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!

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

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

I am looking forward to attending the daily study group. I am currently a graduate student in Mathematics with a major in Applied Mathematics at the Hellenic Open University. Research interest in partial differential equations. You can see some of my projects in my profile here in the community.

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

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?

I think it is because your second NDSolve call is only going out to 20, so the solution isn't calculated past there. I'm getting the same result for both calculation:

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

If you are having trouble with the boundary mesh, you could try forming the full mesh with ToElementMesh. Just as an example with using an arbitrary .dxf file from the documentation:

First, load the mesh and view the wireframe:

<< NDSolve`FEM`
reg = Import["http://exampledata.wolfram.com/gear.6"];
mesh = ToElementMesh[reg];
mesh["Wireframe"]

Solve an arbitrary equation over that region:

sol = NDSolveValue[{Laplacian[f[x, y, z], {x, y, z}] == 0, DirichletCondition[f[x, y, z] == 0, True]}, f[x, y, z], {x, y, z} \[Element] mesh]

Visualize the result

ContourPlot3D[sol, {x, y, z} \[Element] mesh]

If you are still having problems, you may want to try using RepairMesh and FindMeshDefects while the region is still a MeshRegion and before you use ToElementMesh or ToBoundaryMesh

https://reference.wolfram.com/language/ref/RepairMesh.html https://reference.wolfram.com/language/ref/FindMeshDefects.html

When using ToElementMesh and ToBoundaryMesh the options that control the Mesh Quality and the Mesh Order might be useful. These are discussed in the options section of those documentation pages:

https://reference.wolfram.com/language/FEMDocumentation/ref/ToElementMesh.html

There is also the Element Mesh Generation and Element Mesh Visualiation tutorials which are a part of the NDSolve tutorial which may be helpful as well with troubleshooting mesh generation.

https://reference.wolfram.com/language/FEMDocumentation/tutorial/ElementMeshCreation.html https://reference.wolfram.com/language/FEMDocumentation/tutorial/ElementMeshVisualization.html

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.

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!

Thanks for joining the study group.

Question: Wolfram, in general, has, on various levels (math, software syntaxis, etc.) outstanding documentation. A Wolfram user goes through smooth calculations and attendant great results. By most measures, a superior experience.

However, I would like to grow an appreciation for the "overload" brought about by increasing precision, for example. Also, what are some of the complexities involved in attempting to get a plot right? Where are these issues discussed?

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

Thank you so much for joining!

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.

The presentation notebook link is broken.