Preparing for Exam 2
April 10, 2002
Closed Book, Closed Notes
in class (McBryde 216)
11:15am - 12:05pm

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There will be 6 questions, dealing with the topics of numerical
integration, linear systems, and splines (2 questions each). 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: numerical integration
	- how lower and upper sums work
	- how trapezoidal rule works
	  (be able to solve problems like Problem 5.2.8)
	- the basic idea of Adaptive Simpson's rule
	  (you will not be required to work out a numerical solution)
	- different 3-point rules and upto what
	  degree of polynomials they are exact for, e.g.,
	  	- Simpson's three point rule
	  	  (equation (1) on page 222)
	  	- rules with our own choice of nodes
	  	  (e.g., Example 1 on page 230)
		- Gaussian quadrature rules (i.e., magic rules)
	- Gaussian two-point and three-point
	  quadrature rules (know these by heart)
	- should be able to solve problems like 
		- Problem 5.5.5
		- Problem 5.5.12
		- Problem 5.5.9

2 questions: linear systems
	- Gaussian elimination
		- why pivoting is important
		- how to do pivoting
		- operations count (see Box on page 264)
	- LU factorization
		- when is it possible
		- connection between LU and pivoting in GE
	- how to find inverse using LU and GE
	- iterative system solution
		- general format
		- Gauss-Jacobi
		- Gauss-Seidel
		- SOR
	- general condition for convergence of iterative methods
		- using spectral radius
	- specific conditions for convergence of iterative methods
		- what they are
		- for which method are they applicable
		- whether they are necessary and/or sufficient

2 question: splines
	- basic definition of splines
	- types of smoothness possible
	- how to impose (cook-up) extra conditions so that we can 
	  solve for unknown coefficients
	- solving a problem such as from Assignment #9
	  (and the examples we worked in class)