# 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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### Strange behaviour of integrals with Cos, Sin, and Exp

Bug introduced in 8.0.4 or earlier and persisting through 11.0.1 During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would ...
302 views

### Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
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### Workaround for DSolve in V 12 when it gives undefined as solution to 1D heat PDE?

Reported to WRI CASE: 4278450 Comparing the following, all done from clean kernel The strange thing is that V 12 can solve this same PDE without the assumptions ...
267 views

### Possible Symbolic Integration Bug

Bug introduced between 5 and 8 and persisting through 12.0. I think I may have found a bug, and want to verify is this reproducible in other versions and platforms and not a mistake of mine. I ...
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### Huge difference after changing a fraction to decimal

I have a limit to calculate. With[{p = 1/2, q = 0.1}, Limit[a^q Integrate[Sin[x]/x^p, {x, a, Infinity}], a -> Infinity]] gives correct result ...
150 views

I found a few demonstrations on the Wolfram Demonstration Project site that help users to explore the formal definition of a limit. That is, $$\lim_{x\to a}f(x)=L$$ if and only if for every $\epsilon&... 1answer 225 views ### 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 ... 0answers 306 views ### Strange behaviour of MMA in derivatives of some standard functions There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ... 0answers 1k views ### Symbolic matrix calculus: What's new in Version 9 I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ... 0answers 211 views ### Linearised Einstein equations I need to compute the linearised Einstein Equations around a fixed metric $$g_{μν}=\text{Minkowski metric} + h_{μν}$$ which is not the flat metric. Does anyone know a Mathematica package or a ... 0answers 548 views ### Spherical harmonic derivative Consider the following substitution Derivative[2, 0][S][th, ph] /. S -> Function[{th, ph}, SphericalHarmonicY[3, 0, th, ph]] which gives correct answer. While ... 0answers 104 views ### How to test whether an improper integral converges or diverges? To verify the improper integral$\int_{1}^{\infty}x\cdot\left | \sin (x^4)\cdot\sin x \right |dx$converges or diverges,I code ... 0answers 110 views ### Evaluate$\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$Saw this post and noted that it was posted back in 2013. Just tried V11.3 and got no analytic solution. Just wondering if there is a way for Mathematica to give the desired result? Machine VS Human ... 0answers 85 views ### Analytic Integration Bug of Hypergeometric function in Version 11.3? I got this integral ... 0answers 81 views ### Is Mathematica doing this integral of a wave form approximation correctly? I am trying to integrate a square wave approximation I found in this answer by ybeltukov. Nothing wrong with the answer but when I try to integrate it I run into trouble. I modified the code from ... 0answers 142 views ### How can I solve a nonlinear fractional order integro-differential equation? How do I solve the nonlinear fractional order integro-differential equation shown above in Mathematica? 0answers 55 views ### Definite integals that can be expressed in terms of itself I came across the integral$\int_0^\infty \frac{1}{\left(x^2+1\right) \left(x^{2015}+1\right)}\,dx$in a Youtube video. It apparently appeared in the MIT Integration Bee of 2015. In the video, it was ... 0answers 74 views ### Extract explicit region (integration bounds) from ImplicitRegion Using an ImplicitRegion in NIntegrate by far best performance is obtained by using ... 0answers 240 views ### Integrating the Associated Legendre Polynomials I know the following identity:$\qquad \int_{-1}^1 P_l^m(t)^2dt=\frac{2(m+n)!}{(2n+1)(n-m)!}$I would like to verify this result using Mathematica. This is what I entered: ... 0answers 37 views ### Truncated in time derivation I have follogwing equations:$E(n) = \frac{1}{2} ||\vec{\epsilon}(n)||^2$with$\vec{\epsilon}(n) = \vec{y}_{target}(n) - \vec{y}_{prediction}(n) $where n denotes a discrete time.$\vec{y}_{...
Let's try this: I have a function of two arguments, $e$ and $\omega$. First I integrate some function of $(e, \omega)$: ...