# Questions tagged [calculus-and-analysis]

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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### NDSolve with embedded piecewise function for state-variable

Given ODE: $\dot{x}=-2 e^{-x^2} x + U$ where: $U=-u_{as}$ $u_{as} = \begin{cases} \frac{e}{\psi_+-e}, & \mbox{if } e\mbox{>=0} \\ \frac{e}{e-\psi_-}, & \mbox{if } e\mbox{<0} \end{cases}$ ...
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### Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta at one of ...
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### Problems with improper integrals in higher dimensions

Calculating numerically certain energy integrals in three and four dimensions related to the Riesz potential and the capacity, I try ...
76 views

### How do I plot the derivative of the Cantor Staircase?

I know that the derivative of the Cantor Staircase should be close to 0 since the Cantor Set has a measure of zero. I wanted to graph the derivative of Cantor's Staircase in Mathematica to see if it ...
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### Search for terms contatining error functions

question might have an answer in this post (Efficient Search for specific Terms in symbolic Expression) but i don't understand how to convert it to my specific case Through some definite integrals I ...
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### Summation variables aren't recognised as dummy variables

I'm trying to write this expression in Mathematica, and calculate the following quantity However, when I tried the following ...
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### Why are the numerical and analytical evaluation of this integral not the same?

Since my integral and the way I used to solve it was so long, I put a .nb file here including all data which are needed. You can use it to try my question after reading the following details I had ...
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### Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...