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differentiability test

Posted on 2008-11-30 20:20 By almath (Maple Rating 1 18)
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Dear all:

   I wonder if there is any function in Maple checking whether a given function is (m-th) differentiable or continuous? 

 

Thanks,

Peter

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iscont

Comment on 2008-11-30 20:48 from pagan (Maple Rating 2 105)

Have a look at the help page for iscont (and maybe also for discont and fdiscont).

Robert Israel's picture

differentiability

Comment on 2008-11-30 21:06 from Robert Israel (Maple Rating 4 1554)

In principle, you can use limit.  For example, f(x) is continuous at x=a if and only if limit(f(x),x=a) = f(a).

high dimension differentiability test

Comment on 2008-12-01 21:50 from almath (Maple Rating 1 18)

iscont only works for 1-d. Is there a multivariate version of iscont? I hope to test the differentiability of a multivariate function over a region: x1=a1..b1, x2=a2..b2 ...... xn = an...bn

 

Thanks,

Doug Meade's picture

more generally, limits

Comment on 2008-12-02 09:01 from Doug Meade (Maple Rating 4 739)

This remnds me of two of my longstanding requests for improvements in Maple:

  1. multivariate limits
  2. discrete limits (sequences)

Mathematically, there is only one limit, but we have different techniques and tools depending on the specific domain and range: interval, integers, or multi-dimensional.

This is not an area where I can claim any expertise, so I ask:

  1. Is there any work being done in this area?
  2. What are thefundamental issues that make this difficult to implement?

In my mind, it appears that if this functionality existed (efficiently) it could be possible to greatly expand Maple's reliability. It might even make it easier to make Maple "smarter" about what it does in a "student" environment.

I look forward to any insights others can provide.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

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