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.
4,921
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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
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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
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2
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252
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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?
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- 1,753
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91
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Why doesn't NMinimize work with NSolve?
Why does NMinimize throw the error and how to fix it?
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- 1,753
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3
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120
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Gaussian integral not converging
I have a large Gaussian integral to evaluate, and Mathematica claims it does not converge:
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3
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1
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153
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Accuracy of numerical solutions provided by pdetoode
I am interested in solving the following differential equation using pdetoode
(you can find pdetoode here).
...
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1
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56
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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 ...
- 119
1
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1
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113
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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 $n = 1, 2, 3$ (...
- 854
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4
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105
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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.
- 21
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2
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163
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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 ...
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2
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93
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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 ...
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133
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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 ...
- 159
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64
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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, ...
- 307
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1
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94
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Dirac Delta does not converge
I have trouble evaluating a simple integral in Mathematica. I have the code:
...
- 698
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2
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136
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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'...
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2
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102
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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)
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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_{...
- 151
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120
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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 ...
- 159
2
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2
answers
78
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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:
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141
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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 $...
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2
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2
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94
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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.
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- 1,592
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78
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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 ...
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1
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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.
...
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1
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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)...
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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 ...
- 1,560
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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 ...
- 219
7
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2
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636
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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 ...
- 1,524
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306
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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 ...
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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.
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votes
1
answer
94
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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 ...
- 1,753
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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$$
which should gives the result of $\delta(t)$ as you will ...
- 286
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What are some ways to speed up calculations
Below is the code for calculating the eigenfunctions and eigenvalues of the following system:
$HC[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)-\frac{1}{\sqrt{\rho^2+z^2}}u(\rho,z)+\frac{B^2}{8}\rho^2 u(\...
- 1,753
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3
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218
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Integration involving two DiracDelta with variable limit
I want to write a code to evaluate
$$ \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}.$$
I tried to write the code
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- 286
2
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2
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170
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Ramanujan identity [closed]
$$\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 ...
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1
answer
58
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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 ...
- 1,753
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1
answer
85
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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. ...
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109
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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:
...
- 2,879
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1
answer
330
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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}(...
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2
answers
128
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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. ...
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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$. ...
- 1,753
4
votes
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answer
163
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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?
...
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1
answer
174
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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 ...
- 1,000
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1
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112
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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$$ have $x=2$ is a maximum point of the function....
- 1,000
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Generator of limits of successions according to type of indeterminacy. Correct syntax
I am trying to make a limit generator with 3 columns, number of the exercise, the second column is the limit (perfectly written with n-->00), and the third column is the result of the limit.
I have ...
- 11
2
votes
1
answer
48
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How to explore the unchanged eigenvalue with the largest real part?
The provided code below employs the Chebyshev collocation method to calculate eigenvalues. I'm interested in examining the eigenvalue with the largest real part while ensuring it remains almost same ...
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305
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What are some Mathematica packages used for general relativity?
Could you suggest any Mathematica packages that are used for General relativity calculations? Id like to write code to solve the Schwarzchild Lagrangian equation.
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2
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207
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Performing maximum likelihood estimation for SIR Model
The code first produces a plot of the dataset, then simulates the SIR model using the parameter values we found in the manual calibration to the full dataset of the total number infected .
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3
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358
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Integral involving $\cosh$
How can I calculate the following integral using Mathematica?
$$\int_{-\infty}^{\infty} \frac{\mathrm{d} x}{\left(1+x^2\right) \operatorname{ch} \frac{\pi x}{2}} = 2 \ln 2$$
I tried:
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82
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Proving an expression from Mathematica which is clearly visible from Plots
I have the following Mathematica code:
...
- 899
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0
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68
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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. ...
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