All Questions
Tagged with derivative or calculus-and-analysis
5,241 questions
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Integration by parts for Green's first identity
How should one implement
$$\int _{\Omega }\nabla u\cdot \nabla v\,d\Omega \ =\ \int _{\Gamma }v\,\nabla u\cdot {\hat {\mathbf {n} }}\,d\Gamma -\int _{\Omega }v\,\nabla ^{2}u\,d\Omega\,,$$
Symbolically ...
- 141
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0
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45
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Problem Derivative (D) of function defined with Piecewise or UnitStep functions - SIMPLE BEAM PROBLEM, 3 SUPPORTS
I am solving a simple structural beam problem using slope-deflection approach - 3 support A(left- fixed), B(middle- pin), C(right - pin). Beam AB - uniform load, Beam BC - concentrated load in ...
- 63
2
votes
2
answers
205
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How to calculate this improper integral?
How to calculate the Integral involving MarcumQ function whose Integral interval is (0, +Infinity)?
Any help (code or reference) would be greatly appreciated.
...
- 2,067
0
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0
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66
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Analytic expression of the $n$-th derivative of a function of two variables
I am hoping to get Mathematica to find an analytic form for the $n$th derivative of the following function of two variables:
$$f(a,b)=\frac{1}{\left((1-a) b\right)^{-k} \left(1-(1-a) b\right)^{k-n}+\...
- 297
7
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2
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403
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2
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2
answers
224
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Numerical derivative of numerical function
I am trying to calculate the derivative of a numerically defined Hamiltonian. This is a minimal working example (on a simple example):
...
- 133
2
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1
answer
81
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Bugs with `Integrate` when dealing with complex situation?
I'm trying to calculate $\int_0^{\infty } \exp \left(t \left(-x^3+(1+i) x\right)\right) dx$ with mathematica, and different assumptions on t give different results:
...
- 2,295
4
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1
answer
557
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What tools does Mathematica have for solving indefinite integrals?
I haven't used Mathematica regularly in about 15 years, so I'm a bit out of date on what the latest tools are for indefinite integration. I have Mathematica 11 on my computer. through searching online,...
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1
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4
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199
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Can Mathematica solve $\int \frac{\cot^2\left(\frac12\sec^{-1}(x)\right)}{\sqrt{\tan\left(\frac12\csc^{-1}(x)\right)}} \, dx$?
Can Mathematica solve integral $(1)$?
$$\int \frac{\cot^2\left(\frac12\sec^{-1}(x)\right)}{\sqrt{\tan\left(\frac12\csc^{-1}(x)\right)}} \, dx.\tag{1}$$
This is
...
2
votes
2
answers
69
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How to get derivation of a function with respect to another function?
I often have this need: I have some functions that have the same variable and have inclusion relationships, like this.
f[t_] := t^2 + 1
g[t_] := Exp[-I Sin[f[t]]]
...
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61
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Solving a set of non-linear coupled differential equations
Here is a set of first-order differential coupled equations with
...
- 575
1
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2
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180
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How to find the local maximum and minimum of a function
I am trying to find the local maximum and minimum of a function. The code below works if function is an exponential but when function involves a sinusoid, it does not give numerical values and instead ...
- 31
10
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5
answers
318
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How to help DSolve obtain this solution to $y'(x)=\sec (y(x))$
V 14
ode = Cos[y[x]]*y'[x] == 1
ic = y[0] == 2
DSolve[{ode, ic}, y[x], x]
Anything can be done to help DSolve obtain the following solution?
Hand solution
\begin{...
- 151k
1
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1
answer
56
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Laplace transform of special function
The Confluent hypergeometric function of first kind (aka Kummer's function) is defined as
$${\mathbf{M}}\left(a,b,z\right)=\frac{1}{\Gamma\left(a\right)\Gamma\left(b-a%
\right)}\int_{0}^{1}e^{zt}t^{a-...
- 111
1
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1
answer
142
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Derivative of a summation
I need to take the derivative of $\sum_{x=1}^{M}\sum_{a=0}^{J-1}\sum_{t=0}^{\infty}u(c(x,t+a,a),l(x,t+a,a))$ for a generic $c(y,s,b)$, or in other words:
$$\frac{\partial}{\partial c(y,s,b)} \sum_{x=1}...
- 13
0
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0
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50
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Function returning error every other run
Disclaimer: I am new to Mathematica but have some experience with other programming languages.
I have defined the following function (simplified version):
...
- 1
1
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0
answers
50
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Why does functional form of integration output depend on variables used?
The following integration code is identical, except for the use of integration variables x vs k and constants ...
- 1,061
1
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0
answers
48
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How to plot the contour for temperature in a wedge surface?
Through conformal mapping, the temperature distribution $T$ on a wedge sector can be obtained.
With Mathematica, how to display the distribution?
$$
T(x,y)=\frac{T_0}{\theta_0}\arctan\frac{y}{x}.
$$
...
- 243
3
votes
2
answers
301
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Eliminating complex numbers from solutions
In Maple
eq:=ln(y)-1/2*ln(1+y^2) = x-c1;
solve(eq,y)
In Mathematica
...
- 151k
1
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1
answer
58
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Errors in `NIntegrate` - or in coding?
As far as I know, if a set of functions f,g,h,... are all Riemann integrable then the definite integral of the sum f+g+h over ...
- 2,335
3
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2
answers
226
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How to calculate the PDF of product of two random variables from generalized gamma distributions?
Namely, we want to find the explicit formula of PDF of double Generalized Gamma distribution.
...
- 2,067
0
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0
answers
48
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Euler-Maclaurin method of integration
I am trying to calculate the following integral using the Euler-Maclaurin formula. However, when
𝑎a and 𝑏 are not integers but real numbers, defining the sum, for example, between 1/3 and 1/2, doesn'...
- 203
1
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1
answer
109
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How to derive a closed-form expression for the sum of this series?
Mathematica 14.0 on Windows produces
Sum[x^(9 + 6 k)/(9 + 6 k)!, {k, 0, Infinity}]
...
- 29.1k
1
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1
answer
98
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Integral of $1/\sin(y)$ in Wolfram Mathematica vs. Wolfram|Alpha
I was looking at solution of this ode using step-by-step in Wolfram|Alpha:
But in Mathematica V 14
Integrate[Csc[y], y]
gives
...
- 151k
2
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1
answer
92
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7
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3
answers
256
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Evaluating Integral
I am having trouble evaluating the following integral, which they say has a solution! Thanks.
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2
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1
answer
323
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Numerical Simulation of a Damped, Driven Nonlinear Wave System with Spatially Extended Initial Conditions
I am working on a project that requires creating a specific type of graph, but I am having trouble writing the correct code. The graph should look similar to the one I have attached below.
Could ...
2
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0
answers
53
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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
4
votes
1
answer
135
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Different result integrating with integer bounds vs floating point bounds
Someone posted this question at community
https://community.wolfram.com/groups/-/m/t/3178350
Since little attention is paid for it there, I thought here will get more.
...
- 151k
0
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3
answers
112
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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....
- 473
1
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1
answer
51
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FunctionConvexity of power function $x^a$
I'm trying to check convexity of some functions. I encoundered a problem with the line
...
- 15
1
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1
answer
90
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Separation of variables
Is it possible to replicate the same procedure of placing the functions that depend on $r$ on one side of the equation and on the other side leave the equations that depend on $\theta$ in Mathematica? ...
- 169
1
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1
answer
92
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`IntegrateChangeVariables` sometimes doesn't work
For example, the following simple code doesn't work:
IntegrateChangeVariables[
Inactive[Integrate][Sqrt[(1 + x)/(1 - x)] , {x, -1, 1}], t, (1 + x)/(
1 - x) == t]
...
- 2,295
0
votes
1
answer
69
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Asymptotic volume of intersection of n-cube with n-sphere [closed]
I would like to symbolically compute the following:
$$\lim_{d\to\infty} \frac{\text{Vol}(C^d(1) \cap B^d(K\sqrt{d}))}{\text{Vol}(C^d(1))}$$
where $B^d(r) = \{(x_1, \dots, x_d) \mid x_1^2 + \dots + x_d^...
- 1
1
vote
0
answers
66
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Why does the form of the region affect the integration results?
I try to integrate $e^{\sqrt{x^2+y^2}}$ on the region $x\ge y\ge 0 \&\& x^2+y^2\le4$. Obviously it can be solved by changing the variable.
Then I want to verify my result using the Mathematica ...
- 1,374
9
votes
1
answer
464
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Calculating relative error of Ramanujan formula for ellipse perimeter
On this page, they present the Ramajujan's second formula for the perimeter of an ellipse:
$$P \approx \pi (a+b) \left(1+ \frac{3 h}{\sqrt{4-3 h}+10}\right),$$
where $h=(a-b)^2/(a+b)^2$. They expand ...
- 179
0
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1
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94
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Vortex beam profile plot [duplicate]
I want to plot this type of plot for the Lagurree Gaussian beam
$\begin{aligned} u(r, \phi, z)= & C_{l p}^{L G} \frac{w_0}{w(z)}\left(\frac{r \sqrt{2}}{w(z)}\right)^{|l|} \exp \left(-\frac{r^2}{w^...
4
votes
1
answer
190
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Kernel quits while using ParametricNDSolve
I'm trying to reproduce the plots (Figure 1 and Figure 2) of this paper. The plots are obtained by solving the Eqs. 4.3 and 4.4. The boundary conditions described in section 3.3 for Eqn. 4.3 are ...
- 115
0
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0
answers
50
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NIntegrate with depended variables
I have problems in integrating a function with depended variables. I am pasting the code below
...
1
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1
answer
161
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Find the polar plane of the ellipsoid and integrate the Ellipsoid cap
I am working on writing a code to find the polar plane of an ellipse, and subsequently calculate the cap formed by subtending the point $p$ (red) onto a random ellipse.
I think I have managed to ...
- 633
2
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0
answers
57
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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
3
votes
1
answer
120
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Why does singular solution not satisfy the ode?
Should not singular solution also satisfy the ode itself? Since it is a solution.
Why does Mathematica V 14 in this example generate a singular solution which does not seem to satisfy the ode itself
<...
- 151k
1
vote
0
answers
59
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Symbolic integral with piecewise functions
I want to compute the following integral as a function of some positive real parameters, $a, \rho, \lambda$ and three positive real variables $L_a, L_b, L_c$:
...
- 405
0
votes
0
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110
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Integrate takes long time
This Integration does not return for hours, though I don't know why as the graph doesn't look all that complicated. Also NIntegrate returns the result instantly... but I need the exact value!
...
- 1,491
2
votes
1
answer
74
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Two-dimensional integral over data
I am trying to calculate the integral of the data. Following this post, I know what to do with a one-dimensional list. But, let's consider a simple function, just to show you, what I want to do.
...
- 133
2
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2
answers
279
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How to calculate a definite integral with a parameter
I am trying to calculate the following definite integral with the parameter H. So my result would like to be a analytical one with the parameter H. For example for the integral NIntegrate[ax, {x, 1, ...
2
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2
answers
89
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`Integrate` gives an imaginary part for a 1-d definite integral of a real-valued function
I'm using Integrate to evaluate an integral with known result:
$$\int_0^\pi \frac{\cos(n \theta)-\cos(n \theta_0)}{\cos(\theta)-\cos(\theta_0)} d\theta = \frac{\pi\...
- 2,295
0
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1
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62
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About a double integral [closed]
I try to use walfram mathematica to compute a double integral,
my code is
...
2
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1
answer
83
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Generate variables in multiple integral
I want to do a multiple integrate with n variables. When I change the value of n, I do not want to rewrite the variables in the integral manually like here:
...
- 185
3
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0
answers
163
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Mathematica gives zero for non-zero double integral?
Consider the following integral
$$\int_{-\infty}^{\infty} dy \int_{-\infty}^{\infty} dx\, \frac{1}{(xy+i)(x+y-i)^2},$$
where $i$ is the imaginary unit. I can evaluate this integral analytically using ...
- 187