Monday and Wednesday May 12 & 14

5/12
9.2 Exponential growth and decay. Newton's law of cooling.
Nibbling on basil example of exponential growth (possibly negative).
9.4 What the logistic equation means, above carrying capacity.
9.5 First-order linear homogeneous equations.
A derivation of the integrating factor, based on the idea that one solves the homogeneous first and uses it as a stepping-stone.

5/14
Rederivation of the general solution.
Applied to a nonmotivated example from the book.
Then we thought about filling up a bathtub, initially half-full of cold water, with warm water, while it's draining (more slowly than it fills). During this process the water draining becomes warmer and warmer. What's the temperature at the time the bath is full?
This turned out to be a linear inhomogeneous first-order DE.

10.1 Infinite sequences. The definition of "this sequence converges to x", with epsilons and large Ns.