All Questions
Tagged with derivative or calculus-and-analysis
5,242 questions
0
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Variable substitution of a PDE containing the Laplace operator in spherical coordinates
There is a three-dimensional wave equation in spherical coordinates, with the initial value problem as follows:
$\left\{\begin{array}{l}u_{t t}-a^2 \nabla^2 u=0 \\ \left.u\right|_{t=0}= \begin{cases}...
- 2,425
5
votes
2
answers
1k
views
Mathematica will not compute this integral
I am trying to compute the following integral, but regardless of FullSimplify or Assumptions, Mathematica seems unable to compute it. I have already tried computing the indefinite version and evaluate ...
- 16.6k
8
votes
2
answers
418
views
NIntegrate cannot give high precision result for a well-behaved integral
I want to obtain value of following integral to a high precision (say 30 digits),
NIntegrate[DawsonF[Sqrt[t]]^2/t, {t, 0, Infinity}]
Graph of integrand looks like ...
- 245k
0
votes
0
answers
63
views
Efficient way to calculate the limit of a very long expression [closed]
I want to calculate the limit of a very long expression, but simplifying the expression using Simplify or FullSimplify doesn't ...
- 5,820
3
votes
4
answers
321
views
Is there a way to make Mathematica return only the solution to an integral that is real?
I am looking to find a consistent way of finding integrals that result in inverse trig functions. I have been able to convert the output of
...
- 245k
5
votes
1
answer
164
views
Difficult Fourier transform
I need to compute the Fourier transform of a simple rational function times hyperbolic secant distribution
...
- 16.6k
5
votes
2
answers
455
views
Why can`t DSolve solve this second order ode with initial conditions?
This ode from textbook. I was surprised Mathematica 14.1 on windows could not solve it, as one can solve it using Mathematica by solving for initial conditions directly.
So I am hoping some debugging ...
- 31.4k
4
votes
2
answers
287
views
Is there a way to give an analytical result to the following integral?
I hope to obtain the analytical result of gg[r]. Is there a way to give an analytical result to the following integral of function ...
- 4,628
1
vote
2
answers
1k
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Integration of linked PDFs over probability simplex
I'm trying to integrate the following expression:
f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4]
Where
...
CommunityBot
- 1
1
vote
2
answers
397
views
Incorrect results of DSolve
Finding a fundamental solution of a certain
linear partial differential operator, I try
...
CommunityBot
- 1
1
vote
0
answers
59
views
How to explain the behaviour ahout Interpolation?
I encountered an issue while calculating the derivative of an interpolation function. To illustrate the problem, I provide a simple example below, along with the corresponding code:
...
- 779
0
votes
2
answers
63
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Derivative of unknown function with respect to global defined function
I have the following code:
x[t_]:=y[t]+2*t
MyRule = D[z[x[t]],x[t]]>0
y[t] and z[x[t]] are unknown functions.
I get the following error message: "D: 2t+y[...
- 4,628
6
votes
4
answers
448
views
0
votes
0
answers
70
views
Why does Wolfram Alpha's performance on integrals vary by language and now fail in both cases? [closed]
I recently encountered a strange issue while working with Wolfram Alpha (WA). Initially, I attempted to compute the integral
$$\int \frac{1}{\tan\left(\frac{1}{2}\csc^{-1}(x)\right) - \tan\left(\frac{...
0
votes
1
answer
86
views
Issue with Reduction of Complete Elliptic Integral of the Second Kind
I am attempting to reduce the following equation:
y ==
I’ve entered it to be reduced as such, where L = 3.95:
By what means may this be properly reduced for y?
Both WolframAlpha and Desmos provide ...
- 4,628
1
vote
2
answers
180
views
How to find the local maximum and minimum of a function
I am trying to find the local maximum and minimum of a function. The code below works if function is an exponential but when function involves a sinusoid, it does not give numerical values and instead ...
CommunityBot
- 1
0
votes
0
answers
48
views
Solving for the generating function of a function sequence [closed]
I wish to solve for the generating function of a sequence of functions, provided in a list
{$f_1=\ •\ ;f_2=\ •\ ;f_3=\ •\
\ ;f_4=\ •\ ;f_5= \ •$}
such that
$f_n=f(n)$
and the functions $f_n$ may be ...
1
vote
2
answers
171
views
Integration of Gaussian functions takes ages
I am trying essentially to compute a fourier transform with Integrate.
1]Is integrate faster or slower than FourierTransform?
2]Does anyone know how to efficiently calculate these integrals?
My code ...
- 245k
2
votes
1
answer
76
views
Handling of inverse Laplace transform of $e^{a s}$ when $a>0$
Do not know if this was asked before.
Why in V 14.1 this works
ClearAll[a, s];
InverseLaplaceTransform[Exp[a*s], s, t, Assumptions -> a > 0];
% /. a -> 1
...
- 29.1k
5
votes
3
answers
332
views
NIntegrate doesn't calculate a triple integral
I have an integral of dubious origin, which I don't know how to calculate:
...
- 15.3k
1
vote
1
answer
184
views
Can this previously solved three-dimensional constrained integration also be solved with certain added products in the integrand?
In Solved3DConstrainedIntegration
the constrained three-dimensional (Hilbert-Schmidt-metric-based HSmetric) integration problem for the absolute separability probability of the two-qubit (quantum bit)...
CommunityBot
- 1
0
votes
1
answer
97
views
Converting HurwitzZeta function to PolyGamma function
A generalization produces a result in terms of Zeta[s,a] function, which can be converted to PolyGamma[s-1,a] using the ...
- 50k
3
votes
2
answers
244
views
Repeated partial derivatives
Big Mathematica novice here, hopefully this isn't too trivial?
I would like to define a function in Mathematica that takes $f$ as an input and produces repeated applications of the operator $\Theta_\...
- 34.2k
0
votes
0
answers
47
views
Ability of Integrate[ ] to try changes of variable on its own
I have a question about Mathematica's ability to try changes of variable when performing symbolic integration. My example is
$$ \int_0^\infty dx\ x^n \exp \left( -h \sqrt{x^2 + a^2} \right) = \frac{2^{...
- 528
1
vote
1
answer
60
views
0
votes
1
answer
110
views
Integration and elliptic functions
I am trying to solve the following differential equation
$$ \left( \frac{d u}{d \phi} \right)^{2} = Q u^{3} + P u^{2} + c $$
For this, I wrote it as
$$ \left( \frac{d u}{d \phi} \right)^{2} = Q u^{3} +...
- 4,628
0
votes
1
answer
57
views
Series truncation
I am trying to evaluate an integral whose results contain several terms (in thousands) in the form $Ag+Bg^2 sin(gt) + Cg^3sin(gt)cos(gt)+...$with powers of g up to $g^8$. I would like to keep only the ...
- 5,620
-1
votes
1
answer
52
views
Extend of numerical ODE for a special case [duplicate]
I want to continue the plot but I don't know how to do it?
...
- 16.6k
0
votes
1
answer
64
views
Plot3D does not show the image of function
I have a functionR1[x_, t_] = -((t^35 x^2)/10333147966386144929666651337523200000000);
I use the following command in Mathematica to show the graph of Function
<...
- 56.4k
1
vote
2
answers
116
views
Apply Jacobi-Anger expansion and return infinite sum
I have an expression
Sin[z Sin[th]]
I want Mathematica to apply the Jacobi Anger expansion, and it works:
...
- 16.6k
0
votes
3
answers
126
views
How to compute the Jacobian matrix using Mathematica [duplicate]
Apologies if this is posted to the wrong forum. Have been using Maple and Maxima for 20+ years, and have only recently started using Mathematica (v. 14). Having a heck of a time getting Mathematica to ...
- 59.6k
2
votes
2
answers
185
views
Integrate function involving Mod[]
I have a function
f[x_] := Min[Mod[a x, 2], 2 - Mod[a x, 2]]
that I want to integrate
Integrate[f[x], {x, 0, 2/a}]
Clearly, ...
- 29.1k
1
vote
2
answers
261
views
DSolveValue differential equation list of arbitrary values
I have been solving arrays of differential equations, and recently moved to the general case, where my initial conditions are arbitrary constants (either real or complex). However when I moved from ...
CommunityBot
- 1
0
votes
0
answers
61
views
Apply Jacobi-Anger expansion when argument is not a single variable [duplicate]
I have an expression
Sin[z Sin[th]]
I want Mathematica to apply the Jacobi Anger expansion, and it works:
...
- 29.1k
0
votes
0
answers
99
views
How to know the formula of function in mathematica?
When I review BiorthogonalSplineWavelet in official website.
I could not find any formula of how to calculate as below:
How to ...
- 707
0
votes
1
answer
205
views
Reduce does not give me the proper answer
I am considering the function
f[T_, c1_, c2_] := \[Pi] (rh[T]^2 (L^2 - rh[T]^2))/(G (L^2 + 3 rh[T]^2))
(1 + (64 \[Pi] G (c2 - c1))/L^2) + 64 \[Pi]^2 c1
with $G=L=...
CommunityBot
- 1
4
votes
1
answer
438
views
Implementing positivity constraints over a six-dimensional hypercube
This question involves the same subject matter as my previous one (How can one achieve the most accurate estimates of certain six-dimensional integrals under specific constraints?), but with another (...
CommunityBot
- 1
2
votes
1
answer
41
views
Integration giving two different outputs despite equivalent inputs?
Problem:
I have the following integral:
...
- 151k
0
votes
2
answers
82
views
Asymptotic: Issue with constant term of Asympotic of rational function
Here is a simple function to show the issue:
f[x_] := 3 x + 2 + 2/(x + 1)
It is very clear from this expression that the asymptote for ...
- 56.9k
0
votes
1
answer
146
views
NIntegrate can't solve this complicated multiple integration with absolute value in Exp and Cos functions
I'm trying to use NIntegrate to calculate this complicated multiple integration, which has absolute value in the Exp and Cos functions.
$$
\int_{-\infty}^{\infty} dx_1 \int_{-\infty}^{\infty} dx_2 \...
CommunityBot
- 1
0
votes
1
answer
62
views
Compute integrals in singular integral equation
I'm looking at this paper
https://arxiv.org/abs/2404.07307
and in particular I am interested in eqs. (16) (17), meaning I'd like to check the validity of (16) by insert it in (17).
So I'd like to ...
- 56.9k
0
votes
0
answers
41
views
Period of a real function [duplicate]
I noticed that FunctionPeriod[Mod[t,1],t] returns 1 while FunctionPeriod[Mod[t,1.0],t] ...
- 899
1
vote
0
answers
102
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A question about integral and differential equations
I want to use Mathematica to reproduce the result of Eq.(16) under the Case I in the section 2.1 of this Article, but I failed. The result of Eq.(16) is based on differential equation Eq.(14), where, ...
- 193
1
vote
1
answer
430
views
How to obtain the convolution of these functions?
I am starting to use Mathematica. I wanted to compute
$$\nabla F*\phi(x),\;x\in\mathbb{R^2}$$
where $F(x)=\ln\|x\|$ and $\phi(x)=\chi_{B(0,2)}(x)$.
I am a new user of this software, so I don't know ...
CommunityBot
- 1
0
votes
3
answers
112
views
Unable to solve an integration
I would like to solve the following integration:
denom=44.3705 - 17.0692 Pe + 17.0692 Pp - 38.3886 Pe Pp + 35.6879 x -
13.1912 Pe x + 13.1912 Pp x - 43.2119 Pe Pp x + 22.5263 x^2 -
6.59222 Pe x^2 + 6....
CommunityBot
- 1
8
votes
4
answers
622
views
Inverse Laplace Transform of Hypergeometric Function
Any tips how to massage the following to get computed by Mathematica for $p>1$? I suspect the result should be expressible in terms of exponential integral
...
- 29.1k
1
vote
1
answer
153
views
How to assume "much greater than" when there are multiple assumptions? [closed]
Assume $r_{o1} \gg R_S, r_{o2} \gg R_S, g_{m1} r_{o1} \gg 1, g_{m2} r_{o2} \gg 1$.
$$Z_{out} = \frac{r_{o1} (R_S + r_{o2})} {r_{o2} + R_S (1- g_{m1} g_{m2} r_{o1} r_{o2})}$$
Here is what I tried to ...
- 68.4k
0
votes
0
answers
156
views
How to force Mathematica to solve the ODE with respect to h[s]?
I have a problem with the DSolve operator. It just gives me the initial ODE as an answer, however, obviously, I need to find the answer h[s] as a function of f[s] and its powers (or whatever else). It ...
CommunityBot
- 1
2
votes
1
answer
89
views
How to force Mathematica to evaulate some values of LerchPhi function?
Mathematica cannot give LerchPhi[1,0,1]=-1/2, LerchPhi[1,1,1]=0, and LerchPhi[1,1,1/2]=0, as ...
- 17.1k
3
votes
1
answer
352
views
Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities
In a recent posting,
TwoQubits
user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
CommunityBot
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