Learning objectives
- Classify generic critical points of 2-variable functions
- Find maxima by gradient following
Before class
- Read Hughes-Hallett sections 15.1, 15.2
- Ponder Hughes-Hallett problems: 15.1: 1, 3, 9, 20, 22, 28, 32, 34; 15.2: 2, 23, 24, 28.
In class
- Discuss test
- More work with second derivatives
- Mathematica notebook – contour diagram with multiple critical points
- Exercises Feel free to classify critical points by drawing contour plot with Mathematica (or Wolfram Alpha)
- Local and global theory of critical points: On Hills and Dales by James Clerk Maxwell (1870) and Prof Flath’s notes giving the same theory in more modern language. Here are some questions to help you read Maxwell.
Daniel Flath 