Monthly Archives: March 2014

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

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.

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:

A good first guess for a solution would be: .  However, there is a problem with this – when you try to find the constant , everything cancels out on the left side and you end up with something like:  .

Why is this?  It’s exactly because your  guess, , happens to be a solution to the homogeneous equation:

When this occurs, you need to adjust your guess – we do that by multiplying by , so a correct guess in this case should be:

If this guess also fails to work (as might happen in the case of a repeated root for the homogeneous equation), multiply by again:  

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

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