On 2d, you use 4s (rather than 2s), because the centered-difference scheme only has even powers in the error terms.
On 8, you should produce a scheme. It's really a five-point scheme, where we don't use .
15: it's not easy folks, but you've got to give it the old college try. Just skipping the hard ones is not what I have in mind!
Just a hand calculation
You need to do this one by hand!
Computational
This one proved that you still don't get the notion of how to use Taylor series. We need to see that (by the end of the course, certainly!).
Now use Richardson's extrapolation on the results. It's square in .
Quiz 4.3
Trapezoidal:
Simpson's:
Your project proposals
Any questions?
We're only dealing with real-value, univariate functions.
You might have different routines to handle different types of functions (e.g. differentiable, continuous, with asymptote, etc.); nonetheless, you should have a general method which handles a function without input from the (usually oblivious) user (so your general method might step through, trying your various routines).