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visits member for 2 years, 2 months
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Nov
19
answered How do I cut down on file size of exported eps without losing quality?
Nov
18
comment Moving the location of the branch cut in Mathematica
You have a little sign error in there - see my answer.
Nov
18
answered Moving the location of the branch cut in Mathematica
Nov
16
answered Exporting BarChart3D as PDF produces artefacts
Nov
16
comment Can we teach Mathematica about functional differentiation?
@Emerson We can easily handle multiple arguments as soon as you understand what they are supposed to mean in terms of the variational approach. The new rule you added in your edit simply means you're varying f at y in a product of two functionals, one with x1 and the other with x2 as the integration variable. After applying the regular product rule to that, you're back to the FunctionalD in my answer. Of course one could try to automate the regular differentiation parts too - but the core of the calculation is always what I described already.
Nov
15
comment Can we teach Mathematica about functional differentiation?
I had to downvote this because it returns incorrect results as you notice yourself in the previous comment.
Nov
15
revised Can we teach Mathematica about functional differentiation?
Added package loading instruction
Nov
15
revised Can we teach Mathematica about functional differentiation?
Forgot a replacement
Nov
15
comment Awkward output of TeXForm
That's the same thing that NumberFormat does. Here the main point is that you want the flexibility provided by NumberForm to introduce, e.g., the \cdot multiplication symbol.
Nov
15
revised Can we teach Mathematica about functional differentiation?
Added more instructions on how to use `VariationalD`.
Nov
14
answered Awkward output of TeXForm
Nov
13
answered Can we teach Mathematica about functional differentiation?
Nov
12
revised How can I differentiate Numerically?
Use ArrayPad instead of Part - looks cleaner.
Nov
12
comment How can I differentiate Numerically?
@DanielLichtblau If I look at this Wolfram demo, it seems to me that the technique is better classified as a symbolic differentiation trick. But maybe that's a matter of taste. My criterion would be that a numerical differentiation should be able to deal with functions that are calculated by numerical root finding, or using FixedPoint etc. Automatic differentiation requires that the function be calculable using elementary operations.
Nov
11
comment How can I differentiate Numerically?
@acl, yes - and I had upvoted your linked answer back then, too! It's very exhaustive.
Nov
11
comment NDSolve with vectors
Yes, I guess one could change the function argument from p0_ to {p0x_, p0y_, p0z_} etc., but it seems that even then the second-order differential equation is too hard to recognize as vectorial. So your approach is just the safest, I think.
Nov
11
answered How can I differentiate Numerically?
Nov
11
comment NDSolve with vectors
This is also how I would have done it, but it should probably be pointed out that Mathematica does know how to deal with vector functions in some cases. See e.g. this answer.
Nov
10
comment Simple ways to evaluate a derivative at a point?
You may find this question useful, too.
Nov
10
comment Simple ways to evaluate a derivative at a point?
This formatting is also found in my answer here, where I give another link to the Wolfram Blog.