All Questions
Tagged with derivative or calculus-and-analysis
5,242 questions
0
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12
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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 ...
- 63
8
votes
2
answers
419
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 ...
- 311
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
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 ...
- 151k
3
votes
4
answers
322
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
...
- 31
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
...
- 19.8k
6
votes
4
answers
448
views
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
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:
...
- 387
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
$$\int \frac{1}{\tan\left(\frac{1}{2}\csc^{-1}(x)\right) - \tan\left(\frac{...
0
votes
2
answers
63
views
Derivative of unknown function with respect to global defined function
I have the following code:
x[t_]:=y[t]+2*t
MyRule = D[z[x[t]],x[t]]>0
y[t] and z[x[t]] are unknown functions.
I get the following error message: "D: 2t+y[...
- 1
3
votes
2
answers
244
views
Repeated partial derivatives
Big Mathematica novice here, hopefully this isn't too trivial?
I would like to define a function in Mathematica that takes $f$ as an input and produces repeated applications of the operator $\Theta_\...
2
votes
1
answer
76
views
Handling of inverse Laplace transform of $e^{a s}$ when $a>0$
Do not know if this was asked before.
Why in V 14.1 this works
ClearAll[a, s];
InverseLaplaceTransform[Exp[a*s], s, t, Assumptions -> a > 0];
% /. a -> 1
...
- 151k
0
votes
0
answers
48
views
Solving for the generating function of a function sequence [closed]
I wish to solve for the generating function of a sequence of functions, provided in a list
{$f_1=\ •\ ;f_2=\ •\ ;f_3=\ •\
\ ;f_4=\ •\ ;f_5= \ •$}
such that
$f_n=f(n)$
and the functions $f_n$ may be ...
2
votes
2
answers
185
views
Integrate function involving Mod[]
I have a function
f[x_] := Min[Mod[a x, 2], 2 - Mod[a x, 2]]
that I want to integrate
Integrate[f[x], {x, 0, 2/a}]
Clearly, ...
0
votes
1
answer
97
views
Converting HurwitzZeta function to PolyGamma function
A generalization produces a result in terms of Zeta[s,a] function, which can be converted to PolyGamma[s-1,a] using the ...
- 645
1
vote
1
answer
60
views
0
votes
1
answer
110
views
Integration and elliptic functions
I am trying to solve the following differential equation
$$ \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} +...
- 169
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:
...
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 ...
-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?
...
- 465
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 ...
- 101
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 ...
- 193
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 ...
- 1
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
$$ \int_0^\infty dx\ x^n \exp \left( -h \sqrt{x^2 + a^2} \right) = \frac{2^{...
- 528
0
votes
1
answer
64
views
Plot3D does not show the image of function
I have a functionR1[x_, t_] = -((t^35 x^2)/10333147966386144929666651337523200000000);
I use the following command in Mathematica to show the graph of Function
<...
0
votes
0
answers
61
views
Apply Jacobi-Anger expansion when argument is not a single variable [duplicate]
I have an expression
Sin[z Sin[th]]
I want Mathematica to apply the Jacobi Anger expansion, and it works:
...
5
votes
4
answers
552
views
Plot an infinite but convergent series
I would like to plot the following function
$$
f(m)=-2 \sum_{k=0}^{\infty}\binom{1/2}{k} \left(2^{2(k-1)}-1\right)\zeta(2 (k-1))\left(m^2-\frac{1}{4}\right)^k
$$
I am only interested in $m$ between 0 ...
0
votes
2
answers
82
views
Asymptotic: Issue with constant term of Asympotic of rational function
Here is a simple function to show the issue:
f[x_] := 3 x + 2 + 2/(x + 1)
It is very clear from this expression that the asymptote for ...
- 2,740
0
votes
0
answers
99
views
How to know the formula of function in mathematica?
When I review BiorthogonalSplineWavelet in official website.
I could not find any formula of how to calculate as below:
How to ...
- 707
7
votes
2
answers
179
views
Can Mathematica differentiate summation notation with respect to an indexed variable?
My question is whether Mathematica can represent an expression such as:
$$y_i = \sum_{j=1}^N a_{ij} x_j$$
symbolically as a sum over indefinite bounds (unknown $N$), and differentiate it with respect ...
- 173
2
votes
1
answer
41
views
Integration giving two different outputs despite equivalent inputs?
Problem:
I have the following integral:
...
- 463
3
votes
2
answers
585
views
Is it possible to get analytic solution of this integral?
I am trying to evaluate the following integral, but Integrate just returns the input:
...
- 53
1
vote
2
answers
136
views
Solving differential equation through function [duplicate]
Folks! I am trying to obtain the plot the phase portrait of the following differential equation in Mathematica. My task is to do the work through function by numerical solution. The equation is:
$$\...
- 119
2
votes
3
answers
236
views
Trouble with branch cuts plotting a real function
When I plot the following function
...
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 ...
- 31
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 ...
- 1,892
1
vote
0
answers
102
views
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
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
2
votes
3
answers
287
views
Help with derivative command [duplicate]
I am trying to find the Mathematica command for
$$f(k,a,b)=\frac{\partial^k}{\partial {a}^k }\csc\left(ab\pi\right)$$ and here is what typed for the command ...
- 645
3
votes
3
answers
226
views
Reconstruct points on a sphere from matrix of dot-products
Suppose I have a matrix of pairwise dot products corresponding to vectors on a sphere. How do I reconstruct these vectors (up to a rotation?).
Below is a solution that reconstructs a set of vectors ...
- 6,697
1
vote
2
answers
97
views
Parabolas to the right or to the left
I would like some help to make the opening (concavity) of the parabolas go to the right or left, and not up or down.
...
0
votes
2
answers
86
views
Error on the square of sum of binary elements for symbolic upper limit
I'm seeing the following error: as a part of some equations, I have $E[(\sum_{i=1}^n X_i)^2]$, with $X_i\sim Ber(p)$. Using independence between $X_i$ and $X_j$ for $i\ne j$ and that $X_i^2=X_i$, $E[(\...
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 ...
- 645
0
votes
5
answers
285
views
What's the correct answer for $ \oint_{C} \frac{e^{1/z}}{z^{2} - 1} \, dz$?
$$
\oint_{C} \frac{e^{1/z}}{z^{2} - 1} \, dz,
$$
where $ C $ is the unit circle defined by $ |z| = 1 $.
The original question can be found under the answer from Ron Gordon's answer to "contour ...
- 1,892
4
votes
1
answer
146
views
Why equal series written in a little bit different way both diverges and converges?
I am very new to Mathematica, so I am sorry if the answer is obvious. I wanted to calculate the sum of the following series:
...
- 141
0
votes
0
answers
80
views
1
vote
1
answer
69
views
Parallel loop wrecks integration
I am doing a quadruple nested integral and noticed that it produces inconsistent results when in a parallel computing environment.
...
- 310
4
votes
3
answers
212
views
Solving integral equation numerically
I tried to solve a integral equation numerically, but I failed. The equation is:$\epsilon(\beta)=r\cosh{\beta}+\int^{\infty}_{-\infty}\varphi(\beta-\beta')\ln(1+e^{-\epsilon(\beta')})d\beta'$ were $\...
