All Questions
Tagged with derivative or calculus-and-analysis
5,241 questions
2
votes
3
answers
201
views
How to fix this "wrong" analytical integral evaluation?
Integrate[(1/Sqrt[(x + 1)^2 + 1])*(1/Sqrt[1 + x^2]), {x, 0, 1}]
yields
...
- 1,061
0
votes
0
answers
104
views
How to use mathematica for differential geometry
I would like to learn how to efficiently use mathematica for differential geometry and tensor analysis. I googled it and mostly found some old references to packages. I wonder if there is a good ...
- 333
0
votes
0
answers
39
views
Integration or numerical integration over one variable out of many variables
I have a function defined as
AFB = (6*I6parSMM)/(2*(3*I1cparSMM + 6*I1sparSMM - I2cparSMM - 2*I2sparSMM));
where the I'parSMM's are functions of other variables s, ...
- 111
1
vote
1
answer
144
views
I want to plot the group delay of the following mathematica code but it takes too long time
I am working on a Mathematica project where I want to plot the group delay. The problem is this code is running too slow. Is there any possibility of speeding up the code?
Here is the original code:
<...
- 27
0
votes
0
answers
53
views
How to calculate the average stream velocity from the segmentation of video frames?
I have a 10 second video of a river flowing. I want to calculate the velocity of the river flow using optical flow. In this operation, I used the ImageDisplacements ...
- 195
2
votes
1
answer
158
views
How can I find a condition for convergence of an integral? [closed]
Wolfram|Alpha says that
$$ \int_0^\infty \frac{x^n}{(x-1)(x-2)} dx=\pi (1-2^n)(\cot(\pi n)+i)$$
for $\text{Re}(n)>-1$. However, for $n=0$, it says the integral doesn't converge, even though it has ...
- 123
9
votes
4
answers
535
views
Represent and evaluate an infinite expression
I am trying to represent this in Mathematica, then evaluate it:
...
- 1,491
2
votes
2
answers
225
views
Integrate result differs from what's expected
Trying to get a result for this Indefinite integral:
Integrate[1/(2*(x^4 + x^2 + 1)), x]
Mathematica v14 provides this result:
...
- 1,491
0
votes
1
answer
79
views
Difference between the two forms of derivates
Can anyone explain the difference between these two forms of derivatives:
f^(1,0)
and
D[f,x]
where ...
- 47
0
votes
0
answers
44
views
Reliability of DSolve to ensure existence of analytic solutions
So I've been wondering about this for a long time. Of course, Mathematica DSolve can be a monster slayer sometimes but as Mathematica as it can get, the output results usually tend to be not ...
- 1
2
votes
3
answers
235
views
Contour integration over lower half of complex plane
I need to perform this integration as a contour integral over the lower half of the complex omega plane with Mathematica.
$$\int_{-\infty }^{\infty } \frac{e^{-i \left(\omega -\omega _0\right) (t-\tau ...
- 29
1
vote
2
answers
74
views
1
vote
2
answers
76
views
Why is the result of this integration coming out as a list if the function being integrated just returns a numerical value?
I am trying to integrate over a Dirichlet distribution. Instead of using the built-in function, I defined it myself as:
...
- 11
3
votes
1
answer
102
views
Many contradictory results for a single integral
I am interested in solving the integral $$
\int_{\mathbb{R}} dx \frac{e^{i a x^2}}{(x - b - ic)^d(x - b + ic)^d}
$$
for $a,b,c \in \mathbb{R}$ and $d \in \mathbb{N}$. As an early step, I have asked ...
- 131
1
vote
1
answer
79
views
Is there a more efficient way to calculate the variance of a random variable given two sets of data?
Given two lists, one being the values of a random variable and the other being their corresponding probabilities, how can we calculate the variance of the random variable?
...
- 1
2
votes
2
answers
146
views
Incorrect limit involving hyperbolic Kepler equations
I’m trying to work with the Kepler equations for a hyperbolic trajectory in the case of a repulsive force (see Wikipedia for the attractive case). The trajectory can be described by the right branch ...
- 21
0
votes
0
answers
83
views
How to Handle First Variation with Symbolic Computation in Mathematica?
Background
I am currently working on a problem related to surface tension and found a research paper that appears to have the information I need. I am attempting to replicate the calculations in this ...
- 165
2
votes
2
answers
106
views
Why does Replace function not work the first time I try it?
Please explain why in the following mathematica code, the cos term was not replaced in the first try, but got replaced in the second try?
...
- 121
2
votes
1
answer
98
views
How to handle undefined Integral results for excluded conditions in Mathematica
I have a mathematical function where both input parameters x and y are real numbers within the interval [−π,π]:
...
- 1,648
0
votes
1
answer
48
views
LineIntegrate seemingly does not work
The scalar line integral function seemingly does not work, the both expressions remain unevaluated:
...
- 3,712
3
votes
1
answer
128
views
How to run Integrate[Sqrt[(x - a)^2 + (y - b)^2 + (z - c)^2], Element[{x, y, z}, Ball[{0, 0, 0}, 1]], Element[{a, b, c}, Ball[{0, 0, 0}, 1]]]
I find that MMA cannot run the integral below
...
- 1,147
0
votes
0
answers
44
views
1
vote
1
answer
45
views
Allan Variance integral for a first order Markov process
I am using Mathematica to solve this definite integral:
4*(q*T)^2*Integrate[(Sin[Pi*f*t])^4/(Pi*f*t)^2/(1 + (2*Pi*f*T)^2),
{f, 0, Infinity}]
$T$ and $t$ are real ...
3
votes
2
answers
312
views
Problem computing a limit
I have the following function in Mathematica:
$\frac{x! \sum _{i=1}^j (-i+j+1) S_{j+1}^{(-i+j+2)} x^{-i+j+1}}{(x-j)! \left((1-x)_j\right){}^2}$
Defined as:
...
- 197
0
votes
0
answers
81
views
Troublesome output of summation's derivative
I am trying to compute a derivative of a nested sum, but I can't avoid Mathematica to output Kronecker deltas and unexpected cases on complex numbers.
Consider the following setting:
...
- 3
2
votes
2
answers
156
views
Convergence of $\left\{n!\sum_{k=1}^{n!}\frac{1}{k^{\frac{3}{2}}}\right\}$ as $n\to \infty$ using Mathematica or otherwise
Using Mathematica or otherwise, I need to find the convergence or divergence
of$$\lim_{n\to\infty}\left\{n!\sum_{k=1}^{n!}\frac{1}{k^{\frac{3}{2}}}\right\}$$ where $\{x\}$ denotes the fractional part ...
- 301
1
vote
2
answers
119
views
NDsolve does not solve equation
I have a question for system of ordinary differential equations, because Mathematica does not give the solution. To be more specific, it does not give any sign that there is some problem. There is the ...
1
vote
2
answers
171
views
Integration of Gaussian functions takes ages
I am trying essentially to compute a fourier transform with Integrate.
1]Is integrate faster or slower than FourierTransform?
2]Does anyone know how to efficiently calculate these integrals?
My code ...
- 11
1
vote
1
answer
185
views
What methods can quickly determine the coefficient of determination of the data?
The given data is:
x = {0.04, 0.06, 0.04, 0.08, 0.08, 0.05, 0.05, 0.07, 0.07, 0.06};
y = {0.25, 0.4, 0.22, 0.54, 0.51, 0.34, 0.36, 0.46, 0.42, 0.4};
Is there a ...
- 1
3
votes
0
answers
131
views
Trivial Mathematica integral on a cube not computing
I was trying to evaluate some intergal over some cube with variable side length, but for some reason Mathematica spit out the input. The interand was sufficiently nice that I couldn't believe it didn'...
- 208
5
votes
3
answers
762
views
1
vote
2
answers
174
views
Confused about the output of `CosIntegral`
I am interested in the properties of the cosine integral function, in this case the anti-derivative of Cos[Pi*x]/x, which Mathematica evaluates to ...
- 2,335
0
votes
1
answer
49
views
Checking the sign value of the derivatives of a complicated function
Consider the following function:
...
- 765
0
votes
2
answers
92
views
Integration with respect to functions
I observe some strange behaviour of Mathematica when pulling functions into the integrator. I know that Mathematica's capabilities are limited when computing Stieltje or Lebesgue Integrals. But even ...
- 187
4
votes
3
answers
294
views
How is the result of this integral obtained by the function `Integrate`?
When I use Mathematica to calculate
$$
\int_0^{+\infty } \frac{\log (1-\mathrm i x)}{1+x^2} \, \mathrm dx ,
$$
I get different results using functions NIntegrate ...
- 433
2
votes
2
answers
103
views
Partial Derivative after Numerical Integration of a Complicated Expression with Singularity at Zero
I want to generate Fig no. 2,3,4 from https://arxiv.org/pdf/2212.08237
with the help of the following equations. In Fig 3 t_(opt) is the time Q_T reaches its max value Q_T(opt) for each T.
Here is ...
- 297
1
vote
1
answer
100
views
StreamPlot3d for the magnetic field of a loop
I am trying to go beyond StreamPlot in the case of a current loop that produces a magnetic field. My code works for StreamPlot, but does not end when I use the same field expressions with StreamPlot3D....
- 55
3
votes
3
answers
394
views
Integration of the product of two exponential functions
How can I find the value of this integral?
Integrate[E^((-b)*t^a - k*t), {t, 0, Infinity}]
- 1,116
0
votes
1
answer
47
views
Integrate diverges for convergent integral, and returns unnecessary condition
I'm trying to solve an infinite integral using Mathematica. For some reason, Mathematica claims the integral diverges although when solving to a finite limit L and ...
- 433
2
votes
1
answer
40
views
Describing the region of integration $\mathbb{R}_+^n$ for arbitrary $n$
Let $f_n:\mathbb{R}^n \to \mathbb{R}$. I would like to know an elegant way of writing the integral
$$ I_n = \int_{\mathbb{R}^n_+} f_n(x)~\mathrm{d}x $$
in Mathematica.
For fixed $n$, the best I could ...
- 123
0
votes
5
answers
382
views
Possible bug in partial derivative [closed]
In 14.0 on Windows 10 let us consider
D[Min[x, y], x]
Piecewise[{{1, x - y <= 0}}, 0]
As I understand it, the result is ...
- 29.1k
9
votes
8
answers
773
views
Numerical approximation of the integral by using data
I want to use the numerical approximation of the integral of a function given a list of data:
$$\int_a^bf(x)dx\approx\sum_{k=1}^N\frac{f(x_{k})+f(x_{k-1})}{2}(x_{k}-x_{k-1}),$$
where $f(x_0)=f(a)$ and ...
- 685
5
votes
5
answers
294
views
Integration involving Piecewise function and DiracDelta function
I want to calculate an integration, which reads
where $\delta\left(q_{23}^{01}\right)=\delta\left(1+q_1-q_2-q_3\right)$ and $\mathrm{min}(1,q_1,q_2,q_3)$ means the minimum of $(1,q_1,q_2,q_3)$.
What ...
- 495
1
vote
1
answer
66
views
Checking the formula for solving the Poisson equation with an integral over all of space
EDIT: According to 2.2.3 Rigorous derivation, if we find the integral $u(x,y) = \int \int G(x,y,m,n)f(m,n) dm dn$ then we obtain a function that satisfies the Poisson equation $\nabla^2u(x,y)=f(x,y)$. ...
- 2,494
1
vote
2
answers
120
views
How can I check integration $\int_0^c \exp\left(-ax+\frac bx\right)~dx$?
I am trying to integrate
$$\int_0^c \exp\left(-ax+\frac bx\right)~dx$$.
I proceed manually in this way (according to https://math.stackexchange.com/questions/2978887/primitive-of-exp-a-times-x-frac-bx?...
3
votes
1
answer
84
views
How to add a custom analytical integration to integration library
How can I add an unknown analytical integral in Mathematica to its integration library so that the Integrate routine, e.g. ...
- 31
3
votes
3
answers
172
views
Issue in HypergeometricPFQ function:
I have a solution from integral:
A = Integrate[x^n*(1 + x)^n*Exp[-n*x^2] /. n -> 1, {x, 0, Infinity}] //Expand
(*1/2 + Sqrt[π]/4*)
%//N
(*0.943113*)
Then I ...
- 16.6k
1
vote
2
answers
140
views
Solution of an implicit integral equation
The present question is pretty similar to this one.
Here I want to find the solution of the following implicit integral equation:
$$
P_H(u)=\int_{-\infty}^\infty dJ \int_{-\infty}^\infty du_1 \int_{-\...
- 405
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 \...
- 1
4
votes
3
answers
414
views
Why is DSolve unable to solve this first order homogeneous ode with IC?
This is first order homogeneous ode from undergraduate textbook, which can be solved using standard $y=u x$ change of variables. But DSolve can't. Could someone figure out why? I show below that ...
- 151k