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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150 views

How to show critical points of function?

I have the following code: ContourPlot3D[2x*z + 2y*z - y^3 - x^2 - 3z^2, {x, -3, 3}, {y, -3, 3}, {z, -3,3}] which correctly produces a 3D plot of the function ...
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1answer
124 views

Moving a circle on a function

I'm trying to write a code that moves a circle on the graph of a specific function, but I can't find the error in my code. I added values to both coordinates, but the Manipulate fails to count the ...
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2answers
90 views

Why Mathematica is giving “Indeterminate form”

I have an equation for effective potential (Veff). For SS=0, Mathematica gives output, if I take derivate of Veff with respect to r, then I take SS=0, Mathematica gives infinity (indeterminate form). ...
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2answers
160 views

Fast way to check if $f(x)>x$ for what value of $x$

In order to find the value $x$ for which $f(x)>x$, I tried it using the following code: ParallelTable[If[TrueQ[f[x]>x],x,Nothing],{x,0,10^9}] For some ...
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4answers
88 views

Integration of LegendreP

I am trying to integrate a product of 2 Legendre polynomials as follows: Integrate[LegendreP[1, x] LegendreP[2l+1, x], {x, -1, 1}] I get the result: ...
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1answer
90 views

Hypergeometric Function and Elliptic Integral

In the wiki page, complete elliptic integrals of first and second kind are related to the Hypergeometric function via: $$ K(k)=\frac{\pi}{2} \mathstrut_{2}F_{1}(\frac{1}{2},\frac{1}{2};1;k^{2})\\ E(k)=...
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1answer
89 views

Limit takes too long

I want to compute the following limit Limit[ Integrate[BetaRegularized[(2 h - h^2), (d - 1)/2, 1/2], {h, 0, 1}], d -> Infinity ] However, surprisingly, it ...
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1answer
47 views

Fit and find fitting parameters of data given an equation

If I have the following data: ...
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3answers
205 views

How I can solve an infinite system of equations? [closed]

How I can solve an infinite system of equations? Assume nMax = 5 ...
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0answers
83 views

How to plot integral of a gradient function

For $f : \mathbb{R} \longrightarrow \mathbb{R}$ continously differentiable and $\phi \in [0,\pi/2]$ let $$F(x) = \int \frac{f'(x)-\cot \phi}{1+ f'(x) \cot \phi} d x$$ be a clockwise 'rotation' of $f$. ...
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2answers
111 views

Asymptotic behavior of $n^2-n$

I recently became familiar with the Power of Wolfram. As a part of the problem I'm working o, I need to find which of the following is closer to $n^2-n$ $O(n \sqrt n)$ or $O(n \log n)$ or $O(n^2)$. ...
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1answer
92 views

Solve complex heat transfer equation

I am trying to solve a heat transfer problem related to calculating the cooling rate after quenching a sample. The equations (and explanations) are taken from this paper: https://sci-hub.se/10.1029/...
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1answer
36 views

Finding the x coordinate of a point in the solution of NDSolve from its y coordinate

Using NDSolveValue, we can know the y coordinate of the function from an x coordinate. Is it possible to do the reverse, where the input is the y coordinate and ...
0
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2answers
85 views

How can I find equation of the tangent line for a curve given in polar form? [closed]

Basic calculus Please tell me how to find the tangent at $θ=π/3$ in the form $y=ax+b$ of the curve represented by $r=(r-\cosθ)^2$.
3
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4answers
302 views

How to use other methods to realize `Differences`

I know the following method can get the desired result {b-a,c-b,d-c,e-d}: Differences[{a, b, c, d, e}] But I want to know more ...
2
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1answer
131 views

How to make this moving surface a continuous and derivable function?

I'm having troubles in defining a function of three variables: $t$, $x$, $y$, from a moving bumpy surface that should be derivable relative to its three variables. Here's the animated surface code, ...
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2answers
42 views

Parameterized derivative when chain rule usually in order

I have the following problem, which requires the chain rule and can be a little tedious. I'm trying to figure out how to do this in Mathematica, but I can't get a solution. I know the answer, which is ...
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3answers
132 views

How do I solve this integral in Mathematica?

I am trying to solve this integral in Mathematica $$ I=\int_{0}^{1} d x e^{iax} K_{0}\left(\sqrt{\left[q x(1-x)+m\right] b}\right) $$ where $a$, $b$, $m$, and $q$ are real positive constants. I want ...
2
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1answer
61 views

Help on limiting range and domain for critical points

I've been working on some simple scripts to find critical points. I've been using this one. Where the red script is the particular function I'm interested in. But I am struggling to find a way to ...
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1answer
73 views

Line Integral Help?

This forum has been an amazing resource as I learn Mathematica. I could use some help in putting together a simple program for line integrals. I'm especially puzzled by ones you have to reparametrize ...
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4answers
58 views

I want to maximise my function over a particular domain

I have tried NMaximise. But I am getting an error always. Even if my command is correct. My function is Cos[π E^x] and I want to maximise it over the range (-3,3)
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0answers
57 views

Nonlinear Differential Equation with Paramaters in Sqrt Function

For a university project, I am trying to see if my system will have choked flow and also plot the resulting pressure spike. I set up the system below to try to model the transient response. I am able ...
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1answer
68 views

Not getting full evaluation from my integrations

I am trying to evaluate the expression Subscript[u, θ]. However, the results of the integration show another integral. I want to find the final equation. with all ...
2
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1answer
36 views

I need help using manipulate solve and plot in the same time

So this is my code so far ...
2
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2answers
96 views

How to shorten the length of the tangent line

I have all the equations down to manipulate the tangent line on the graph... but the tangent line is too long, what would be the best way to shorten it? ...
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1answer
93 views

Why mathematica can't evaluate this integral?

Why mathematica can't evaluate this integral? It just gives me symbolic form. I can work it out by hand. ...
2
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1answer
75 views

NDSolve second-order PDE with 4 variables

I'm trying to numerically solve a second-order partial differential equation in 4 dimensions. The PDE is a Fokker-Planck equation and the variables are the real and imaginary parts of the field of two ...
7
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3answers
152 views

Confused by results of FunctionDomain

Why does Mathematica give me the function domain of $$f(x)=(2x-3)^{\frac{1}{5}}-(2x+1)^{\frac{1}{5}}-(x - 3)^{\frac{1}{5}}$$ as $x\geq3$? I used this command: ...
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1answer
59 views

FindMinimum for a large range

I have a function functionSL[0.01,zl,zh] where I want to find at which zl its minimum value occurs for each different ...
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0answers
33 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 ...
0
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1answer
58 views

Two inequalities with Mathematica [closed]

How can I prove these two statements: For any $x,y \in \mathbb{R}$ and $p \geq 2$ the inequality $\left(|x|^{p-2}x-|y|^{p-2}y\right)(x-y) \geq 0$ holds and the second inequality $\left(|x|^{p-2}x-|y|^{...
2
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1answer
46 views

Two different variables in a Do Loop

I am trying to use the code developed by @Alex Trounev here: Numerical solution of an iterative equation for different kind of q. I am not sure how to incorporate ...
2
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1answer
54 views

Clarification needed for two different D[…] operations [closed]

ClearAll[sus]; D[sus[i, t], t] /. i -> 1 generates (0,1) sus [1, t] And ...
1
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1answer
95 views

How to perform symbolic integration of six variable function?

I have a function of six variables in total - x1, x2, x3, x11, x22, x33 and I need to perform symbolic integration to get a symbolic expression. Before showing my ...
2
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2answers
213 views

Integral giving a Dirac delta

I have the following type of integral Integrate[ r BesselJ[n, a r] BesselJ[n, b r], {r, 0, Infinity} (where a and ...
4
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2answers
68 views
1
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1answer
173 views

Integral over Laguerre Polynomials

I would like to solve Integrals of the type $\int_0^{\infty}dx e^{-x}x^{m+2}L^m_k(x)L^m_{k+j}(x)$, for $m,k,j$ integers (and $m,k\geq0$). On this page I found an expression which should do the job: ...
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2answers
274 views

Plot of the derivative of a function

I have a function functionSL as a function of t (t<0) where I want to find the extremum ...
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0answers
30 views
1
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1answer
98 views

How to compute the following definite integral

I am having trouble calculating definite integrals of the form In practice I have unknown real parameters within the exponentials and therefore am looking for a symbolic evaluation of the integrand. ...
3
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2answers
182 views

Figures as a one column panel with same x axis but changing y axis

I have plots of 6 different figures in a command decon so that if I use decon[[1]] I plot the first figure and if I use ...
0
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2answers
46 views

Help with Integration with two functions

How to solve and speed up the following integration? ...
1
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2answers
49 views

How do I calculate the distance covered by an particle, which is moving on a given trajectory?

I am new to Mathematica and was wondering how one could calculate the distance an particle will cover while moving on a given trajectory over a given time. Example: trajectory is $\qquad r(t) = (\sin(...
0
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2answers
120 views

Simple Physics and Calculus in Mathematica V4

Here is how I used to do this in V4. I can not find an equivalent way in V12. Any ideas would be appreciated.
3
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2answers
265 views

Numerical solution of an iterative equation

I am trying to solve the following iterative equation: where the parameter tao (needed in the previous equation) is defined as: Here's the parameters and my approach to solving the equation in ...
10
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6answers
1k views

Tower of Pisa function

I'm trying to construct a 'smooth' function $f : \mathbb{R}^2 \longrightarrow [0,1]$ such that all level sets $$\{ x | f(x)=y\}$$ are circles in a way that $f$ looks like the 'Leaning Tower of Pisa'. ...
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1answer
114 views

Why the integration command for this function gives no answer? [closed]

I have a function wfVAR2[r1, r2] which has the following form: ...
0
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1answer
118 views

Zeros or minima of a multivariable function [closed]

what is the most reliable method for finding the zeros or at least the minimum of $f(x,y,z,w,r)= - \frac{3}{96 \pi^{2}z^{4}} \int_{y}^{\infty}\sqrt{x^{2}-y^{2}}x^{2} e^{-x} dx+ \frac{3}{16 \pi^{2}(1-r^...
0
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1answer
74 views

How can I make an FFT in Mathematica using data from a file? [closed]

I need to calculate the seismic moment of an earthquake data, but I don't know how the FFT is applied in some data, my data is a plain text that I must import it to Mathematica ...

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