Thanks, Richard. That's a good suggestion. We can include units in a few of those problems to show how to include units in a calculation.

Problems 11 through 14 of Problem Set 4 entail physical equations with actual physical units. The use of physical units such as {kilograms, meters, seconds} was mentioned in the class, so I tried using pounds, inches, and seconds, (converting pounds to mass by dividing by gravitational acceleration). Mathematica allowed me to enter pretty-looking equations and initial conditions, but then did not seem to know what to do with them when I tried DSolveValue. Presumably I'm doing something wrong, but the sample problems don't help here.

SUGGESTION: Demonstrate use of physical units in one or two problem set solutions.

Hi Rich. Please send your solution to wolfram-u@wolfram.com They will forward your solution along to me and I will get back to you over email.

Hello Richard,

I've created a ticket per your inquiry for review.

Christine Owens
Wolfram U Project Manager
Wolfram U

Thank you, Richard. It looks like that is doing the right thing.

Thank you very much for your comments, Richard. Sorry that I couldn't give a better reply during the session today, but posting these comments here helps us keep track of everything that needs to be improved in the course.

In both Lesson 24 (Discontinuous Forcing Functions) and Lesson 25 (Impulse Functions), plots are shown of the complementary solution (forcing function is zero) and the particular solution (forcing function/impulse function applied). It would be interesting to see a plot of the DIFFERENCE between results with/without forcing function.

In Lesson 24, there's not much to see. However, the difference plot of (sln2 - sln3) in Lesson 25 makes it easier to see the effects of the applied impulse functions, particular the first negative hit at t==2Pi. It's harder to see the effect of the positive hit at t==3Pi because it simply adds to the already-positive motion of the curve. SUGGESTION: Create a Manipulate box to allow the student to tinker with the timing and magnitude of the second hit. That should provide a nice feeling for coherent and destructive effects.

Yes, you are absolutely right. It should be Integrate[ ( 0 + s^2) ^2, {s, 0, t}]. Thank you for pointing this out. We'll get it fixed.

That can't be controlled from within DSolveValue, but you can use the TrigToExp function to do that conversion. For example:

In[1]:= TrigToExp[DSolveValue[y''[x] + y[x] == x, y[x], x]]
Out[1]= x + 1/2 E^(-I x) C[1] + 1/2 E^(I x) C[1] + 1/2 I E^(-I x) C[2] - 1/2 I E^(I x) C[2]

Picard's Theorem works best when the initial condition when the dependent variable equals zero when the independent variable equals zero. Exercise 3 shows how to transform a differential equation where y[0] is not equal to zero into an equivalent problem where the initial condition at zero equals zero.

I have notice between the Exercise 11-1 and Exrcise 12-1. They are changed.

Richard, it sounds like you have an issue logging into the BigMarker servers. The link Cassidy sends out every day contains your BigMarker credentials: they're embedded in the long list of characters in that URL. Cassidy should be able to reset and re-send to you. An email to wolfram-u@wolfram.com should get the ball rolling.

As a temporary workaround, I bet you could "register" with another e-mail address and use that to access the session today. Wolfram U would prefer to fix your permanent account (since that's how they track users for certifications they earn), but that can get you running today.

Good luck. This course is hard enough for me with my BigMarker login working smoothly. :)

I see. You should be getting an email after each lesson with a link to the recording. I'll talk to Cassidy today to see if we can resend those links to you.

Here is a link to the course: https://www.wolfram.com/wolfram-u/courses/mathematics/introduction-to-differential-equations/

REQUEST: Can you please post a URL for the daily study group sessions? Everything I try just takes me to the registration page. It has dial-in information that doesn't work (no Dial-In ID Number), and I can't find a link to the session that has surely started by now.

It does seem like the symbol f has some other definition attached to it. If you clear f before evaluating the derivative, it should give the expected result. For example:

Clear[f]
D[Exp[f[x]], x]

Something seems odd in the "Integrating Factor Method" section of Lesson 5 (Linear 1st-Order Eqns). The input

D[Exp[f[x]],x] 

generates Exp[f[x]] f'[x] on my system, as expected. However, in the lesson notebook it generates output with an exponent that seems to be a detailed list of possibilities. Pasting it into this box gives an unholy mess, but the first set of possibilities seems to be

1 if 0 <= x < 1 and
0 otherwise

and the second set of possibilities looks like

0 if x is not equal to zero or one;
Indeterminate otherwise

My guess is that the function f is carrying a definition over from a previous cell. SUGGESTION: clear the contents of f before calling D[Exp[f[x]],x]

You can get different sized arrows using VectorScaling and VectorSizes. For example:

VectorPlot[{y, -x}, {x, -3, 3}, {y, -3, 3}, VectorScaling -> Automatic, VectorSizes -> {0, 1}]

The advantage of using all vectors with a unit length and specifying the magnitudes with colors is to make the plot less cluttered when vector lengths differ a lot in the plot. When using the default unit lengths for the vectors, you can get a legend that shows the length that corresponds to a particular color using PlotLegends

VectorPlot[{y, -x}, {x, -3, 3}, {y, -3, 3}, PlotLegends -> Automatic]