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Ahh, yes. The nasty beastie...<br>
<br>
In this problem you are numerically approximating the integral of a
gaussian function only along the positive X-axis. The function
starts at 1 on the y axis and asymptotically approaches zero as X
goes to infinity. The value of the integral MUST be positive. The
problem is that if you put in 1e99 for the upper limit of
integration the calculator may actually try to evaluate that --
which will result in an overflow.<br>
<br>
For problems like this I recommend putting a smaller value in for
the upper limit (say 10) and get the calculator to give you a
result. Then put in a bigger number for the upper limit of
integration (say 20) and see how much the answer changes. Repeat
this process until you get a consistent value. <br>
<br>
This problem introduces you to some interesting numerical
mathematics that we will see again and again. There is a limit to
what you calculator can actually do. If, as you saw in the case,
the integral does no longer changes as you enter larger upper limits
of integration, then you have reached the limit of your calculators
precision.<br>
<br>
<br>
As an aside, this is a function you will see a lot in chemical
physics. In fact, you will find the exact value of this integral in
the appendix of your P-Chem book as well as your Steiner math book
-- sqrt(pi)/2.<br>
<br>
<br>
On 08/25/2012 01:58 PM, wrote:
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<div style="direction: ltr;font-family: Tahoma;color:
#000000;font-size: 10pt;">Thanks! That worked. But I do have one
more question. <br>
<br>
How do you input an integral with infinity like part three on
problem b. I looked it up online and it said to use 1E99, but
that just got me an error:overflow. <br>
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<div style="direction: ltr;" id="divRpF979974"><font
color="#000000" face="Tahoma" size="2"><b>From:</b> Andrew
J. Pounds [<a class="moz-txt-link-abbreviated"
href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>]<br>
<b>Sent:</b> Friday, August 24, 2012 6:28 PM<br>
<b>To:</b> <a class="moz-txt-link-abbreviated"
href="mailto:chm371@theochem.mercer.edu">chm371@theochem.mercer.edu</a><br>
<b>Subject:</b> Re: computational exercises 371 calculator
question<br>
</font><br>
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<div>On 08/24/2012 05:41 PM,wrote:
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<div style="direction:ltr; font-family:Tahoma;
color:#000000; font-size:10pt">I was working on the
computational exercises from 371. On the first one (the
one we did in class), I can't get my solver on my ti83
to work. It seems like my x is already set at some
certain value and not a variable because I get the same
answer no matter what I put in. Do you know how to take
that value away for x so that it can be used as a
variable?<br>
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<br>
Excellent question. I'll explain the details behind what I
am about to tell you next week, but here is what you need to
do to move on right now.<br>
<br>
After you enter the equation in the solver, move down and
set the bounds. If I remember correctly, the bounds for
this problem are between zero and one. So on the bounds
line you enter<br>
<br>
{0,1}<br>
<br>
Now, your X value, which is an initial guess at the
solution, needs to be between those two boundaries. In this
case I would enter 0.5 for X and then try to solve.<br>
<br>
Let me know if you have other questions!<br>
<br>
<br>
<br>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a moz-do-not-send="true" class="moz-txt-link-abbreviated" href="mailto:pounds@theochem.mercer.edu" target="_blank">pounds@theochem.mercer.edu</a>)
Associate Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
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<br>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds@theochem.mercer.edu">pounds@theochem.mercer.edu</a>)
Associate Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
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