All Questions
Tagged with derivative or calculus-and-analysis
812 questions with no upvoted or accepted answers
3
votes
0
answers
112
views
Calculate PDF of difference of Max and Min for Gaussian random variables
Although this should be a standard question I didn't find it in SE, and it was a nice exercise in Mathematica.
Let $x$ and $y$ be two independent Gaussian random variables with distribution $N(0,1)$. ...
- 13.1k
3
votes
0
answers
97
views
How can one achieve the most accurate estimates of certain six-dimensional integrals under specific constraints?
I have three positivity constraints (f1, f2, f3):
...
- 2,385
3
votes
0
answers
783
views
Differentiation of a matrix function
I'd like to compute the derivative (Jacobian) of the function $\mathbf{\Psi\left(\mathbf{F}\right)}$ w.r.t. $\mathbf{F}$ where $\mathbf{F}$ is a 2x2 matrix and $G$ and $v$ are just real constants;
$$
...
- 215
3
votes
0
answers
218
views
Limit of an infinite nested radical?
Is it possible to compute the limit of this infinite nested radical in Mathematica:
Limit[Sqrt[n+Sqrt[n+Sqrt[n+Sqrt[n+...]]]], n->0]
- 31.8k
3
votes
0
answers
100
views
Integrate gives wrong result?
Computing the integral of the Euclidian distance of two points in a plane, Mathematica seems to give a wrong result. This is a simple integral that should not be tricky and can easily be computed by ...
- 263
3
votes
0
answers
139
views
Formatting derivatives in traditional output
This is related to this question, but goes a bit further. I have also seen Vitalyi's Blog Post on the topic. I, on the other hand, have used a modified version of Pekka Janhunen's DFormat package to ...
- 4,159
3
votes
0
answers
85
views
2-dimensional formatting for integration
So I am trying to integrate the function x^2 * Sin^2[n Pi x / a], {x,0,a}.
The code I am using is in the "two-dimensional formatting" of mathematica: I am using Esc ...
- 195
3
votes
0
answers
690
views
Integration error from Plot3D
I am trying to visualize diffusion distribution from an equilateral triangle with 45 degrees. Assuming that diffusion is a Gaussian with sigma=1 this should do:
<...
- 767
3
votes
0
answers
103
views
Wrong limit involving sine?
Using Mathematica 9.0.0.0, I was trying to calculate the sum
$$
B_n = \sum_{i=1}^n \sin^4\left(\frac{(i-1)}{(n-1)}\cdot\frac{\pi}{2}\right).
$$
where I thought it would be $B_n = \frac{3(n-1) + 4}{8}$....
- 213
3
votes
0
answers
124
views
Bug or feature? If statement inside double integrals
(taken from https://math.stackexchange.com/questions/1592901/bug-or-feature-if-statement-inside-double-integrals)
Generally speaking,
$$ \int_c^a f(x) dx = \int_c^{a-b} f(x) dx + \int_{a-b}^a f(x) ...
- 291
3
votes
0
answers
301
views
How can I improve the solution of my PDE?
I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
- 33
3
votes
0
answers
115
views
Indeterminate expression 0(I*Infinity]) on indefinite integrals on first use only
I do not know if this is new or not, I googled before.
Windows 7, 10.1 64 bit: Integrals generate this error message
The strange thing also is that the message shows up the first time the command is ...
- 151k
3
votes
0
answers
100
views
3
votes
0
answers
528
views
How to prevent simplification of hypergeometric functions resulting from integrations?
Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
3
votes
0
answers
673
views
Is this result wrong because of calculation time? (and more questions about Assumptions)
I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case:
...
- 1,755
3
votes
0
answers
285
views
Numerical-Symbolical Integration (Calculus)
I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals.
The problem with my function is ...
- 91
3
votes
1
answer
423
views
Mathematica is unreliable about recognizing orthogonal functions
Hermite polynomials should be orthogonal over a Gaussian measure. However when the orders of the polynomials are larger than a few, Mathematica gets this wrong. Strangely, it seems to hinge on whether ...
- 31
2
votes
0
answers
53
views
How to generate lattice by integrating over curves on a modular form domain plot?
I was watching this video (2:30 of https://youtu.be/zLEyIT_BCgk?si=ji5NyjR7vcwzaNxi ).
Here in the video he said that to get the lattice , we just integrate over the curve(silver line) and we will ...
- 194
2
votes
0
answers
57
views
Drawing cycles around and across cuts
I want to draw cycles (or paths) around and across the cuts on the complex plane for the following function (where I have put the cuts between [z1,z2] and ...
- 479
2
votes
0
answers
47
views
Take symbolic derivative of summation expression and display as unexpanded sum
My main problem here is two-fold:
Take symbolic derivative of summation expression
Stop summations from being "unrolled"/expanded, e.g., displayed as the sum of terms
I also have some ...
2
votes
0
answers
186
views
How to plot the sum of this function series?
Let us consider the sum of a function series
$$ \sum _{n=1}^{\infty } \frac{z^n}{\left(z^n+1\right)^n}.$$
This series absolutely converges if Abs[z] < 1 or ...
- 29.1k
2
votes
0
answers
175
views
How to perform the following deduction symbolically?
$$i \frac{d}{dt}a_n = (a_{n+1} + a_{n-1}) + |a_n|^2 (a_{n+1} + a_{n-1}), \; n \in \mathbb{Z}$$
In the above, $a_n := a_n(t)$. Consider $P = \sum\limits_{n}g(|a_n|^2)$ where $g$ is some function to be ...
- 597
2
votes
0
answers
100
views
Why does HeavisideTheta give different value at the point 0 and 0.?
As the following figure described, why does HeavisideTheta give different value at the point 0 and 0.? Especially at the coordinate origin, one gives the value 1 and another 0 when HeavisideTheta[0]=0....
- 693
2
votes
3
answers
83
views
Strange behavior when integrating vector valued piecewise function
The following straightforward integral should clearly equal $\{0,0\}$ for any $R\in\mathbb R$:
...
- 166
2
votes
0
answers
104
views
Workarounds for unevaluated results of ContourIntegrate of non-analytic functions
There is a new useful command ContourIntegrate since 13.3.
I find that the command is well-done, but even the Sun has spots.
...
- 29.1k
2
votes
1
answer
186
views
What does "{True,True}" mean in the result of IntegrateChangeVariables?
I want to change variables in the following integral:
Integrate[q*D[z[x, y],x]^2, {x, -∞, ∞}, {y, -∞, ∞}]
as follows:
...
- 40k
2
votes
0
answers
277
views
Symbolic integral with UnitStep functions
I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ...
- 405
2
votes
0
answers
120
views
Fractional derivatives (FractionalD) of an InterpolatingFunction to retun another InterpolatingFunction
Question
I want to calculate the FractionalD of an InterpolatingFunction object, however, evaluating
...
- 37.4k
2
votes
0
answers
161
views
Closed form for a sum involving Bernoulli numbers
I need a closed form for the sum $$\sum_{n=1}^{\infty}\frac{(-1)^{n-1}(2^{2n}-1)\pi^{2n}B_{2n} {2n+4 \choose m}x^{2n+4}}{(2n)!}$$
where $0<x<1$, $B_{2n}$ denotes Bernoulli numbers , $m\in\mathbb{...
- 301
2
votes
0
answers
72
views
How to verify the Riemann hypothesis up to a given height?
According to the Wikipedia article on Riemann hypothesis,
The number of zeros of the zeta function with imaginary part between $0$ and $T$ is given by
$$N(T)=\frac{...
- 21
2
votes
0
answers
62
views
Computing residue of the resolvent
I'm looking at this Mathematica tutorial
where the author defines matrix function by summing over (matrix-valued) residues of the resolvent.
...
- 6,697
2
votes
0
answers
86
views
Calculate the value of dt in reverse
Firstly, I gave the value of $dt=0.00006$ and the range of $0<=t<=0.08$, and then calculated the maximum value of cond, as shown in the following code:
...
- 165
2
votes
0
answers
132
views
Mathematica 12 notebook shuts down unprompted
I have a piece of code that calculates and plots solutions of a set of 4 differential equations - coordinates of an object moving in a Kerr spacetime to be exact - with customizable initial parameters....
- 21
2
votes
0
answers
95
views
Why does this finite integral blow up in Mathematica?
I am having some trouble understanding the output of a particular integral. I think I am misunderstanding something about how Mathematica is used, or about how the Integrate function works, and I ...
- 21
2
votes
0
answers
63
views
Efficient powers of DPR1 matrices
I'm looking to compute the following quantity for $A$ where $A$ is a convergent positive definite $d\times d$ diagonal + rank1 matrix (DPR1).
$$f(s)=\operatorname{Tr}(A^s)$$
Earlier answer answer by ...
- 6,697
2
votes
0
answers
183
views
Decoupling many second-order linear ODEs
I am doing mesh/loop analysis on a fairly complex electrical circuit, and the result is a system of 45 second-order coupled differential equations such as
$$ (\ddot{q}_{23} - \ddot{q}_{24}) L_{3} + (\...
- 21
2
votes
1
answer
186
views
How to separate parameters from a list based on certain conditions?
The following codes create a table of parameters Br and Dr based on corresponding parameters b and c. How to separate/divide the list/table of Br and Dr for which corresponding b or c are negative ...
- 99
2
votes
0
answers
62
views
Is this a bug in InverseLaplaceTransform or LaplaceTransform?
Let us consider in version 13.1 on Windows 10
ClearAll["Global`*"]; a = InverseLaplaceTransform[s*Log[(s - 1)/(s + 1)], s, x]
...
- 29.1k
2
votes
0
answers
145
views
Asymptotic does not give asymptotic?
Expression Asymptotic[Exp[(1 + E^x)/(1 + x)], x -> Infinity] gives Exp[(1 + E^x)/x] as the answer but these functions are ...
- 3,712
2
votes
0
answers
60
views
Why does Mathematica not know some integrals diverge?
I want to analyse the convergence of some complicated 1d integrals that may have divergences at $x=0$, similarly to the harmonic integral $\int_0^a 1/x \ \mathbb{d} x$, which I know is divergent.
When ...
- 21
2
votes
0
answers
60
views
Possible bug in Integrate: convergent integral reported divergent
$Version
"8.0 for Microsoft Windows (64-bit) (October 7, 2011)"
on Windows 10
Consider the calculation of this integral
...
- 13.1k
2
votes
0
answers
96
views
Limit for some the variable in Mathematica
I have this limit but Mathematica can't solve it??!!
...
- 153
2
votes
0
answers
262
views
Understanding results from Rubi integrator
I am just starting out with Mathematica and more specifically Rubi. I just tried to integrate the following.
...
2
votes
0
answers
84
views
Analytical Cross-Correlation between two time lagged Sinc functions gives complicated result
I'm trying to calculate the analytical Cross-Correlation between two time-lagged Sinc functions, i.e.,
\begin{align} R(\tau) = \int_{-\infty}^{\infty} \overline{\textrm{sinc}\left(\pi f \left(t - d_1\...
- 33
2
votes
0
answers
60
views
How to find the regions for which the derivative of my function changes sign?
I have an energy function of the angles of the electrons' spins. th1 is vector with (2l+2) elements and each element represents the angle of an individual electron spin. I need to eventually find the ...
2
votes
0
answers
135
views
Non-convergent integral converging after variable transformation
When I try to integrate the following function with Integrate[...]
$$\int_0^1 dx \frac{1}{1-x}\left(\frac{1-x}{x} \right)^i$$
with $i$ the imaginary unit, mathematica says that it is not convergent. ...
- 307
2
votes
2
answers
375
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 ...
- 21
2
votes
0
answers
83
views
One more an incorrect result of FunctionAnalytic
Studying a new in 12.2 command FunctionAnalytic, I execute
...
- 29.1k
2
votes
0
answers
47
views
Finding region, between four hyperplanes, useful for integration
Consider the function
$$
f(x,y,u,v)
=
\exp\bigl(
-x^2
-y^2
-u^2
-v^2
\bigr),
$$
and the region $\mathcal{R} = \cap_{i=1}^4 \mathcal{R}_i$ defined by four hyperplanes as follows
$$
\begin{align}
\...
- 299
2
votes
0
answers
101
views
How to do a fast numerical computation of an oscillatory integral including HeunC function using Mathematica?
I am trying to numerically compute the following integral in Mathematica
...
- 119