# Monthly Archives: March 2014

## Office hours today

If there is no-one in my office hours, I will be sitting in an event today from 11:30-12:30.  If you show up and would like to meet with me, send me an email at:  jonasreitz (at) gmail.com, and I should return to my office within a few minutes.

Regards,
Prof. Reitz

## WeBWorK error: Assignment 9, problem 4 parts (e) and (g)

Hi everyone,

There is an error in Assignment 9, problem 4, parts (e) and (g) – several students have reported entering the correct answer (which I have confirmed), but WeBWorK rejects it.

Even more strange, part f is graded correctly, even though it includes the answer that was rejected in part e.

I am following up with our WeBWorK administrator on this problem.  For now, please complete all parts of the problem except (e) and (g).

Sincere apologies for any mental or emotional harm this may have caused.

Regards,
Prof. Reitz

## Exam #2 Review Sheet is posted

NOTE: Problem #11 was updated on 3/24/14.

You can view it by clicking here.  Note: the answer key will be completed this week.

## More on nonhomogeneous equations and WeBWorK 9

Or:  What to do when everything cancels out, and I’m left with nothing….

I wanted to address a problem that shows up when solving nonhomogeneous equations.  Consider this problem, similar to those in WeBWorK 9:
$y'' + 8y' +15y=2e^{-3t}$

A good first guess for a solution would be: $Y(t) = Ae^{-3t}$.  However, there is a problem with this – when you try to find the constant $A$, everything cancels out on the left side and you end up with something like:  $0 = 2e^{-3t}$.

Why is this?  It’s exactly because your  guess, $Y(t) = Ae^{-3t}$happens to be a solution to the homogeneous equation:
$y'' + 8y' +15y=0$

When this occurs, you need to adjust your guess – we do that by multiplying by $t$, so a correct guess in this case should be:
$Y(t) = Ate^{-3t}$

If this guess also fails to work (as might happen in the case of a repeated root for the homogeneous equation), multiply by $t$ again:  $Y(t) = At^2e^{-3t}$

Let me know if you have any questions,
Prof. Reitz

## OpenLab #2: Feedback on the course

We are currently in the eighth week of the semester.  For this OpenLab assignment, I am asking you to provide some feedback on your experience of the course so far.

Assignment (Due Thursday, March 26th, at the start of class).  Your assignment consists of two parts:

1. Complete the survey by clicking here.  The survey consists of 10 questions, and should take 5-10 minutes to complete.  It is anonymous (I will see the answers, but I will not know who submitted them).
2. Confirm that you have completed the survey by leaving a comment in reply to this post (for example, you could just write “I completed the survey just now”).

Extra Credit.  Tell me what music you are listening to these days.  What’s in heavy rotation on your iPod?  Give us a brief description.  I’m listening to Parov Stelar (“compulsively listenable electroswing”) and Shpongle (“a unique concoction of lounge driven downtempo encased in an endless sphere of production”).    A few ground rules:  No offensive lyrics, be considerate of others, feel free to include a link but only to a legal site such as YouTube or SoundCloud.

## Office Hours Thursday 3/13/14

Hi everyone,

This week I will be in my office hours only for the first half hour, 11:00 – 11:30.  I will also be available directly after class for questions.

If you’d like to find another time to meet with me, please let me know.

Regards,
Prof. Reitz

## A few notes on WeBWorK 5b – Euler’s Method

Hi everyone,

I just wanted to send a few comments about WeBWorK assignment 5b.  The problem consists of three parts – in the first part, we use Euler’s method to generate a sequence of approximate values of y for various values of t (in my version of the problem it’s t=0, t=0.2, t=0.4, t=0.6, t=0.8, and t=1). Of course, these values are not exactly correct – they are approximations.

In parts b and c of the problem, we compare the approximate values with the actual values – this will give you some idea of how effective Euler’s method is.  In part b, we find the actual solution to the differential equation (using the techniques from Exam #1).  In part c, we compare (for various values of t), the actual value, given by the solution we found in part b, and the approximate value found in part a. To compare, we subtract the approximate value from the actual value (and then take the absolute value, since we don’t care about positive or negative, we only care about how far apart they are).

One more comment about notation:  the symbol y with a dot over it means the same thing as y’, or dy/dt – that is, it means the derivative of y.  This is fairly common notation, but we have not previously run into it this semester.

I hope this helps clear up confusion about parts b and c – let me know if you have questions.

Regards,
Prof. Reitz