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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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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 ...
kahless96's user avatar
9 votes
5 answers
308 views

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{...
Nasser's user avatar
  • 147k
1 vote
1 answer
53 views

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-...
K.K.McDonald's user avatar
1 vote
1 answer
104 views

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}...
Marco's user avatar
  • 13
0 votes
0 answers
50 views

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): ...
Leksa99's user avatar
1 vote
0 answers
50 views

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 ...
WillG's user avatar
  • 980
1 vote
0 answers
43 views

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? $$ T(x,y)=\frac{T_0}{\theta_0}\arctan\frac{y}{x}. $$ ...
MathArt's user avatar
  • 243
3 votes
2 answers
250 views

Eliminating complex numbers from solutions

In Maple eq:=ln(y)-1/2*ln(1+y^2) = x-c1; solve(eq,y) In Mathematica ...
Nasser's user avatar
  • 147k
1 vote
1 answer
57 views

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 ...
Richard Burke-Ward's user avatar
3 votes
2 answers
209 views

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. ...
138 Aspen's user avatar
  • 1,683
0 votes
0 answers
42 views

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'...
capea's user avatar
  • 191
1 vote
1 answer
102 views

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}] ...
user64494's user avatar
  • 27.3k
1 vote
1 answer
92 views

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 ...
Nasser's user avatar
  • 147k
2 votes
1 answer
90 views

Integrate regions in Plot/Piecewise

I have the following code: ...
vladpopovcev's user avatar
7 votes
3 answers
243 views

Evaluating Integral

I am having trouble evaluating the following integral, which they say has a solution! Thanks. ...
Chan 13's user avatar
  • 71
2 votes
1 answer
268 views

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
2 votes
0 answers
48 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
4 votes
1 answer
127 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
  • 147k
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....
Sahabub Jahedi's user avatar
1 vote
1 answer
45 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
84 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
  • 157
1 vote
1 answer
84 views

`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
  • 1,811
0 votes
1 answer
67 views

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
64 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
  • 811
9 votes
1 answer
427 views

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
  • 179
0 votes
1 answer
70 views

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
181 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
0 votes
0 answers
49 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
143 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
  • 613
2 votes
0 answers
56 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
112 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
  • 147k
1 vote
0 answers
59 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
0 votes
0 answers
20 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
  • 1,169
0 votes
0 answers
105 views

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
  • 523
2 votes
1 answer
72 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
  • 133
2 votes
2 answers
201 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
82 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
  • 1,811
0 votes
1 answer
60 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
80 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
160 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
  • 187
4 votes
0 answers
91 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
  • 2,151
1 vote
2 answers
131 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
43 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
41 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
314 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
73 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
115 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
  • 1,572
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
65 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
137 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
  • 157