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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36 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 ...
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1answer
45 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 ...
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1answer
32 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 ...
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0answers
38 views

Problem with numerical solution of a system of PDEs

I am having a problem with with NDSolve. Background There is a fast-moving rope in closed path. The variables are: T is tension. a is angle beetwen rope and ...
7
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1answer
202 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 ...
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1answer
57 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 <...
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2answers
58 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 ...
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1answer
26 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 ...
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2answers
56 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, ...
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48 views

Mathematica won't integrate basic functions with antiderivatives but Wolfram Alpha will? [closed]

Below is the simple integral I wish to evaluate, mathematica just returns my input in different format but Wolfram will calculate no problem: As you can see the integral is easily calculable by hand ...
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0answers
23 views

Successive Numerical integration with interpolation [closed]

How to perform successive integrations with interpolation in mathematica with sinusoidal arguments (F, C1(w) and C2(w)). Note: F' has to be done by NIntegrate F'' has to be done by Interpolation. $$\...
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0answers
49 views

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

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: ...
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1answer
309 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 ...
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1answer
71 views

Mathematica derivative not matching when I take derivative by hand

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 ...
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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. ...
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0answers
54 views

Stieltjes inversion formula [closed]

I need to compute the Stieltjes inverse transform $$ -\frac{1}{\pi}\lim_{\beta\to 0^+}\int_{-\infty}^{\lambda} \Im (R(\alpha+i\beta)) d\alpha$$ for a resolvant $R$ of the form $$ R(z)=\frac{P_1(z)+...
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1answer
203 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: ...
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1answer
57 views

Integrating a function “bit by bit”

I am trying to integrate a function. But for this task I need to do it "bit by bit". I created a working example that shows the problem. ...
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2answers
65 views

NIntegral failing to converge

I have the following integrals that I am trying to calculate: ...
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1answer
83 views

Double integration of an exponential function which includes a Csch function and complex numbers

Mathematica couldn't solve following using just integrate function. I checked on interpolating as well, that also turned to be a dead end. Can someone help me with evaluating this integral? If it ...
6
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3answers
257 views

How to compute curve integrate

I want to compute this integral. $$∮_{L}(x-y)^2\,\mathrm{d}x+(x-z)(y-z)\,\mathrm{d}y+(x+3y-2z)\,\mathrm{d}z$$ which $$\begin{cases}x^2+y^2+z^2=1\\x+y+z=1\\\end{cases}$$ counterclockwise and ...
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2answers
102 views

How to evaluate Integrate[Exp[Csch[(x - τ)]^2], {x, 0, x}]

I have been trying to integrate the following and Mathematica couldn't integrate it. Can someone help me on this? ...
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2answers
35 views

Defining a function with variables that were previously introduced

I have coefficients in a list: allAs = {1,2,3,4,5} And another list that is created with the Table function, with an "x" in each element which I want to find ...
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0answers
33 views

How to solve an Integral analytically using a predefined definition for Besselfunctions (phi part of angular spectrum representation)

I'd like to use mathematica to calculate an Integral that is dependent on phi and theta (to obtain the intensity distribution of a tightly focused TEM20 mode using the angular spectrum representation)....
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0answers
37 views

How solve integral with three moment and delta function

I am trying solve this integral in mathematica: \begin{equation} \int \dfrac{d^3 p_3}{(2\pi)^3 2 E_3} \dfrac{d^3 p_4}{(2\pi)^3 2 E_4}(p_1 p_2)(p_3 p_4) \delta (p_3 + p_4 - p_1 - p_2). \end{equation} ...
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0answers
41 views

How can I force the output of a computation to be as compact as possible, yet complete, by using functions?

I am computing some derivatives in Wolfram Mathematica 11.3. The functions that I have to differentiate (with respect to the state variables) are the equations of motion of a rocket in the atmosphere. ...
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0answers
45 views

How to properly evaluate a Green's equation in FeynCalc (or any other package)?

In 4D, the Green's function of the box operator with respect to $p$ is $1/p^2$,i.e. $$\partial_p^2 \frac{1}{p^2} = -(2\pi)^2 \delta^{(4)}(p). \tag{1}$$ I use the package FeynCalc, in which the ...
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0answers
53 views

Error when trying to solve elastic PDEs using FEM: “Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments.”

I'm trying to solve the following linear elastic problem: The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons. The part of codes that probably have no ...
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1answer
68 views

Limit of a two variable function at the origin

How can I show that the limit of the following function, when the variables {x, y} tend to zero, is zero? Mathematica gives the error {x,y} is not a valid ...
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2answers
45 views

Summations on Variables with subscripts

One of my equations uses a set of variables which ultimately for a set of certain values gives a list of 8 numbers: c=13.9506 (31 - k) following cc(sub k) = Round[Table[13.950621339931203...
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1answer
63 views

Second derivative peculiarity: Black-Scholes

This is the function for a call option ...
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0answers
71 views

How can I shorten the time to perform nested integrations? [closed]

I'm trying to define the function 'Cumul1' by integrating other relevant functions. The problem is that, since the relevant functions consist of special functions as well as a bunch of terms, the ...
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1answer
62 views

System of nonlinear differential equations

I used the following commands: ...
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2answers
58 views

Differential equation system, Jacobian matrix, characteristic equation

We assume the differential equation system: $X'=σ(Y-X),Y'=X(ρ-Z)-Y,Z'=XY-βZ$. I can calculate the equilibrium points as: ...
4
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2answers
102 views

Area of region bounded by $y^2=4x$ and $y=2x-4$

I have to plot, put color and calculate the area of $y^2=4x$ and $y=2x-4$ with Mathematica. By hand, I found that the area is the integral of $\frac{y}{2}+2-\frac{y^2}{4}$ in the interval $[-2,4]$. I ...
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2answers
72 views

Given a set of points in a plane, find the maximum number of the all collinear points [closed]

Given a set of points in a plane, For example:RandomInteger[{1, 10}, {50, 2}] How to find the maximum number of the all collinear points Reference link:https://blog.csdn.net/u014253011/article/...
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1answer
130 views

Speeding up Integration over Implicit Region

Similar to my previous question, running ...
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1answer
43 views

Exits and beeps on Integration

Evaluating ...
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1answer
117 views

Mathematic cannot evaluate this integral. Why? [closed]

Mathematica will evaluate this integral: $$\int_1^x\frac{1}{(1+C_1(\eta)(-1+x))^3}dx$$ but not this one: $$ \int_1^x\frac{1}{(1+C_1(\eta)(-1+x)+C_2(\eta)(-1+x)^2)^3}dx $$ I'm trying to solve this, ...
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1answer
57 views

How can I plot this function?

I'm trying to plot this function without any success, any help is more than welcome. The function f contains a sum of integral which depends on T and then the function g is a derivative of the ...
3
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1answer
141 views

Solving partial integro-differential equation

I want to solve a partial integro-differential equation of this form: using NDSolve, something like ...
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1answer
88 views

Why am I not getting output from Integrate? [closed]

I encountered a problem when using Integrate. I think Mathematica did the computation, but it did not show the output. Please see the following image.
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1answer
106 views

Testing the accuracy of numerically computed derivatives - alternative method

So I have asked this question earlier today: Testing the accuracy of numerically computed derivatives, This method works well for DifferenceOrder methods but upon reading https://reference.wolfram....
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1answer
64 views

Is it possible to plot a manifold from it's metric / line element in Mathematica?

i'm very new to using Mathematica and mostly just trying to work out what it can or can't do. I'm doing a course on differential geometry and was wondering if there might be a better way for me to ...
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2answers
70 views

Testing the accuracy of numerically computed derivatives

I am calculating approximate derivatives by using NDSolve`FiniteDifferenceDerivative, so this works: ...
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2answers
40 views

Plot multiple solutions for different t terms

I want to integrate a a simple function for different t values. At the moment I have the following code; ...
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4answers
306 views

Integration of three dimensional function gives wrong answer!

I have the following integration $$\int_{-\infty}^{\infty}d^{3}\mathbf{p}\nabla\cdot\frac{\mathbf{p}}{(p_{x}^{2}+p_{y}^{2}+p_{z}^{2}+m^{2})^{3/2}}$$ $$=\int_{-\infty}^{\infty}d^{3}\mathbf{p}\left(\...
2
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1answer
52 views

Average value of a function with two variables

How would I determine the average value of a function of two variables over two intervals, both of which have given bounds. Assume the function f[x,y] (below) has ...
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1answer
39 views

Average value of function of two variables

I'm wondering how to determine the average value of a function of two intervals, both of which have given bounds. Say the function f[x,y] (below) has bounds x,y=[0,5]. How would I go about this? I ...
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0answers
39 views

Why does Mathematica miss some solutions for my integral?

When computing the integral of two orthogonal sine functions $\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0 Mathematica seems to miss the solution where $n=m$. I don't ...