Q. What do I do to solve L4.1?

A. Use a pencil and paper. Apply the variables seprable method
   from section 1.4 of the textbook, which applies to equations dy/dx =
   F(x)G(y). The equation y' = (1/2)(y-1)^2 can be put into this form
   with F(x)=1/2 and G(y)=(y-1)^2.

   Include an answer check.

   There is no numerical work in this problem, only symbolic solution. A
   similar report for a different problem using the linear integrating
   factor method from section 1.5 of the textbook appears as

http://www.math.utah.edu/~gustafso/f2007/symbolicSol2.4-3.pdf

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Q. How do I solve L4.2?


A. Start with an example already solved, such as the examples in

http://www.math.utah.edu/~gustafso/f2007/2250numerical-hints.txt

Modify the example for the current problem y' = (1/2)(y-1)^2, y(0)=2.
The data appendix should be as short as in the example

http://www.math.utah.edu/~gustafso/f2007/2250SampleProblem2.4-3.pdf

Because the dot table has either 101 or 201 entries, please do not print
all of it, but just the portion used in the comparison table.

Do all percentage error calculations by hand calculator and transcribe 
the answers to the table by pencil. Please: don't try to make maple 
print tables, it is wasted time.

Note: This sample includes the symbolic solution report, similar
to that done in L4.1. The solution to L4.2 should not a include a 
duplicate of L4.1.

Note: You must include hand calculations for only line 2 of the dot 
table, as in the sample.


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Q. How do I solve L4.3?


A. Start with the L4.2 code and modify it to match the example in

http://www.math.utah.edu/~gustafso/f2007/2250numerical-hints.txt

The only thing that changes is the algorithm in group 2, from Euler to 
Heun.

Note: You must include hand calculations for only line 2 of the dot 
table, as in the sample.



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Q. How do I solve L4.4?


A. Start with the L4.3 code and modify it to match the example in

http://www.math.utah.edu/~gustafso/f2007/2250numerical-hints.txt

The only thing that changes is the algorithm in group 2, from Heun to 
RK4.

Be sure to change the step sizes 0.01 ==> 0.2 and 0.005 ==> 0.1.
Because the dot table has very few entries, print the whole dot table.

Do all percentage error calculations by hand calculator and transcribe 
the answers to the table by pencil. Please: don't try to make maple 
print tables, it is wasted time.

Note: Do not include hand calculations. But do compare answers, 
expecting increased accuracy from Heun to RK4 answers.

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