# 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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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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### 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 ...
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 ...
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, ...
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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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: ...
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. ...
65 views

### NIntegral failing to converge

I have the following integrals that I am trying to calculate: ...
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 ...
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 ...
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? ...
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 ...
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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### 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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### 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. ...
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 ...
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 ...
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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### 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...
63 views

### Second derivative peculiarity: Black-Scholes

This is the function for a call option ...
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 ...
62 views

### System of nonlinear differential equations

I used the following commands: ...
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### 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: ...
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 ...
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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### Speeding up Integration over Implicit Region

Similar to my previous question, running ...
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Evaluating ...
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### 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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### 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 ...
141 views

### Solving partial integro-differential equation

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

### Testing the accuracy of numerically computed derivatives

I am calculating approximate derivatives by using NDSolve`FiniteDifferenceDerivative, so this works: ...
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; ...
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(\...
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### 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 ...
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 ...