- Reminder: Daniel Otero
will be here today, at 3:00, to speak on The History of Determinants. I
hope that some of you will be able to make it....
- Let's have a quiz Monday, over 4.3.
- In-class parts of the second exam are graded:
- Deriving methods using Taylor series (with error term!)
Didn't we do a quiz very much like this just shortly before the exam, and didn't I express the terrible importance of this application of Taylor series?
- Examples of interpolating polynomials (and their error
terms!)
- When I say "Don't simplify!" I mean it! You're wasting your own time....
- One little mistake screws up a table, but you can find your error by verifying that your polynomial interpolates. If you find a mistake, it points to about where that mistake occurs in your table!
- You'll need to bound a fifth derivative, and don't
forget that the error term's polynomial part is made up
of a product of terms of the form
- I only wanted a portion of the Hermite spline: the good thing about a Hermite spline is that you can do each pair of points separately. Using difference tables is easiest, with repeated x-values.
- Linear algebra is important in numerical analysis:
- We teach these courses so that you can use these methods later on! You need to step up now, and understand why and how linear algebra is coming into play.
- What are we looking for? We're looking for those 16 coefficients!
- Did we not construct one of these matrices in gross detail in class? I know that they're big and ugly, but there are lots of things that make them nice. They're repetitive, for one thing.
- RHS: We don't match actual derivative values with a natural spline: we just make sure that neighboring splines agree on their first and second derivatives.
- Muller's Method:
We know of several ways to write the interpolating quadratic: choose one, find the roots, and choose one (with reason). That's all that problem was.
- Deriving methods using Taylor series (with error term!)
- Max: 51.5 (out of 60)
- Mean: 32.6
- Min: 22.5
- SD: 9.9
- If you'll fix your exam, then come and see me about it, I'll give
back 40% of the points you missed. Fix your mistakes first,
however. Here's a copy of Exam
II.
- The take-home part of the final is due.
- Homework 4.2 is due, as well.
- Homework for Monday, 11/23: you should provide me with a typed, one-page project proposal by Monday. It will include the description of the project you're taking on, indicate whether you're working with a partner or not, and give me an indication of the software you'll be using to work on the project (you'll need to use something that I can access, so that I can test your method).
Andy's "DEs-in-a-Day":
- Population Growth
- The simple pendulum (p. 249)