the old days, I'd hand those out. In these times of tight budgets, I'll just be putting them on-line.
Sometimes I'll refer to them, and sometimes I won't!
Drawing surfaces
- Axes in 3 dimensions: here a summary from another class. Let's take a look.
- Let's start with planes! I was doing some construction this summer...
  p. 913, #25
Today I'd like to take a look at some of the problems in Section 14.1, and perhaps talk through the 14.1 directed reading worksheet questions.
We should also see how to use technology -- perhaps Mathematica -- to help us to visualize multivariate functions.
Discussion/Problems:
- Multivariate functions defined by tables, e.g. wind chill (p. 903)
- Contours: "isobars"; "isotherms"; "isochills"? Topo maps are examples of contour maps (e.g. p. 907, Lonesome Mountain).
- p. 913, #34-36
- p. 915, 59-64
- Others?

Next time: 14.2

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