[CSC 335] Section 4.9 Problems

[Andrew J. Pounds]

At t = 0

$t \cos(1/t)$

  will be zero because

$\lim_{t \to 0} t \cos(1/t) = 0$



On 10/20/13 18:09, Bryan B Danley wrote:
> Yes. I'm sorry. I had a question about part c of that problem when 
> after swapping x for 1/t, I get t*cos(1/t). How would I use Simpson's 
> on the bound 0 to 1?
> ------------------------------------------------------------------------
> *From:* Andrew J. Pounds <pounds_aj at mercer.edu>
> *Sent:* Sunday, October 20, 2013 6:06 PM
> *To:* Bryan B Danley; csc335 at theochem.mercer.edu
> *Subject:* Re: [CSC 335] Section 4.9 Problems
> 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


-- 
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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/fa9e01f7/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-14.png
Type: image/png
Size: 1188 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/fa9e01f7/attachment-0003.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-15.png
Type: image/png
Size: 1750 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/fa9e01f7/attachment-0004.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: image/png
Size: 2570 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/fa9e01f7/attachment-0005.png>