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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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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 ...
Athanasios Paraskevopoulos's user avatar
1 vote
0 answers
34 views

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 ...
Kazi Abu Rousan's user avatar
3 votes
1 answer
110 views

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. ...
Nasser's user avatar
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1 answer
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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....
Sahabub Jahedi's user avatar
1 vote
1 answer
40 views

FunctionConvexity of power function $x^a$

I'm trying to check convexity of some functions. I encoundered a problem with the line ...
oanesdof's user avatar
1 vote
1 answer
81 views

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? ...
Dayzk's user avatar
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1 vote
1 answer
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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] ...
Jie Zhu's user avatar
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1 answer
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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^...
Capybara's user avatar
1 vote
0 answers
60 views

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 ...
houzw's user avatar
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9 votes
1 answer
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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 ...
Ytrewq's user avatar
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1 answer
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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^...
Himani Juneja's user avatar
4 votes
1 answer
176 views

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 ...
Entangled Quark's user avatar
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0 answers
45 views

NIntegrate with depended variables

I have problems in integrating a function with depended variables. I am pasting the code below ...
Ioannis Polopetrakis's user avatar
1 vote
1 answer
134 views

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 ...
MKF's user avatar
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2 votes
0 answers
51 views

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 ...
Physics Moron's user avatar
3 votes
1 answer
107 views

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 <...
Nasser's user avatar
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1 vote
0 answers
56 views

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 $L_a, L_b, L_c$: ...
Ruth Murphy's user avatar
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0 answers
17 views

Is it possible to find a closed-form expression for determinant of the $k+1$-dimensional three-diagonal matrix whose entries obey particular rules?

I have this $k+1$ dimensional three-diagonal matrix in which $k=0,1,2,3,...$. I want to compute its determinant. Of course, for each fixed $k$ it is easy to compute the determinant. My question. Since ...
charmin's user avatar
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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! ...
Steve237's user avatar
  • 435
2 votes
1 answer
55 views

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. ...
blahblah's user avatar
2 votes
2 answers
173 views

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, ...
Dinos Volanis's user avatar
2 votes
2 answers
75 views

`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\...
Jie Zhu's user avatar
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0 votes
1 answer
55 views

About a double integral [closed]

I try to use walfram mathematica to compute a double integral, my code is ...
Vanellope's user avatar
2 votes
1 answer
77 views

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: ...
Zsombor's user avatar
  • 185
3 votes
0 answers
156 views

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 ...
jkb1603's user avatar
  • 155
4 votes
0 answers
89 views

How to obtain the boundary of a two-dimensional ParametricRegion surface in order to apply Stokes' theorem to compute surface integrals?

On the help page of the SurfaceIntegrate, an example of Stokes' theorem is listed: Compute the Curl ...
lotus2019's user avatar
  • 2,141
1 vote
2 answers
116 views

Contour integral with radius infinite [closed]

How can I get compute a contour integral of the function $f(z)=\exp(i z)/z$ in the upper circle with center in $(0,0)$ and radius $R$? I want verify that $\lim_{R\to \infty}\int_C f(x)=0$ in ...
eraldcoil's user avatar
  • 203
1 vote
1 answer
40 views

Issue with FullSimplify in StirlingS2 definition

I have previously asked a question about a problem simplifying an expression in Mathematica. The solution was to expand the definition of StirlingS2. This time, I ...
Cardstdani's user avatar
0 votes
1 answer
38 views

Problem calculating mean of probability distribution

I have a discrete probability distribution where $P(X=x)=(Factorial[n]/(n^x))*StirlingS2[x-1,n-1]$. So, when trying to calculate its mean with the following property: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
Cardstdani's user avatar
3 votes
3 answers
306 views

Parabola from a focus and a directrix

The code below is an attempt to obtain the graph of a parabola from two pieces of information: a focus and a directrix. I am not able to get the correct graphical shape of the parabola. I appreciate ...
Rubens Vilhena Fonseca's user avatar
1 vote
0 answers
71 views

How can I ask Mathematica to give the explicit real form of the given function?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, ...
MsMath's user avatar
  • 195
4 votes
2 answers
113 views

Questions About the FunctionExpand Function

Today, while helping someone solve a problem, I encountered an issue with the Abs function in their expression. I needed to derive the ...
我心永恒's user avatar
  • 1,562
9 votes
3 answers
1k views

Taxicab Geometry

According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some ...
Rubens Vilhena Fonseca's user avatar
0 votes
1 answer
62 views

Trying to find divergence of 4-D second rank tensor

I want to find a divergence of a 2-rank 4-dimensional tensor(one time and three spherical spatial), and the following is the code I've tried. : ...
Deven Desai's user avatar
1 vote
3 answers
135 views

Maximum value of a constant in a function [closed]

I'm trying to find the maximum $B$ of the following function: ...
Dayzk's user avatar
  • 147
0 votes
1 answer
56 views

Convergent Taylor series unrecognized by Sum

I am trying to understand why Sum does not recognize a particular Taylor series as convergent. I have defined a function 'series' like this, that computes the Taylor series of a function 'f' at 'x', ...
Glenn Welch's user avatar
0 votes
0 answers
49 views

performance of the NDEigensystem and DEigensystem

I can't find any result and I can't understand what is going wrong. Any help please? My code is: ...
HarrisModel's user avatar
5 votes
1 answer
59 views

Integration of function in Mathematica where the variable has dimension

I want to Integrate a function $f(x)=\dfrac{1}{x-a}$ where both $x$ and $a$ have the dimension of length. After doing the integration in Mathematica it is returning the solution $\log(x-a)$. But here ...
darkphysics's user avatar
1 vote
2 answers
88 views

How to demonstrate the acceleration using spherical coordinates and spherical unit vectors?

I've been trying to use Mathematica to demonstrate using spherical coordinates and unit vectors the acceleration for a particle moving in a sphere. Nevertheless, I'm actually not that skilled in ...
not_aphysicsdr's user avatar
3 votes
3 answers
203 views

Finite Differences:

I am having difficulty implementing finite differences in the correct columns of my code. ...
Rubens Vilhena Fonseca's user avatar
3 votes
1 answer
65 views

Integral of interpolation function is not evaluated

I am having a misunderstanding with Mathematica about integration of InterpolatingFunction. Consider this example: ...
atapaka's user avatar
  • 3,962
0 votes
0 answers
37 views

Regarding Poincare section

I got a code from Mathematica to plot the Poincare section and in this code, so many initial conditions are taken at a time. The link and the code is given below. link ...
Arssat's user avatar
  • 81
0 votes
2 answers
58 views

How to find value of parameter for given number of maxima simpler?

Let us consider a function f[x_,a_]:=Exp[x]*Sin[a*x/5].The question is: how to find the minimum value of a parameter a > 0 s....
user64494's user avatar
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0 votes
2 answers
71 views

Comparing Closed-form to Numerical Integral Result

When I numerically calculate this integral NIntegrate[(1/2)*Log[1 + Sin[x]]^2, {x, 0, Pi}] The result is $0.416217488896557$ and I verified it using another tool....
Moo's user avatar
  • 3,334
0 votes
1 answer
106 views

Analytically solving this second order ODE

I try to solve this second order differential equations to get $\phi$: $$ 4 \Psi \left( \ddot{\phi}_0+ \frac{a^2}{2\phi_0}\dot{\phi}_0 \right) = -\ddot{\phi}+ \left( \frac{a^2 \mathcal{H}}{2\phi_0} ...
Dr. phy's user avatar
  • 287
0 votes
1 answer
130 views

Mathematica code to compute a constant

I am reading an interesting paper One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational by Zudilin. We fix odd numbers $q$ and $r$, $q\geq r+4$ and a tuple $\eta_0,\eta_1,...,\eta_q$ of positive ...
Max's user avatar
  • 145
2 votes
3 answers
148 views

Finding $\frac{\cos(b)}{\cos(a)}$ given $\cos(x) e^{i y} = \frac{\sin(a)}{\sin(a+b)}$ and $-i \sin(x) e^{i y} = \frac{\sin(b)}{\sin(a+b)}$

I have real $x$ and $y$, and I have the following implicit definitions of (complex) $a$ and $b$: $$\cos(x) e^{i y} = \frac{\sin(a)}{\sin(a+b)}$$ $$-i \sin(x) e^{i y} = \frac{\sin(b)}{\sin(a+b)}$$ I ...
user196574's user avatar
2 votes
0 answers
39 views

Take symbolic derivative of summation expression and display as unexpanded sum

My main problem here is two-fold: Take symbolic derivative of summation expression Stop summations from being "unrolled"/expanded, e.g., displayed as the sum of terms I also have some ...
ImagineBaggins's user avatar
0 votes
1 answer
64 views

Clear Guidelines for Symbolic Calculation With Units?

The following notebook performs a relatively simple physical calculation interacting position, velocity and acceleration of two charged point particles according to Weber electrodynamics.It is simple ...
James Bowery's user avatar
1 vote
0 answers
37 views

Integral within another integral [duplicate]

I have to evaluate the following integral: $I(k) = \int^{42}_{0} dt \hspace{0.1cm} 3t^3*e^{i \int_{0}^{t}dx( x^2 - \sqrt{x^4+k^2/x}) }/\sqrt{t^4+k^2/t}$ The answer in : Iterated integral numerically ...
Antonis Kyriazis's user avatar

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