[CSC 335] Section 4.9 Problems

[Andrew J. Pounds]

On 10/20/13 11:03, Bryan B Danley wrote:
> How would you use Simpsons rule on that last one with those bounds? 
> You would need to divide by zero.
>
> Bryan
>

The argument of the integral can be rearranged with a little manipulation...

$\int_0^1 t^{-2} \left[ \frac{1}{1+\left(\frac{1}{t}\right)^4} \right] 
dt = \int_0^1 \frac{t^2}{1+t^4} dt$


> On Oct 20, 2013, at 10:17 AM, "Andrew J. Pounds" <pounds_aj at mercer.edu 
> <mailto:pounds_aj at mercer.edu>> wrote:
>
>> On 10/19/13 13:48, Levi M Mitze wrote:
>>> Hello again, Dr. Pounds.
>>>
>>> I'm having some difficulty understanding what to do for problem 3 
>>> from section 4.9. I figured I was supposed to follow a procedure 
>>> similar to all the examples in the section, but there doesn't seem 
>>> to be a way to get the function (after inverting the variable [t = 
>>> 1/x]) into a form such that the numerator is a function that can be 
>>> used to form a Taylor polynomial. Am I just supposed to perform the 
>>> inversion and then approximate the integral using Composite 
>>> Simpson's (and not worry about Taylor polynomials)? What about part 
>>> c and problem 4?
>>>
>>> Sorry for all the questions,
>>>
>>> Levi
>>
>> No Taylor polynomial needed here.  Look at the paragraph around 
>> around and including equation 4.47 in your text.  If I want to integrate
>>
>> <tblatex-8.png>
>>
>> I can use the substitution provided and convert it to the integral
>>
>> <tblatex-9.png>
>>
>> which is easily integrated with Simpson's rule.  Hopefully this puts 
>> you on track for the others.  If not let me know.
>>
>>
>>
>>
>> -- 
>> Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
>> Professor of Chemistry and Computer Science
>> Mercer University,  Macon, GA 31207   (478) 301-5627
>> http://faculty.mercer.edu/pounds_aj
>> _______________________________________________
>> csc335 mailing list
>> csc335 at theochem.mercer.edu <mailto:csc335 at theochem.mercer.edu>
>> http://theochem.mercer.edu/mailman/listinfo/csc335


-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

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