## Final Exam for Math 151A, March 21

The final Exam is on Monday, March 21, between 3:30 and 5:30, in MS 6229. Note: it is only a two hour exam, and not 3 hours !!

The final will essentially cover all the material covered in class until (and including) March 11. This is chapters 1, 2, 3, 4, and 6. In general, you should be able to do problems that are similar to the theory problems in the homeworks and similar to the problems in the midterm. In general, you will not have to remember theorems (or the proofs), but certain results/implications of theorems (see below). You might be asked to derive or proof a certain expression, but in that case I will give sufficient hints.

The final will be with closed books and notes! You can (and might want to) use a calculator.

This page is not neccessarily complete, and will be changed/updated ! Last update was March 10, 2005.

### Here is a list of things you should know for the final

• Everything from the midterm list !
Exceptions:
I don't expect you to know the formula for Neville's Method (complicated indices). You should, however, understand Theorem 3.5 (which is the basis for Neville's method). You should also know/understand the principle difference between Neville's method and Divided Difference method (i.e., in the latter you compute the coefficients of the entire polynomial). I also don't expect you to know the expressions for Newton's forward/backward divided difference formulas (eqs. (3.12) and (3.13) in the book).
(so this covers chapters 1, 2 and 3).

• What are (n+1) formulars for numerical differentiation ? How do we get them ?
• I do not expect you to memorize all the coefficients in the (n+1) point formulas; the only exception is the centered difference 3-point formula (i.e., eq. 4.5). This one you should know !
• Ideas behind extrapolation schemes.
• Trapezoidal, Simpson's, and Midpoint rule (you don't need to memorize the exact error terms; it might be useful to know the order (i.e., power of h in error term).
• degree of accuracy, or precision.
• open vs. closed Newton Cotes formulas (the general idea)
• What are composite rules ? Don't memorize them, but understand how we obtained them.
• You should know what it means to do Gaussian Elimination and Backward Substitution.
• You should know what pivoting means, and the basic ideas behind partial pivoting, scaled partial pivoting, and complete pivoting.