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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1
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0answers
22 views

Integrate 2D Gaussian over a segment

I have the following 2D Gaussian: ...
1
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1answer
79 views

Constructing and plotting a special periodic function

I need to program and plot the following special function in Mathematica 12.0: $$ a_{1}(t)= \sum_{n\geq 1} \beta_{n}(t), $$ such that, for every $ n \geq 1 $ $$ \beta_{n}(t)= \displaystyle \sum_{...
1
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1answer
24 views

define function as a result of gradient returns unexpected result

This is probably very simple problem, but what am i doing wrong? c[x_, y_] := x*y; Grad[c[x, y], {x, y}] d[x_, y_] := Grad[c[x, y], {x, y}]; d[1, 1] Returns: <...
4
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1answer
49 views

Area of circle segment

Why does it take so much time computing a simple area of segment of a circle radius $a,$ width $h<a?$ Integrate[Sqrt[x ( 2 a - x)], {x, 0, h}] Would it ...
1
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0answers
88 views

How to calculate volume under f(x,y)

I have the following function: σ = 0.3; μ = 5; cy =0; cx=0; f[x_,y_]=Exp[-(1/2)((Sqrt[(x-cx)^2+(y-cy)^2]-μ)/σ)^2]/(σ*Sqrt[2*π]) Plotting this with: ...
2
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1answer
53 views

WolframAlpha does not give stepwise solution for a simple twodimensional integral

Why does the behave this particular way: ...
0
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0answers
47 views

How to simplify an expression with implicit vector functions and cross product operation?

1.The pattern is set in order to calculate the integral of a derivate of a function (to return original function, first fundamental theorem of calculus) ...
0
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0answers
34 views

Radial Mathieu functions, divergence problem

I am working on a project that requires the utilization of even Mathieu functions. This is the definition of my functions: Even Mathieu function: ...
2
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2answers
359 views

Integration of probability density function

I would like to integrate the function so that I know the probability between values between 0 and 90000 ...
1
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1answer
83 views

Is it possible to use an assumption that a parameter is an odd or even number?

I am trying to integrate: Integrate[(Exp[x]*(x^m)/((Exp[x] + 1)^2)), {x, -Infinity, Infinity}] I know that for odd m the result is zero. How can I tell ...
0
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0answers
33 views

Product[(n - 1)/n, {n, 1, 1 k}] [closed]

Could someone explain why Product[(n - 1)/n, {n, 1, 1 k}] always returns zero? I tried using different equations and it worded fin but when I use $\frac{n-1}{n}$ it won't work.
0
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0answers
26 views

Inconsistency in complex line integral using 2 parameters vs 1 parameter

I am trying to numerically verify that, over a closed circular path, the line integral of a physics-inspired complex quantity $z_Q = P \cdot \frac{\partial}{\partial Q} S$ is the same regardless of ...
5
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2answers
100 views

Integration of a piecewise function with parameters

Here is a simple piece-wise and continuous function: f[t_,a_,b_]:=Piecewise[{{a t,t<1},{a,t<1+b},{a(2+b-t),t<2+b}}] When I integrate ...
1
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1answer
59 views

Limit calculation

I want to calculate this limit, but when I enter, the result is 0. But I don't think the result is 0, because every item here is greater than 1. So the result should not be 0, is the Mathematica ...
3
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0answers
106 views

Show a function is decreasing

I'm quite new to mathematica, so most of what I know is just the very elementary basics of the language. I'm working on showing that a function is decreasing for $x>0$, but it has two other ...
0
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1answer
83 views

How can I analytically integrate a BesselK function

I want to integrate the function below analytically, so that later on I can use the result for numerical calculations. But it seems Mathematica can not handle it the way I express it. However, if I ...
-3
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0answers
102 views

Getting wrong value from evaluating my definite integral

Consider f[x_] := Exp[-x] I*Integrate[(f[I*t] - f[(-I)*t])/(E^(2*Pi*t) - 1), {t, 0, Infinity}] On my system Mathematica returns 0 while the correct answer is ...
4
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2answers
108 views

Analytical full-width half-maximum of hyperbolic functions composition

I'm trying to find the analytical FWHM of the following function (that I know has a Bell-type envelope): ...
6
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1answer
119 views

How to prove that relation with DiracDelta in Mathematica?

Up to Encyclopedia of Mathematics (see example 7 here), the relation $$\delta(\sin x)=\sum\limits_{k\in \mathbb{Z}} \delta(x-k\pi)$$ is valid. Trying to verify it in Mathematica, I obtain ...
0
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2answers
117 views

Why am I getting complex results when I evaluate may integral?

Consider (1/h)*Integrate[-Log[Abs[Cos[x]]], {x, 0, h}] This integral should be real-valued. P.S. The result I receive is ...
2
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1answer
62 views

Finding a monotonic polynomial over an interval

I want to find a polynomial of specified degree $d$ defining the function $f:[0,1]\to[0,1]$ satisfying $f(0)=0,f(1)=1$ and $f$ is monotonically increasing over the interval. This seems like an easy ...
1
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0answers
63 views

How much can we trust NIntegrate when NIntegrate::eincr is shown? [closed]

I have been dealing with a high oscillation integration using NIntegrate. The warning of eincr shows that no matter how large (X)...
2
votes
2answers
115 views

Need help with using Bessel functions [closed]

I'm new to Bessel functions, especially those of the first kind. I'm working with a problem that goes as such: With that said, is my code for said problem correct? ...
10
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1answer
415 views

Define a New function like Log

I want some help here. I want to define a function called Lg[z] that has the property that Lg[a/b] is always converted automatically to the form Lg[a] - Lg[b] , when a and b are polynomials of some ...
6
votes
2answers
355 views

An example from a Mathematica tutorial on integration returns a different answer from the tutorial

This page on "Integrals that Can and Cannot Be Done" suggests that, almost surprisingly, Mathematica can express the following integral in terms of elementary functions: ...
6
votes
3answers
146 views

Calculating the integral points of an elliptic curve

I asked this question on Math stachexchange. The question I have is: Can I use Mathematica to find the (integral points on the following elliptic curve) or can I find when the number $\text{n}$ is a ...
5
votes
3answers
132 views

Plotting graph of a function with an imposed a condition

I have to plot a function $f(x,y,z)=\sin[x+y+z]$ with an imposed condition $\sin[y]\sin[x]=\sin[z]$. How do I plot it in Mathematica using Plot3D?
0
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1answer
41 views

Double integral over X * bivariate normal [closed]

I would like to compute the integral of (bivariate normal distribution times X) over the limits X = {-inf, inf} and Y = {0, inf}. Using the double integration calculator in Wolfram Alpha, I enter ...
2
votes
2answers
99 views

How can I find the coefficients which minimize my non elementary integral?

I have the integral which I express in Mathematica code as: Integrate[ (-((x^2 (c + x^2 (b + a x^2)))/(m + x^2 (v + d x^2))) + Abs[x])^2, {x, -1, 1}] I ...
1
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0answers
36 views

Integrate much faster if function split in two pieces

I have the following function ...
0
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2answers
96 views

Finding the global maximum of a function

I've the following code: ...
9
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1answer
298 views

Deep learning outperforms in symbolic integration and ODE?

There comes a new paper on arXiv (arXiv 1912.01412, Deep Learning for Symbolic Mathematics by Guillaume Lample, François Charton) claiming that a deep learning model outperforms Mathematica a lot in ...
0
votes
1answer
47 views

Double integral is not solved [closed]

I am trying to solve the following double integral: $$\int_{0}^k \int_{d+rk-rx}^s \frac{d-[(1-r)x+rk-c]}{ds^2} \mathrm{d}y \mathrm{d}x $$ Here is my Mathematica code: ...
1
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1answer
39 views

Show, if possible, small isolated “islands” in the unit cube using RegionPlot3D

I have a certain three-dimensional constraint ...
1
vote
1answer
52 views

SphericalPlot3D taking sign of $r$ into account [closed]

I want to plot Re[SphericalHarmonicY[l,m,Theta,Phi]], with the lobes having different colors depending on the sign of the function. I can’t use ...
0
votes
0answers
38 views

Convex conjugate

What is the easiest way to compute the convex conjugagte of a real convex function $f: \mathbb{R} \to \mathbb{R}$, defined by $f^*(s) = \sup_{x} \{ s x - f(x) \}$ I know I can compute the derivative ...
0
votes
1answer
47 views

Fractional Euler-Lagrange equation [closed]

Using Mathematica, I need to perform the derivation of the fractional Euler-Lagrange equation as derived in this article. Regarding this, I searched many links, but I was not able to master the ...
0
votes
1answer
47 views

The graph doesn't generate

I try graph the partial derivative of this function but it keeps giving me the "invalid variable". What I am trying to follow is: 1. Take the derivative of the function respect to T only (To and Eo ...
3
votes
1answer
47 views

How to take derivative using the Math Palette

I have a basic question on how to take derivatives using Math Palettes: I would like to get the derivative of cos(k*x - w*t) with respect to ...
2
votes
1answer
168 views

Problem with numerical solution of a system of ODEs

Background Good evening, I have a big problem with num. solution NDSolve of differential equation. To start with, the model: There is a fast-moving rope in closed path. Where $T$ is tension, $a$ ...
8
votes
2answers
301 views

Elliptic Integrals: Mathematica and Gradshteyn and Ryzhik

In Gradshteyn and Ryzhik, (specifically starting with the section 3.13) there are several results involving integrals of polynomials inside square root. These are given in terms of combinations of ...
0
votes
1answer
61 views

How to get the analytical solution or numerical solution of the double integral

i just want to calculate this double integral but can't get the analytical solution,so it there a way to get the analytical solution or numerical solution of the double integral? codes are as this <...
1
vote
2answers
73 views

Obtain only positive complex solutions

By setting the determinant of a matrix to 0, I obtain 6 complex solutions for w and plot them. However, You can clearly see that the negative solutions mirror the positive solutions as the solution ...
0
votes
1answer
32 views

Numerical Double Integral with symbolic bounds to normalize function

I'm trying to use mathematica to normalize this trial wave function which requires finding the following integral and solving for A so that the total propability equals 1. 'a' is the constant width of ...
0
votes
2answers
57 views

Simplify Integrate results

I wish to simplify the overlap of two gaussian-type orbitals, primGauOrb = ((2 α)/π)^(3/4)E^(-α (x^2 + y^2 + z^2)); And then integrate it, ...
1
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0answers
52 views

How to find the derivatives from Solve after obtaining 6 complex solutions? [closed]

I have a 3x3 matrix. By setting the determinant to 0, I find the values of w in terms of ka and graphed the complex solutions. m, M, k, l are constants: ...
9
votes
1answer
325 views

Integrate over a region

I am trying to calculate a integral over a region defined by But I dont really know how to do it, I dont know if I have to work in cartesian coordinates or polar coordinates. The function that I ...
0
votes
1answer
77 views

Mathematica derivative not matching when I take derivative by hand [closed]

I want to take the derivative of this with respect to eta: fabc = 1/2 (-3 + 27/(2 + x)^2 + (1 - 1/(1 + (-1 + x) c[eta/cc])^2)/ c[eta/cc] + 2 Log[x]) Here I ...
0
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1answer
32 views

Fourier sine series

p[t_] := (1/12) Sign[Sin[428 \[Pi] t]] + (11/12) Sign[ Sin[428*2 \[Pi] t]] FourierSinSeries[p[t], t, 10]] I want to expand this function but it takes forever. ...
5
votes
1answer
213 views

Orthogonality Sin(nx)Sin(mx)

I want to prove that $$ \int_{0}^{\pi } \sin(n \, x) \, \sin(m \, x) \, \mathrm{d} x=0 $$ for m,n integers and $$ m\neq n$$ My try is: ...