Much thanks to the wonderful participation we enjoyed with this group! Quiz results have been determined with sharable links sent to everyone who earned their completion certificate. Congratulations! If you weren't notified and have specific questions about your results, please send email to wolfram-u@wolfram.com.

So it has been several days since the quiz deadline has passed. I wrote the quiz about a week ago and got a passing grade. I was wondering about how to check if the certificate has been issued (or if there is a certificate for this course).

Thanks in advance.

Thank you for joining!

Luke, Cassidy and everyone else involved in developing this course ... many thanks ! I'm excited about trying out the new tools I've learned about.

There is not anything built into NDSolve for doing wavelet analysis, but as Athanasios pointed out, Mathematica has a lot of functionality related to Wavelet Analysis.

https://reference.wolfram.com/language/guide/Wavelets.html

In addition to that guide page, the following tutorial may be helpful as well.

https://reference.wolfram.com/language/tutorial/DefiningYourOwnWavelet.html

Great course so far - thanks! This question might be answered tomorrow, but as that will be the last day I'd like to ask it here. My main usage of FEM will involve complex (complicated) boundaries which I can create in Autocad and Import the dxf into MMA, for example as LineObject's or as a MeshRegion's. Can do this separately for each object, so for example creating two MeshRegion's. I'm having trouble converting a MeshRegion into a BoundaryMesh using ToBoundaryMesh. Can you recommend any resources for meshing dxf objects, generating a BoundaryMesh from a complex MeshRegion, or dealing with multiple complex (=complicated) objects?

Is it possible to implement wavelets into NDSolve? For instance to solve PDE.

In the second case, I have changed the Growth rate : $0.7(1-\frac{P(t)}{750})$. Now I have used the NDSolve to solve the problem

eqn = {P'[t] == 0.7*(1 - P[t]/750)*P[t] - 20}
cond = {P[0] == 30}
sol = NDSolve[{eqn, cond}, P[t], {t, 0, 30}]

Then I calculated the equilibrium points

eqn = 0.7*(1 - P[t]/750)*P[t] - 20;
equilibriumPoints = Solve[eqn == 0, P[t]];  

And I have the following plot

p1 = Plot[P[t] /. sol, {t, 0, 20}, PlotStyle -> {Thick, Green}]

Now I am trying to solve with Euler's Method:

sol1 = NDSolve[{P'[t] == 0.7*(1 - P[t]/750)*P[t] - 20, cond}, P[t], {t, 0, 20}, Method -> "ExplicitEuler", MaxSteps -> Infinity]
p2 = Plot[P[t] /. sol1, {t, 0, 30}, PlotStyle -> {Dashed, Red}]

And then I am trying to compare the two solutions

Show[p1, p2, PlotLabel -> "Comparison of Solutions"]

Here it is what I ask for an explanation.

Hi Athanasios. Thanks for sharing the notebook. There is a lot there so I may have missed something, but it appears to me that the growth rate is quite large. The results from DSolve have the term Exp[0.7*t] in them, which is going to make the population grow extremely fast. Considering just the birth rate, if you want there to be 0.7 births per year, I think what you want is the following

In[1]:= DSolve[{P'[t] == 0.7, P[0] == 30}, P[t], t] // Simplify
Out[1]= {{P[t] -> 30. + 0.7 t}} 

I continued exploring the model for a while but at the end, I have a question as you will see. Could you explain to me why this is happening?

Thank you for sharing. It looks like that pet store is going to have a lot of rainbow fish!

Thanks for joining the study group.

Thank you for joining the study group. I hope your are finding this useful for your research.

Two classes so far, and I'm really finding the information useful. My thanks to Luke, Cassidy and Juan.

Hi.. I'm a complette outsider to this topic, but always interested in learning more about Wolfram Technologies and fields of application. Thanks to the authors for putting this training together. J!

This Daily Study Group offers a unique opportunity to learn about all aspects (symbolic, numerical, ODEs and PDEs) of differential equations in the Wolfram Language.

@Luke Titus is an outstanding instructor and has a deep understanding of this important area.

I strongly recommend the Study Group to everyone!