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Questions tagged [calculus-and-analysis]

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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0 votes
1 answer
41 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? ...
2 votes
2 answers
189 views

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. ...
1 vote
1 answer
66 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 ...
0 votes
0 answers
43 views

Contour integral around a circle centred just off the origin [closed]

In the documentation, a Basic Example of ContourIntegrate is given as $1/z$ integrated along the unit circle: ContourIntegrate[1/z, z \[Element] Circle[]] which ...
0 votes
1 answer
128 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 \...
0 votes
0 answers
74 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 ...
0 votes
1 answer
355 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 ...
2 votes
2 answers
99 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? ...
0 votes
3 answers
99 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....
2 votes
1 answer
91 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]: ...
0 votes
1 answer
130 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 ...
3 votes
1 answer
122 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 ...
0 votes
1 answer
43 views

LineIntegrate seemingly does not work

The scalar line integral function seemingly does not work, the both expressions remain unevaluated: ...
5 votes
3 answers
719 views

Mathematica integral wrong

I need to evaluate the following integral: ...
1 vote
1 answer
320 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 ...
0 votes
0 answers
41 views

Issue solving recurrence relation

I´m trying to solve the following recurrence relation: ...
1 vote
2 answers
121 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 ...
3 votes
2 answers
290 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: ...
1 vote
2 answers
132 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 ...
1 vote
1 answer
41 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 ...
0 votes
0 answers
77 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: ...
1 vote
2 answers
162 views

Problem with evaluation of integral

My code is creating an error when I try to evaluate an integral. Could I ask you to reproduce this code and see what is wrong? Thank you. Here I simply define two variables: Find ...
1 vote
2 answers
116 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 ...
0 votes
1 answer
203 views

Symbolic partial differentiation of a Lagrangian function including a summation

I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
13 votes
1 answer
1k views

Could anyone please suggest me MATHEMATICA code to solve Fractional-Order Time Delay Differential System?

We are familiar that the Predictor-Corrector Algorithm is applied to solve the Fractional-Order Differential systems. I need to solve the following Fractional Order Delay Differential System. Please ...
1 vote
1 answer
94 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 ...
1 vote
1 answer
170 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 ...
4 votes
3 answers
252 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 ...
3 votes
0 answers
129 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'...
9 votes
8 answers
742 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 ...
0 votes
0 answers
50 views

Numerical Integral and Partial Differentiation Of a Complicated Expression

I need help plotting Figures 1 and 2 solving EQ 36 and 37 from https://arxiv.org/pdf/2310.12445. here I am trying to find \Gamma,\phi and their Q values for ...
0 votes
1 answer
54 views

Finding an increasing or decreasing function

I have a problem where I am given the derivative of a function, asked to graph it, then state where it is increasing or decreasing using Mathematica. f'(x)=(x^2-3^x)/2x 0<x<4 I've tried the line ...
1 vote
2 answers
147 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 ...
0 votes
2 answers
80 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 ...
0 votes
1 answer
49 views

Checking the sign value of the derivatives of a complicated function

Consider the following function: ...
2 votes
1 answer
162 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 ...
2 votes
2 answers
96 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 ...
0 votes
1 answer
129 views

Is it possible to get rid of `Root` and have an explicit closed-form solution for the given equation?

I want to solve the given equation for m>0 where all parameters are Reals and a<0. ...
4 votes
3 answers
296 views

Plotting a parametric function on xy, xz, and yz planes

I'm trying to plot a trefoil with a parametric function in Mathematica. How would I do that? I know I can use Parametric3D to depict all of it but how do I project it on the XY, XZ, and YZ planes? It'...
4 votes
4 answers
220 views

How to get multiplication of the elements of a specific list/matrix

Assume there is a list: List1={a,b,c,d}; Then I want to get these calculation: ...
1 vote
1 answer
62 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....
3 votes
3 answers
351 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}]
8 votes
1 answer
547 views

Finding Euler spiral convergence point for powers other than 2

I'm playing around with Euler spirals, using a variable power to see how the plot changes, $ \left\{\begin{matrix} x = \int_0^s \cos \left ( s^n \right ) ds \\ y = \int_0^s \sin \left ( s^n \right ) ...
0 votes
1 answer
165 views

Concept of tangent and residual in AceFem and automation

here trying to solve the pde: ut + ux = 0 in acefem. I have two questions regarding tangent and residual. Tangent shows the s$$ and residual shows ...
5 votes
5 answers
250 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 ...
0 votes
5 answers
370 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 ...
0 votes
1 answer
44 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 ...
1 vote
3 answers
330 views

Slope of a line

Just a quick question. Is there a fast inbuilt function to calculate the slope of a line segment passing through two points {p11,p12} and ...
2 votes
1 answer
36 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 ...
1 vote
2 answers
128 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_{-\...

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