Preparing for Exam 1
February 22, 2002
Closed Book, Closed Notes
in class (McBryde 216)
11:15am - 12:05pm

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There will be 7 questions, dealing with the topics we have 
learnt thus far. Here's a list of things you should know
or be able to do, along with the number of questions devoted
to each topic.

2 questions: number representation and errors
	- rewriting formulas so that cancelation error
	  doesn't happen
	- estimating how many terms are needed in series
	  expansions to obtain a certain accuracy

2 questions: root finding
	- different methods
		- bisection
		- newton
		- secant
	- working out 1-2 steps in each method
	- convergence rates for each (if they converge)
	- conditions for convergence
	- when they fail
	- when is one preferable to another
	- fixed-point iteration
	    or functional iteration
		- newton and secant are special
		  cases of functional iteration

2 questions: interpolation
	- lagrange form
	- newton form
	- shifted power form
	- power form
	- connections between
		- # nodes
		- degree of interpolating polynomial
	- divided difference table and derivatives
	- problems with equally spaced nodes
	- Chebyshev nodes
	- Errors in interpolation
		- how to estimate them

1 question: interpolation combined with numerical differentiation
	- how to derive differentiation formulas, e.g.,
		- central-difference
		- forward-difference
	- errors in formulas
	- Problems such as 4.3.13 of your textbook
	  (this was worked out in class)