Welcome to Math 221, Calculus 1
I’m Doug Baldwin
- Example of where the math in this course leads: computer graphics is just a mathematical model of shapes, their motions, their interactions with light, etc.
- e.g., “Ariala in CG Land” movie
Talk about syllabus
- Office hours? appointments via Google calendar are best (but you need to sign in to Google Calendar with your Geneseo user ID, then type my name in the “add a coworker’s calendar” box to be able to make appointments on it)
- Where is my office? In the “nose” of the 3rd floor of South Hall:
- Grading
- Assignments born with 80%
- Face-to-face grading
- Real-world math bounty. Example: how fast does the shadow of the silo outside my house shrink as the sun rises?
Functions and Change
- How fast did the army shrink as Napolean campaigned? At what times did it shrink faster?
- Take width of line, or numbers given with it, at two points on chart and subtract to get change in size of army. Make points closer together for more of a snapshot of shrinkage rate at specific time
Yeast in brewing beer
- Yeast population initially grows rapidly as there is ample sugar available for them, but as they eat all the sugar they eventually go dormant and stop reproducing.
- Brewer wants to know when yeast population is growing fast (beer isn’t fermented yet), when it’s leveling off (fermentation is done), etc.
- Gauge rate of growth from secant line on curve: plot straight line between 2 closely-spaced points, its slope approximates that of growth curve near those points.
- The closer the points, the finer the approximation to a particular point on the curve, the farther apart the points are the more the secant line gives you long-term average information.
What do these have in common? Dividing into smaller and smaller intervals
Next
The concept of “limit”
Read Section 2.1 and 2.2 through “Limits of Function Values”
- Pages 41 - 50