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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4answers
423 views

How to explain these results of integration of DiracDelta?

Let us consider ClearAll["Global`*"]; Integrate[DiracDelta[1 - x^2 - y^2], {x, -1, 1}, {y, -1, 1}] (*\[Pi]/2*) Let us verify it, making use of ...
2
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1answer
56 views

Help on script for parametric surface integral

I'm working on a short script that I can repeatedly use to solve parametric surface integrals. There is a post on this elsewhere on MSE, but it is a complicated doublecontourintegral function. It is ...
11
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2answers
412 views

Cubic equation and tangent circle

I have a cubic equation as below, which I am plotting: Plot[(x + 1) (x - 1) (x - 2), {x, -2, 3}] I like Mathematica to help me locate the position/equation of a ...
5
votes
1answer
148 views

Integral of a function defined with a loop

I have defined a function g as ...
2
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1answer
105 views

Cannot understand the meaning of Derivative[1, 0][BesselK][-M, 2]?

When I do the following integration Integrate[(Log[x]/x)*x^M*Exp[-x-1/x],{x,0,\[Infinity]},Assumptions->Element[M,PositiveIntegers]] Mathematica return a very ...
4
votes
1answer
153 views

Is this second solution to this ODE correct?

Mathematica V 12.2 on windows 10. I was using Mathematica to check my solution for this ODE. Mathematica gives 2 solutions. Any idea where the second solution came from? and is it correct? Here is ...
1
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2answers
89 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). ...
3
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1answer
86 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 ...
0
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1answer
44 views

Fit and find fitting parameters of data given an equation

If I have the following data: ...
1
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1answer
45 views

How to find integrals including certain expression

how do I find some terms in an integral containing some expression, e.g. in $$ \int \int \int \beta\phi(x,y,z) + \gamma\omega(x,y,z)\,\textrm{d}x\textrm{d}y \textrm{d}z +\int \int \alpha\phi(x,y,z) + \...
1
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0answers
79 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 $f$. ...
0
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2answers
106 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 $O(n^2)$. ...
0
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1answer
35 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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1answer
79 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/...
0
votes
2answers
83 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 $r=(r-\cosθ)^2$.
1
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1answer
115 views

Integral for Bhattacharyya distance between two Cauchy distributions

I need to perform the following integral to calculate the Bhattacharyya distance between two Cauchy distributions: $$ I = \frac{\sqrt{b_+ b_-}}{\pi}\int_{-\infty}^{\infty}dx\,\frac{1}{\sqrt{\left[(x-1)...
1
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2answers
41 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 ...
1
vote
3answers
130 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 ...
1
vote
1answer
67 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 ...
0
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0answers
56 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 ...
2
votes
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 ...
0
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1answer
60 views

Laplace Transform - Differentiation in Time property demonstration

I have a signal x[t_]=t/3 Exp[-3t] UnitStep[t] and the laplace transform as ...
2
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1answer
128 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, ...
1
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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 ...
0
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2answers
70 views

Problem with integral of the type (x^2-y^2)^a/2 x^2 Exp[-x]

I tried to calculate the following integral using Mathematica Integrate[(x^2 - y^2)^(3)/2 x^2 Exp[-x], {x, y, Infinity}] The answer was a conditional expression ...
0
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1answer
92 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
votes
1answer
58 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 ...
2
votes
1answer
158 views

(Numerical) calculation of nested integrals

The problem I'd like to (numerically) compute nested integrals of the type $$I(a;k) \equiv \left( \prod_{i=1}^k \int_0^\infty \mathrm{d}x_i \right) \exp \left( - \frac{1}{4a} \sum_{i=1}^k \left( x_i - ...
7
votes
3answers
149 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: ...
0
votes
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 ...
0
votes
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
votes
1answer
57 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
votes
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
votes
1answer
53 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
vote
1answer
93 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 ...
4
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2answers
68 views
1
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1answer
64 views
0
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0answers
28 views

Manipulation of a symbolic matrix expression

I have the following code: ...
0
votes
2answers
46 views

Help with Integration with two functions

How to solve and speed up the following integration? ...
3
votes
2answers
160 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
votes
2answers
117 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.
1
vote
2answers
45 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(...
1
vote
1answer
48 views

Function that accepts functions and returns an expression containing their partial derivatives

I would like create a function that takes functions as input and includes different partial derivatives of the input functions, for simplicity's sake say: $\qquad m(f(x,y),g(x,y))=f_{xxx}(x,y)+g_{xyy}(...
10
votes
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'. ...
3
votes
0answers
55 views

Mathematica Refuses to Output ContourIntegral and DoubleContourIntegral in Nice Mathematical Notation

I experience a strange behaviour of handling the Contour and Double Contour Integral symbols \[ContourIntegral] and \[DoubleContourIntegral] in Mathematica. Whatever I try theyy behave differently ...
-1
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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
votes
1answer
67 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 ...
1
vote
1answer
53 views

Symmetric part of a 4th rank tensor in mathematica

I am quite new to Mathematica and would like to know how to compute the symmetric part of a 4th order tensor $A_{ijkl}$. Since there are 4 indices (i,j,k,l), we have 4!=24 permutations. The symmetric ...
0
votes
0answers
22 views

Can't plot derivative of Hankel function [duplicate]

I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...
3
votes
2answers
253 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 ...

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