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Newest 'calculus-and-analysis' Questions - Mathematica Stack Exchange
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Learn more about TeamsQuestions 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.
5,355 questions
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3
votes
1
answer
91
views
Partial derivative of a matrix with respect to a vector dimension?
So I found this definition in this paper, but I wanted to double check that this is actually correct because I heard that the Partial derivative of a mxn matrix with respect to a p vector is supposed ...
0
votes
0
answers
91
views
Handling abstract power series
I would like to do some abstract power series manipulation. I am defining a power series like this
func = Sum[Subscript[a,i] * x^i, {i, 0, M}];
When I try to take ...
4
votes
1
answer
192
views
Generating Poincaré sections
I would like to reproduce the Poincaré sections presented in this and this papers, which look like
The figures are for energy values of E=0.2 (a) and E=0.25 (b) in the Hamiltonian, which reads
$$H=\...
3
votes
0
answers
154
views
Mathematica demonstration of the expected volume of a random polytope in a ball
Related MSE post
I'm trying to make Mathematica demonstration of the paper The expected volume of a random polytope in a ball.
In the $d$-dimensional Euclidean space $E^d$ ($d \geq 2$), consider the ...
4
votes
2
answers
240
views
Speeding up conditional integration
I was wondering if there is a way to make this function faster
...
2
votes
1
answer
129
views
Overriding derivatives: function composition
I am having trouble overriding when I compose functions. Here is a simple example. I would like the first output below to be 10 g[x] as opposed to ...
2
votes
3
answers
190
views
Recursive Function with Integral
I am trying to recursively define the following function:
...
8
votes
1
answer
439
views
Mathematica code involving floor function
I am reading an interesting paper One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational by Zudilin. Define $$\varphi_0(x,y):=\sum_{j=1}^{3}([y]+[\eta_0x-y]-[y-\eta_j x]-[(\eta_0-\eta_j)x-y]-2[\...
2
votes
1
answer
272
views
Calculating $\lim_{k\to\infty} \cos \left(\pi \sqrt{k^2+k+1}\right)$
It's easy to prove that Limit[Cos[π Sqrt[k^2 + k + 1]], k -> ∞] equals 0, however the latest Mathematica version claim it's ...
3
votes
0
answers
103
views
Difference in convergence behavior of Sum for two equivalent series
I am perplexed by the output of the following code:
...
2
votes
1
answer
102
views
Calculating Residual From PDE
Bug introduced in 14.2 or earlier.
I am trying to determine if my solution converges, by calculating the residual of my PDE.
...
0
votes
1
answer
123
views
Plotting branch cut along `Im[z]=0` axis
I have expressions $\log\frac{z}{z-1}$ and $\frac{1}{z \left( 1 + W_0\left(-\frac{1}{e z}\right) \right)}
$ visualized below. There's a branch cut along the Im[z]=0 ...
9
votes
1
answer
183
views
InverseMellinTransform unexpected result after Simplify
I'm having unexpected difference applying inverse Mellin transform after a simple algebraic rearrangement (1/(-1 + 2 s) vs ...
7
votes
6
answers
446
views
NDSolve not able to adjust condition in ODE
I'm trying to solve the equation
\begin{align}
\epsilon_b\:\theta''(s)-(l-s)\cos\theta(s)=\epsilon_\gamma\sin\theta(s)\cos\theta(s),
\end{align}
with $0\leq s\leq l$ and
\begin{align}
\theta(0)=0\:\:\:...
0
votes
0
answers
102
views
How to solve a regular integral with divergence analytically
I want to analytically integrate this integration
$$\int_0^{1 - 3/rs}\left(\frac{9 \sqrt{3} \sqrt{\frac{1}{\left(1-\frac{2}{\eta }\right) \eta ^2 \left(\frac{\eta
^2}{1-\frac{2}{\eta }}-27\right)}}}...
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