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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 integrate a logsumexp function?

I am trying to integrate a logsumexp function which is a smooth function of another piecewise function. Run ...
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2answers
54 views

How to output the level of the contour plot based on the desired area enclosed in the contour level?

I am a beginner using Mathematica. I am doing a physics experiment that involves this 3D surface; the function $ f(x, y) $. I need a program that can give me the contour level in the $ z $-axis which ...
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37 views

Laplace Transform of Complementary Error Function [migrated]

I need to apply one Laplace transform formula while I have no idea how to prove it: $$\int_0^\infty e^{-st}e^{a k}e^{a^2 t}erfc(a \sqrt{t}+\frac{k}{2 \sqrt{t}})dt=\frac{e^{-k \sqrt{s}}}{\sqrt{s}(\sqrt{...
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3answers
55 views

Solution… 2nd Transcendental Equation with Graphical method [on hold]

If $ 2x^3 + \ln x = 5 $, then what is $ x $? For beginning we started to find a solution for equation $$ \begin{align}\label{eq:eq} \ln x + cx = b \tag{1} \end{align} $$ We know from W function ...
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1answer
29 views

numerical integration with intermediate variables

I'm trying to perform the following integral, where the bounds of the inner integrals become the integration variable in the next integral. disregarding the stuff in the exponential in the sample ...
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2answers
63 views

Define a partial derivative of a composite function

I would like to define the function $ \dfrac{\partial}{\partial y}\left(\dfrac{f(x,y)}{g(x,y)}\right)$, for example ...
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1answer
53 views

gradient of Legendre polynomials

I need help to check my code if my way to generate the gradient of a function that contains Legendre polynomials is correct or not. if f is a function in θ and κ ,I need the gradient of f with ...
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1answer
42 views

Solve for: When does the area bound by three curves == area desired

The program I've been making an attempt to write does the following: Plot 2 lines, f(x) = –x and g(x,a) = e^(x – a) –a Find area bound by the 2 lines and x-axis (shaded in red) A "desired area" value ...
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2answers
178 views

How to check whether Laguerre polynomials are orthogonal?

I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal. I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. ...
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1answer
41 views

Laplace transform giving incorrect result

In Mathematica: LaplaceTransform[Exp[-Exp[-t]], t, s] Out:= Gamma[s]-Gamma[s,1] But performing InverseLaplaceTransform on the ...
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1answer
294 views

Symbolic integration of potential over a disc : branch cut problem?

Context I am trying to explore the geometry of a crystal made of irregular bubbles. See animation here. very vaguely in the spirit of this post (it is in fact motivated by cosmology and galaxy ...
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1answer
49 views

Volume computation not returning expected result

I have tried to integrate the expression (0.5*(3*Cos[t]*Cos[t]-1))*(0.5*(3*Cos[t]*Cos[t]-1)) where t is in [0, π], as a ...
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1answer
21 views

Function that takes derivative of another function (with any number of arguments) and evaluates it

I would like to supply a function as an argument to another function which then differentiates the function and evaluates it at a set of points. Suppose I want to differentiate this function, ...
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1answer
69 views

Mathematica failing to compute function to calculate integral over a region bounded by straight line

Statement of the problem Consider the following situation: You have a model which employs a bivariate distribution with known parameters. You have a random realization from the distribution ...
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1answer
134 views

What does “ Im' ” mean? [closed]

I am trying to take the curl/derivative of the function A. What does " Im' " mean here? Why does Mathematica attempt to take the derivative of the Im function here? ...
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1answer
59 views

How to use a previous numerical solution to solve a differential equation numerically?

When I solve this differential equation with NDSolve, I get a numerical solution for H[x]: Code for the differential equation: ...
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1answer
639 views

Why can Mathematica solve integral(a)+integral(b), but not integral(a+b)?

I am new to Mathematica and came across the following problem. The integral at hand cannot be solved. $$ \text{Integrate}\left[\frac{2 \left(3 t \epsilon \text{Li}_2(t)+3 \epsilon \text{Li}_2\left(...
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1answer
33 views

How to solve this differential equation? Error (NSolve :: ifun)

When I solve the differential equation I get an error: error: Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. ...
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2answers
159 views

Simplify Derivative with Substitution

I try to evaluate: $$ \frac{\partial}{\partial x} \log{u(x, y, z)}$$ Mathematica gives: $$ \frac{1}{x+y+z}$$ I want to simplify the expression with my function: $$ \frac{1}{u(x, y, z)}$$ How to ...
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0answers
34 views

Series doesn't seem to work on functions

When you try to use the Multivariable option of Series, it doesn't work as intended, since it keeps terms of higher order than intended. Example: Expand a two-variable gaussian exponential to second ...
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1answer
55 views

Simplify sum of unnatural conditional functions generated by derivative

I try to use Mathematica to evaluate: $$\frac{\partial}{\partial A_{abc}} \sum_{j=1}^{J}\sum_{k=1}^{K}\log\left(\sum_{l=1}^{L}A_{jkl}B_{jkl}\right)$$ I get: $$\sum_{j=1}^J \sum_{k=1}^K \frac{\begin{...
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1answer
56 views

Derivative with respect to any element of a matrix

I try to evaluate $$ \frac{\partial s}{\partial A_{ab}} $$ where $$ s = \sum_{i} \sum_{j} A_{ij}$$ The result should be 1 regardless of $a$ and $b$. But the following code gives zero. ...
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2answers
150 views

Expansion of the Meijer G Function

I'm trying to do the integral Integrate[ B^2*BesselK[0, ko*ρ]^2*2 π*ρ, {ρ, a, ∞}] which I figured should be relatively simple as the integral of a Bessel ...
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1answer
35 views

Derivative of sum of elements of array [closed]

I try to get derivative of sum of an array with respect to an element of the array. $$s = \sum_{i = 1}^{3}A_{i, 1}$$ Evaluate $\frac{\partial s}{\partial A_{1,1}}$ Below is the code. ...
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1answer
67 views

Computing an integral : Mathematica seems to say it's diverging or not defined and I think it is

I would like to compute : Element[a, Integers] Element[b, Integers] Integrate[Exp[-a^2*(x (1 - x/b^2))^2], {x, 0, Infinity}] which is obviously not diverging. ...
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38 views

Different integral results within equivalent conditions

I input 3 functions as following, ...
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2answers
48 views

How to deal with the loss of significant digits in this expression with Fresnel integrals?

I needed to solve this integral: $$\int_1^\infty \frac{dx}{\sqrt{x}} \cos \left(a x-\frac{\pi}{4} \right) \cos \left(b x-\frac{\pi}{4} \right) \cos \left(c x-\frac{\pi}{4} \right)$$ Coming from ...
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0answers
96 views

Trouble solving the integral with mathematica

I have the following function: ...
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2answers
100 views

Why won't Mathematica evaluate my integral?

I would like to integrate: Integrate[ 1/((0.64*E^(2*(a/d)^1.7)*Sqrt[Pi *a]))^3, {a, a0, ac}, Assumptions -> {d > 0, a > 0, ac > a0 > 0} ] I ...
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0answers
50 views

Integral converges only if Mathematica kernel has just started?

After just starting Mathematica (or quitting the kernel) if I run: ...
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0answers
32 views

Solve nonlinear differential equation system - Plot

When I solve the system of differential equations I get two solutions for each variable (See the picture). My question is how I can neglect one of the solutions at the plot. Thanks. Code: ...
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1answer
35 views

Output of Apart as a list?

I have a rational funtion of one variable that I know will always have a simple partial fraction decomposition of the form $$\sum_{n=1}^N\frac{\alpha_n}{z- \beta_n},$$ but I do not know the values ...
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1answer
71 views

Linearity of the Dirac delta function [closed]

It is known that the Dirac delta function is linear. I do not understand why Mathematica says that a DiracDelta[x] + b DiracDelta[x] is not equal to ...
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1answer
61 views

Making StreamPlot draw phase plane streams near saddle points

For example, I want to draw the phase portraits near the saddle points $(-\pi,0)$ and $(\pi,0)$, but the code that follows can not plot traces near those points, because $(y,\,-10 \sin x - y) = (0,\,0)...
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0answers
80 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
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1answer
376 views

How to calculate this n dimensional integral?

The integral such as It's easy to evaluate the first few items ...
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1answer
35 views

Total derivative after numerical solution of a system

I have a system of three equations in three unknowns, $k$, $\theta$ and $w$. I am interested in the behavior of the variables when one parameter changes. I first specify the system: ...
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1answer
42 views

Table of function derivative evaluation

I want to create a table with numerical values of a function derivative by using the following code: ...
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0answers
41 views

Convolve taking too long and producing error message Integrate::idiv:

The following functions do not produce an output."f1" is a convolution of Gaussian function and my model. It took too much time and gave an error message. I have attached that error message also. How ...
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2answers
47 views

Finding the 1st and 2nd derivatives of a function of two variables [closed]

I have an oscillatory function f(ф, ф'), and I want to differentiate it. function like this: ...
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2answers
258 views

Calculating curvature of a contour

I have an equation of a scalar field in the form $$ f(x, y) = x^2 + y^2 + xy + c. $$ I want to find the curvature of the contour of the curve at $ f_c = f(0.5, 0.5) $. So I need to calculate the ...
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2answers
43 views

Integrate over matrix elements

I wish to perform the integral $$ \int \prod_{i,j}dM_{ij}\exp\left(-Tr(M^2)\right) $$ where we integrate over the matrix elements of $M$. I tried ...
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1answer
42 views

How to change the integral variable and integral upper/lower limit?

I am dealing with the symbolic operation of taking the antiderivative, e.g., Integrate[f, x] (where $f$ represents a complicated function which cannot return ...
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0answers
52 views

Discordance between the results of AsymptoticIntegrate and calculations

Mathematica 11.3 finds r = Integrate[Cos[k*(x^4 - x)], {x, -Infinity, Infinity}, Assumptions -> k > 0] ...
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1answer
91 views

Problem with pendulum code cant get to plot Mathematica 11.3 [closed]

I copied from an example about a pendulum. (A Mathematica Primer for Physicists, p38). Can't get the LogPlot to work. Get just the axis. Using version 11.3 on ...
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0answers
35 views

How to differentiate with respect to sum of variables?

If f is a function of x,y,z. How do I differentiate f wrt x+y+z?
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1answer
39 views

How to define a function that can transform integrands to the unit hypercube?

We know most integrands can easily be transformed to the unit hypercube: $$\int_{a_1}^{b_1}\cdots\int_{a_d}^{b_d}{\rm d}^{d}x\, f(\vec{x})=\int_0^1{\rm d}^dx\,f(\vec{x})\prod_{i=1}^{d}(b_i-a_i)\ ,$$ ...
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1answer
77 views

Wrong limits of very simple problems in Mathematica running on Ubuntu

I tried to find the limit$$\lim_{x\rightarrow0} e^{-\frac{1}{x}}$$ with the assumption $x\in \mathbb{R}$ on my Macbook Air, and I got Indeterminate, but on my ...
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2answers
66 views

Why does my integral not evaluate?

I just started using Mathematica today, so I'm sure there is something I am doing incorrectly. I am trying to evaluate this integral: ...