Day 2 in MAT229

Today:

• Announcements:
  • Roll
  • Remember to shut off your phones.
  • Reminder that Prof. Zarnowski will be joining you for Thursday and Friday.

• Any questions about the readings from Stewart?

• Any questions about anything at all? Logistics? Syllabus?

• Quick review from 6.1
  • Mostly we've done algebra so far, and reminded ourselves that there are some equations that we can solve to give a unique answer, and some that we can't.
  • We've introduced some important compositions, which is really crucial: if we define $y=f(x)$, and $f$ is invertible, then \[ f^{-1}(f(x))=x \] and \[ f(f^{-1}(y))=y \] are two identity maps -- they take a thing, and return the same identical thing.

    Why do I use different variables $x$ and $y$ for these two? Is it essential?

  • Is the function that maps students to seats in this classroom right now one-to-one?
  • Is the function that maps dorm students at NKU to dorm rooms one-to-one?
  • But we can't do any calculus with those functions....:(

• Let's get into 6.2: we're going to use these exponential functions to help us review Calc I!