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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Why does Area produce finite values for this area? [closed]

Let us consider in 13.3.1 on Windows 10 the region reg = ImplicitRegion[{x*y >= 8, y >= 8 x^3, y <= 27}, {x, y}]; and its area ...
user64494's user avatar
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The relationship between dependent decision variables in a function

Given objective function f(x1,x2,x3) in a optimization problem, and don't know if all these variables are independent or not. How to know if dx2/dx3 is greater/less than/equal to zero. I could
Doublehappy Tough's user avatar
1 vote
2 answers
252 views

How to interpolate an implicit function?

chi(t) is implicit function. The implicit function can be plotted by ContourPlot. Is it possible to obtain chi(t) explicitly using function interpolation? ...
Mam Mam's user avatar
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Why doesn't NMinimize work with NSolve?

Why does NMinimize throw the error and how to fix it? ...
Mam Mam's user avatar
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1 vote
3 answers
120 views

Gaussian integral not converging

I have a large Gaussian integral to evaluate, and Mathematica claims it does not converge: ...
Pedro Hablespanyos's user avatar
3 votes
1 answer
153 views

Accuracy of numerical solutions provided by pdetoode

I am interested in solving the following differential equation using pdetoode (you can find pdetoode here). ...
umby's user avatar
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-2 votes
1 answer
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Help with limit without using Taylor series [closed]

I would like help solving the following limit: $\lim_{x \rightarrow 0} \frac{x^6 - \arctan(x^6)}{(x - \sin(x))^6}$, but I do not want to use Taylor series. It would be nice to have an answer that does ...
Seven9's user avatar
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1 answer
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Can the Debye functions be implemented using built-in functions?

It is claimed in the comments here that the Debye functions can be implemented using built-in special functions. This is clearly true for some Debye functions, e.g., $D_n^{(1)}(x)$ for $n = 1, 2, 3$ (...
WillG's user avatar
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2 votes
4 answers
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Plot the surface $xy+z=1$, plane $x+y+z=1,$, and their curve of intersection in different colors

Plot the surface $x y + z = 1$, plane $x+y+z=1$, and their curve of in intersection in different colors.
Parker James's user avatar
0 votes
2 answers
163 views

Sierpinski Triangle and Benford's Law (Edit)

I would like some help solving the following problem using Mathematica: Show that, no matter what the initial area of an equilateral triangle is, the sequence of areas (painted in black) of the ...
Rubens Vilhena Fonseca's user avatar
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2 answers
93 views

Finding the maximum of a equation

Hi guys I have the following function $R_t = \exp(-2 k_x^2 \sin^2(\frac{t}{2})) k_x^2 \theta(t) \bigg[ -\sin(2t) - \sin(t) (1 - k_x^2 \sin^2(t)) \bigg]$ and I want to find the maximum value of it. I ...
Lohrasb's user avatar
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How to calculate the depth of the lake in mathematica?

I want to calculate mean depth of Goose lake (mean depth=4.6 m), I use bellow command for this operation, But this command is not automatic and we have to create the coordinates manually, and on the ...
Erfan's user avatar
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How to give conditions and solve an integration? [closed]

I want to solve an integration, $\int \frac{da}{\sqrt{\frac{8 \pi G \Lambda}{3}a^2 - K +c_1 a^{-(3k+1)}}}$ Here, how to give conditions k $\ge$ 0, G$>$ 0, $\Lambda$ $>$ 0 and K can be zero, ...
apk's user avatar
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1 answer
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Dirac Delta does not converge

I have trouble evaluating a simple integral in Mathematica. I have the code: ...
Nitaa a's user avatar
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2 answers
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Mathematica gives wrong answer to integral of $\ln(x^x)$ [closed]

I want to calculate $\int \ln\left(x^x\right) \, \mathrm{d}x$. It seems that the result is wrong since integrating first and then taking derivative, the result should be the original function, but it'...
Baboo J. Cui's user avatar
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2 answers
102 views

How do I find the derivative of y^n=x? [closed]

impartial differentiation. I have already logged both side and gotten to nln(y)=ln(x) then differentiated, but then it just turns into a mess and the last place I got to was y(1-xln(y))/(xn)
Mathguy's user avatar
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How do I integrate over this region?

I want to compute this integral: $$\int_{\Omega}e^{i\sum_{n=1}^{N}\frac{(p_n+p_{n-1})(q_n-q_{n-1})}{2}}dq_1\cdots dq_{N-1}dp_1\cdots dp_{N-1}\,,$$ where $$\Omega=\{|q_n-q_{n-1}|<\epsilon,\, |p_n-p_{...
JLA's user avatar
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How to estimate Lake area and volume in Mathematica?

I have a satellite image of the lake and I want to estimate its area and volume. Actual volume:1.49*10e8 m^3 Actual Area:36.9 km^2 I did the following command to find the volume, but it is not very ...
Erfan's user avatar
  • 159
2 votes
2 answers
78 views

Restrict the background colour in a ParametricPlot region

I am trying to plot this diagram, distinguished into three separate regions by the white curve. The code that I used for this purpose is provided below: ...
codebpr's user avatar
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Iteration show different values in solving a pde in mathematica

I have a pde given below: $u_{t}-u_{xx}+\frac{1}{4}u=0, $ with boundary conditions $u(0,t)=1,\ \ u(1,t)=\frac{1}{2}e^{\frac{-t}{4}}+e^{\frac{-1}{2}},$ where $0\leq x\leq 1$. If the initial iterate is $...
Junaid Ahmad's user avatar
2 votes
2 answers
94 views

Computing a limit with assumptions

This program solves the recurrence for the expected time to extinction of a linear birth and death process with arrival rate A and death rate q A, and then attempts to simplify. ...
florin's user avatar
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1 answer
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How to force Wolfram 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 ...
Denis D. Bavrin's user avatar
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1 answer
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Why am I not getting a result? Can you please help me take a look? [closed]

Why am I not getting a result? Can you please help me take a look? I really appreciate it. ...
Weixin's user avatar
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1 answer
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Piecewise integration doesn't evaluate

I'm trying to integrate the following function: $$q(d, \theta) = q_x(d, \theta) + q_y(d, \theta) - 2q_x(d, \theta) q_y(d, \theta)$$ where $q_x(d, \theta) = \min\left(2 - d\cos\theta, d\cos\theta\right)...
Reality Check's user avatar
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How do I find the definite double integral of a real number over a complex region?

This is a follow-up question of How do I take the integral of a real number over a complex region? Given that $\tau'$ is imaginary, how would you calculate the definite double integral over a complex ...
Quark Soup's user avatar
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1 vote
1 answer
108 views

Extend the code for more variables (at least 100)

I have this code (not in best shape) for a problem in 3 variables. It does the job. The problem is I want to extend this to more number of variables around 100 at least. It is very painful to extend ...
Learner's user avatar
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7 votes
2 answers
636 views

The Poincaré Sections of Yang-Mills-Higgs System [closed]

In the papers Quantum Chaos in a Yang-Mills-Higgs System and DIFFERENT FACETS OF CHAOS IN QUANTUM MECHANICS, the authors have plotted three Poincaré sections for different values of ...
user84456's user avatar
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3 votes
4 answers
306 views

Volume of Region Contained by 3D Data Points

I have a dataset consisting of (x,y,z) data that describe a surface, and I need to find the volume of the region bounded by that surface. The data do not follow any mathematical equation, but the ...
John's user avatar
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1 answer
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I am trying to plot the function below, however, it does not seem to be working [closed]

Do you know what I am doing wrong? The image I put below shows the function I would like to plot.
Josh T's user avatar
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3 votes
1 answer
94 views

Using GraphicsGrid for density plots with color scales

I would like to arrange the density plots in a certain order using GraphicsGrid. But when using GraphicsGrid, there is problem with the color scale, it doesn't display completely. How should ...
Mam Mam's user avatar
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2 votes
2 answers
476 views

Mathematica and WolframAlpha gives wrong result about DiracDelta function

Wolfram alpha says the integral does not converge and also Mathematica didn't give answer to the integral: $$\int_0^t\delta(z)\delta(t-z)dz$$ which should gives the result of $\delta(t)$ as you will ...
Mohamed Mostafa's user avatar
1 vote
1 answer
77 views

What are some ways to speed up calculations

Below is the code for calculating the eigenfunctions and eigenvalues of the following system: $HC[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)-\frac{1}{\sqrt{\rho^2+z^2}}u(\rho,z)+\frac{B^2}{8}\rho^2 u(\...
Mam Mam's user avatar
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4 votes
3 answers
218 views

Integration involving two DiracDelta with variable limit

I want to write a code to evaluate $$ \int_0^{t-1}\frac{\delta(z-1)}{z}\frac{\delta(t-z-1)}{t-z}dz$$ which should gives the answer $$\frac{\delta(t-2)}{t-1}.$$ I tried to write the code ...
Mohamed Mostafa's user avatar
2 votes
2 answers
170 views

Ramanujan identity [closed]

$$\sum _{j=1}^{\infty } \frac{1^j}{\sqrt{j} \left(\sqrt{j-1}+\sqrt{j}\right)^2}=\left(\sqrt{2}+1\right) \sum _{j=1}^{\infty } \frac{(-1)^{j+1}}{\sqrt{j}}$$ although numerically they do not coincide ...
Capeamate's user avatar
2 votes
1 answer
58 views

Plot several graphs of a function density distribution using Table

I would like to plot the density distribution graphs of the eigenfunction en[B][[2, 1]] when a parameter B is changed. But the ...
Mam Mam's user avatar
  • 1,753
1 vote
1 answer
85 views

Plot wavefronts of Laguerre-Gaussian modes

I am trying to plot wavefronts of Laguerre-Gaussian modes, and want to show the changing number of twists with the change in l values. If anyone has the code or any insights. Kindly help me about it. ...
Qubit's user avatar
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0 votes
1 answer
109 views

For parametrized functions, can we determine function range directly? [closed]

H[t_] = Log[t] - (t - 1)/(λ t + μ) The definition domain and the parameter ranges for the function H are: ...
csn899's user avatar
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1 vote
1 answer
330 views

Why can't Mathematica do an easy integral?

Mathematica can't do this integral: $\int \sqrt{1-x^2} \cos ^{-1}(x) \cos ^{-1}\left(\sqrt{1-x^2}\right) dx$ However if I replace $\cos ^{-1}\left(\sqrt{1-x^2}\right)$ with $\frac{\pi }{2}-\sin ^{-1}(...
user1477339's user avatar
1 vote
2 answers
128 views

How to do edge detection in Mathematica?

I have some pictures of water level and I want to do edge detection, I used the following command, but this command is vertical edge detection and I want horizontal edge detection and water level. ...
Erfan's user avatar
  • 159
0 votes
1 answer
59 views

How to make a density plot for an isotropic function written in cylindrical coordinates?

$f(\rho,z)=2\rho^2+\frac{2}{3}z^2 \quad$ is a function in the cylindrical coordinate system $(\rho,\theta,z)$ The function $f(\rho,z)$ is isotropic because it does not depend on the angle $\theta$. ...
Mam Mam's user avatar
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4 votes
1 answer
163 views

Calculating integral with exponential function and parameter

I want to calculate this integral but Mathematica does not solve it. Why? Can it be solved by Mathematica? ...
lia's user avatar
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3 votes
1 answer
174 views

Extremum of the graph of a function has integer coordinates

Graph of the fuction $y=\dfrac{(x-26)(x+9)}{(x+14)(x+19)}$ has maximum point and minimum point are (-16,-49) and (-4,-1) whose ...
Laurenso's user avatar
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3 votes
1 answer
112 views

How can I check all results in this code about the extremum of a function?

I am trying to find three integer numbers, a, b, m, so that the function $$x^3/3 + a (m + 1) x^2/2 + b (m^2 - 5 m) x$$ have $x=2$ is a maximum point of the function....
Laurenso's user avatar
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1 vote
0 answers
28 views

Generator of limits of successions according to type of indeterminacy. Correct syntax

I am trying to make a limit generator with 3 columns, number of the exercise, the second column is the limit (perfectly written with n-->00), and the third column is the result of the limit. I have ...
wilma's user avatar
  • 11
2 votes
1 answer
48 views

How to explore the unchanged eigenvalue with the largest real part?

The provided code below employs the Chebyshev collocation method to calculate eigenvalues. I'm interested in examining the eigenvalue with the largest real part while ensuring it remains almost same ...
Fun123's user avatar
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4 votes
1 answer
305 views

What are some Mathematica packages used for general relativity?

Could you suggest any Mathematica packages that are used for General relativity calculations? Id like to write code to solve the Schwarzchild Lagrangian equation.
Rishabh sharma's user avatar
2 votes
2 answers
207 views

Performing maximum likelihood estimation for SIR Model

The code first produces a plot of the dataset, then simulates the SIR model using the parameter values we found in the manual calibration to the full dataset of the total number infected . ...
Athanasios Paraskevopoulos's user avatar
5 votes
3 answers
358 views

Integral involving $\cosh$

How can I calculate the following integral using Mathematica? $$\int_{-\infty}^{\infty} \frac{\mathrm{d} x}{\left(1+x^2\right) \operatorname{ch} \frac{\pi x}{2}} = 2 \ln 2$$ I tried: ...
lotus2019's user avatar
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1 vote
1 answer
82 views

Proving an expression from Mathematica which is clearly visible from Plots

I have the following Mathematica code: ...
codebpr's user avatar
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0 votes
0 answers
68 views

Find knee by intersecting line method

I have an x-y data list. The data is here. It looks like below: I want to mark the knee location. I mean I need to find the point of greatest slope change and get the x coordinate of this point. ...
Mr.2023's user avatar
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