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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70 views

Numerical Mixed Partial Derivatives: How to Choose Scale?

For illustration purposes, consider the function $$ f(x, y) = (x - 1)^2 + (y - 1)^2 + \sin[25(x+y)] . $$ The mixed partial derivatives at the origin are $f^{(x,x)}(0,0) = f^{(y,y)}(0,0) = 2$ and $f^{(...
5
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1answer
180 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
93 views

Derivative of -I (Log[-x] - Log[x]) - why is it zero? [closed]

Mathematica gives the derivative of the function -I (Log[-x] - Log[x]) as $0$, but on the real domain the expected result is $\pi\delta(x)$ and on complex domain it ...
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0answers
23 views

Replacement of functions bound by sums and integrals in NCAlgebra

I want to use the NCAlgebra package to do some simplification on non commutative expressions involving integrals. For example, one such expression would be $$ I=\left(\int f(x)g(x) dx\right) * h $$ ...
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3answers
309 views

Conjugate & Derivative

I have some problem with the derivative of the 'conjugate' expression: Here I define the functions: ...
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0answers
32 views

How to write these kinds of integrals in a more compact way?

I wanted to calculate the average distance between two points both lying inside $B^2(\vec 0, R)$, and ended up writing ...
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0answers
24 views

Error using ParallelMap to evaluate NIntegrate of numerical derivative ND

I want to evaluate a numerical integration in which the integrand is constructed out of a function f and its derivative f'. <...
2
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2answers
91 views

How to solve this differential equation with a square root?

I've to solve this differential equation but I don't know how to do it. Someone can help me? $\frac{dy}{dx} = \frac{1}{x} \Bigg( -1 - \frac{2a}{\sqrt{a^2 - 3x L f^2 e^{3y}}} \Bigg)$ where a, L and f ...
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1answer
791 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
2
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1answer
47 views

Evaluation of divergent hypergeometric function

I try to calculate the following hypergeometric function: HypergeometricPFQ[{n+1, n+1, n+3/2}, {2n+3}, -1] for several positive natural values $n=0,1,2,\ldots$, ...
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1answer
164 views

Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities

In a recent posting, TwoQubits user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
7
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1answer
248 views

Incorrect integration from article

Recently I came across an interesting article by Daniel Lichtblau, where the integral Integrate[Abs[x - y]^n, {x, 0, 1}, {y, 0, 1}] ...
1
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1answer
53 views

Plot with three functions and three parameters [closed]

I think my code doesn't have any problem but the program shows me this error and I'm confused! Plot::argr: Plot called with 1 argument; 2 arguments are expected. ...
2
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2answers
179 views

How do you get substitution to recognize a derivative?

I have a simple expression involving a derivative: x[t_] = Q/T[t]; Simplify[Derivative[1][x][t] /. Q -> x T[t]] That produces:$$-\frac{x T'[t]}{T[t]}$$I have ...
0
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0answers
44 views

Parameter sensitivity when integrating in Mathematica [duplicate]

When I try to integrate this MMA freezes: ...
1
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1answer
35 views

Variable substitution when integrating with Mathematica

When I try to integrate this MMA freezes: II = (2 fx R Cos[ϕ] Sin[θ])/(R^2 + ρz^2 - 2 R ρz Cos[θ])^(3/2) ...
0
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1answer
48 views

How do I plot the derivative of the Cantor Staircase?

I know that the derivative of the Cantor Staircase should be close to 0 since the Cantor Set has a measure of zero. I wanted to graph the derivative of Cantor's Staircase in Mathematica to see if it ...
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0answers
37 views

Wolfram alpha query works online but not through mathematica?

Bit of a bizarre problem I'm having (well, more a question than a problem). I am trying to solve an integral, which I queried using the online wolfram alpha website. The input and output are ...
4
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2answers
143 views

Evaluating an improper integral

So I have this function: $$ \int_{-\infty}^{\infty} \mathrm {sech}(x+s)^{2} {\rm sech}(x)^{2}dx$$ And when I try to integrate it, I can obtain the indefinite integral: ...
7
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3answers
586 views

How can I draw a vector field on a curve?

For didactic purposes (a line integral of a vector field) I'd like to plot a vector field along a curve in 2D and 3D, like in this picture: Mathematica is able to vizualize vector fields. Here is my ...
0
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0answers
71 views

Incorrect outputs of Limit command

Version 12.0 produces a generic result Limit[Cos[a*x], x -> Infinity, Assumptions -> a \[Element] Reals] Indeterminate ...
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0answers
29 views

Numerical integration involving divergence

I was just trying to perform the following numerical integration NIntegrate[1/(x - 5)^2, {x, 0, 10}] The problem I am facing is the divergence at ...
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1answer
55 views

Mathematica does not simplify divergent integrals

I get this as output: $\frac{1}{6} \int_0^{\infty } 6 t \, dt$ Why it cannot cancel the coefficients?
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3answers
139 views

Error with NIntegrate of a two variables integration

This is mathematica code for my integration, ...
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2answers
386 views

Plotting an approximated Dirac Comb

I am trying to approximate a Dirac Comb to use in an NDSolve calculation but when I Plot it over a large interval, it misses ...
0
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2answers
81 views

How to solve this inequality? [closed]

solve for the smallest N value for this inequality, I tried several online calculators and they are not working.
2
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1answer
61 views

How to compute the limit of a subdivided rotation applied to itself n times?

I have the following function: f[n_, angle_, axis_] := Simplify[RotationMatrix[angle/n, axis]^n]; where n is a positive integer, angle is real and axis is a 3d ...
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1answer
64 views

DSolveValue differential equation list of arbitrary values

I have been solving arrays of differential equations, and recently moved to the general case, where my initial conditions are arbitrary constants (either real or complex). However when I moved from ...
2
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1answer
251 views

How do you turn this statement into a Mathematica formula?

I'm reading a book on Nucleosynthesis. It has this formula for the number density of a species:$$n_i=g_i\space e^{\mu_i/T}\int\frac{d^3p}{(2\pi)^3}e^{-E_1/T}$$I don't recognize this notation. How do ...
2
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2answers
46 views

How to get exact analytical integral for the basic polarization bubble integral?

In theoretical condensed matter physics, a very common integral that is repeatedly solved is of the following form: $$ \int\limits_{-\infty}^{+\infty}\text{d}\omega\frac{1}{i\omega + i\Omega-a}\frac{1}...
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0answers
22 views

How to set PDE coefficient as a list of discrete data

How to set a pde time-dependent coefficient, not as an analytic function in time, but as a discrete data vector or list, each element of that list represents the coefficient value on a specific time ...
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0answers
44 views

How to compute an indefinite integral for a general parameter choice?

I am trying to compute the integral: Integrate[E^(a*InverseCDF[NormalDistribution[0, 1], (1 - x)]), x] for a >= 0. The ...
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0answers
58 views

One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
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1answer
57 views

Solving a complicated time-dependent function

I want to solve the following time-dependent system of equations: ...
1
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2answers
123 views

Why can't Mathematica express a minus operation between two decimal numbers with several places? [closed]

A example of the problem. This is a print from mathematica with the demonstration of the issue.
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1answer
87 views

Asymptotic value of an integral [closed]

When I evaluate the integral $$ n \int_0^1 t^{r-1}(2t-t^2)^{n-1}(2-2t) dt$$ I get the following : $$2^{(-1 + 2 n)}\,n\,t^{(-1 + r)}(\mathsf{Beta}(1/2, n+r-1, n) - 4 (\mathsf{Beta}(1/2, r + n, n))$$ ...
4
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2answers
171 views

Is there a possibility to keep variables virtual?

It is general knowledge, that when we deal with derivatives of function in Mma we have to inevitably indicate variables of such functions. Namely, this D[f[x],x] ...
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2answers
109 views

Incorrect results of differentiation

Let us consider the derivative D[Floor[x]*Sin[Pi*x]^2, x] // Simplify ...
5
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1answer
101 views

How is Mathematica treating $x^x$ when finding roots?

When I enter Solve[x (-x + x^x) == 0, {x}, Reals] It returns three roots as $$\{\{x\to -1\},\{x\to 1\},\{x\to 1\}\}$$ Is MMA treating ...
0
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2answers
55 views

Slope of a line

Just a quick question. Is there a fast inbuilt function to calculate the slope of a line segment passing through two points {p11,p12} and ...
0
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1answer
97 views

Why are the results of integrations of a DiracDelta related integrand and its approximations strikingly different?

Let us consider a double integral, treating it as a functional which corresponds a number to a function, ...
-1
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1answer
33 views

How can I do partial derivation for F(y,y') with respect to y'? [closed]

This is a part of a question on the master/doctor degree graduate school entrance test for Tokyo Univ. in 2016. The conditions are below ( ) Here is the question. I have to make a differential ...
2
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2answers
306 views

center of mass of a 2D square

Using Mathematica, find the center of mass of a 2D square not centered at the origin. center: (x0, y0) ...
0
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0answers
30 views

Assume some expression is false

I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
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1answer
64 views

Simplify not working

I am trying to simplify the following expression code: ...
2
votes
3answers
115 views

How to get out coefficient of term in series?

Suppose I have a function $f(s,t) = [(1-t^2)(1-s^2t^2)]^{-1/2}$. Is there a way to get the general coefficient in this power series of the form $s^{2k} t^{2n}$?
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0answers
34 views

Four dimensional symbolic integration using HalfSpace

Consider the regions $r1 and $r2 defined as follows, ...
0
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2answers
57 views

Error in Integration of special functions using mathematica 12.0

When I try to integrate the following, Integrate[-GegenbauerC[22,-1/2,x]/(1+k*x),{x,-1,1}] where -1<k<1 and k!=0, Mathematica gives different results if I ...
3
votes
1answer
103 views

Superposition of the differential operators

My problem can be easily solved without Mathematica, however, I am curious how to do it in Mathematica. Moreover, I can be stuck with a similar, but more cumbersome problems in the future. Following ...

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