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.

Filter by
Sorted by
Tagged with
0
votes
0answers
5 views

Finding a function that has no minimum

I started looking for a non-negative function that has no minimum. I used the necessary condition for an extremum with partial derivatives, but the found functions still did not satisfy the condition ...
0
votes
0answers
67 views

Madelung Constant

I would like to clarify some sums that being divergent can be calculated by different methods, but I find discrepancies with calculations with certain series already calculated xExamples $$M=\sum _{m=...
0
votes
1answer
20 views

NDSolve with embedded piecewise function for state-variable

Given ODE: $\dot{x}=-2 e^{-x^2} x + U$ where: $U=-u_{as}$ $u_{as} = \begin{cases} \frac{e}{\psi_+-e}, & \mbox{if } e\mbox{>=0} \\ \frac{e}{e-\psi_-}, & \mbox{if } e\mbox{<0} \end{cases}$ ...
8
votes
3answers
649 views

Exact Differentials

I just started using Mathematica so my apologies if this is a very basic question. I tried to find related questions on this forum but couldn't, so here goes. I have an equation, $\quad \quad dp =\...
2
votes
1answer
64 views

How to find the integrand by fitting data - spectrum reconstruction

Problem statement I have some experimental data of measurement values vs. temperature. Now, I want to find the spectrum which causes the measured temperature dependence. The measurement values are the ...
0
votes
0answers
49 views

Command to find the pre-image of a set that is mapped to by the function $f(x)=3^x \mod{17}$

$$f(x)=3^x \mod{17}$$ How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
1
vote
1answer
129 views

Help with an integral

I want to know if the following integral can be evaluated in Mathematica: $$ g(t)= c\int_{0}^{1-t} t^{m-1}\left[(u+t)^{m}-u^{m}\right]^{n-2}(u+t)^{m-1} d u$$ where $$ c= m^2n(n-1)$$ ...
0
votes
1answer
72 views

Sketch the region bounded by the surfaces; $2 \sqrt{x^2+y^2}$, $z=2$ [closed]

Sketch the region bounded by the surfaces, which are $2 \sqrt{x^2+y^2}$, $z=2$.
3
votes
0answers
67 views

Why is the convergent product with GoldenRatio evaluated as ComplexInfinity?

It is true that the following product has a singularity for k = 1, but from k = 2 it is convergent. We can be convinced of this by numerical calculation: ...
0
votes
1answer
47 views

Complex infinity with integration

In trying to compute following integral (spherical coordinates): $$\int[\rho+p_r]4\pi r^2dr$$ With:$$\rho=\frac{1}{2} f_0 \left(\frac{\sqrt{b_0 r}}{r^2 \sqrt{r \sqrt{b_0 r}}}\right){}^n$$ $$p_r=\frac{...
1
vote
1answer
39 views

I have a list of coefficients and I am trying to make a power series. How?

I noticed the Series[] command that would be perfect for Taylor polynomials. Unfortunately, I do not have the function available. I just have a list with the ...
0
votes
1answer
52 views

Double integral with a variable in limits

I am trying to solve this integral: This is what I tried: ...
1
vote
0answers
115 views

Evaluating a 2d integral

I would like to calculate this integral \begin{align*} I(s_1,s_2,s_{12},m) = \int_{0}^{1} {\rm d}x \int_{0}^{1-x} {\rm d}y \Big( x y \Big[ y(1-y)s_1 + x(1-x)s_2 + 2 xy s_{12} -m^2 \Big]^{-1} \Big), \...
0
votes
1answer
85 views

How to show the resulting function hidden by Mathematica?

I have u0[r_, phi_] := Sum[I^(-n) BesselJ[n, r] Exp[I n phi], {n, -n, n}]; Limit[u0[r, phi], n -> Infinity] but the result is not exportable to TEX, as it is ...
19
votes
3answers
619 views

Heuristics, tricks, and hacks in symbolic math

Mathematica sometimes fails to compute symbolic solutions when posed in the direct or obvious code, but succeeds when the same fundamental problem is posed in a slightly different way, or when ...
1
vote
0answers
84 views

Why can't Mathematica integrate my function?

I am very new to Mathematica and have been trying to integrate a function p[f] that is expressed as follows ...
0
votes
2answers
90 views

How to integrate faster

I always wanted to know how to speed up my integral computation in Mathematica. Is there some techniques that i am unaware to make the integration faster. Here an example: ...
1
vote
1answer
57 views

Function that accepts functions and returns an expression containing their partial derivatives

I would like create a function that takes functions as input and includes different partial derivatives of the input functions, for simplicity's sake say: $\qquad m(f(x,y),g(x,y))=f_{xxx}(x,y)+g_{xyy}(...
1
vote
1answer
87 views

Question about forcing derivatives

I'm here with another probably simple question. So I am taking derivatives of a function with respect to another variable not used in that function. So first I define that derivative ...
0
votes
1answer
43 views

EllipticPi argument is complex and can not be plotted. How to handle this problem?

inttau[r_]=-(1/Sqrt[0.0345106153943703 - ((37.3042 - r) (-25.578 + r) (62.8822 + r))/(3000 r)]) This is my function of r, now I integrated it w r t r ...
3
votes
1answer
435 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
1
vote
1answer
46 views

Integration taking too long

Mathematica is having issues with the following code: ...
0
votes
1answer
67 views

How to make traditional output of derivatives display like an equation

I was following a code given by Jens in the following Question and I want to improve the way my equation is displayed. The current code I'm using: ...
1
vote
3answers
62 views

How to ask Mathematica to do the given operation for a set of parameters?

I have a set of numbers like this s = {a, b, c, d, e, f, ..., g, h} and I would like to ask Mathematica to do the following operation (to sum the subtractions of ...
0
votes
2answers
59 views

Something does not work when minimizing a function

So basically I am trying to minimizing a function. I use the command "FindMinimum" since "Minimize" just returns the input. FindMinimum gives me the minimized potential and the ...
1
vote
1answer
65 views

How to assign values of variables with index

I'm trying to plot the following function $V(\{r_j\})=\sum^n_{i<j,j=1} \frac{1}{|r_i-r_j|^2}$ in Mathematica. For the expression of this function, I wrote ...
5
votes
1answer
462 views

Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta[0] at one of ...
2
votes
1answer
130 views

Problems with improper integrals in higher dimensions

Calculating numerically certain energy integrals in three and four dimensions related to the Riesz potential and the capacity, I try ...
1
vote
1answer
76 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 ...
0
votes
1answer
29 views

Search for terms contatining error functions

question might have an answer in this post (Efficient Search for specific Terms in symbolic Expression) but i don't understand how to convert it to my specific case Through some definite integrals I ...
3
votes
0answers
96 views

Summation variables aren't recognised as dummy variables

I'm trying to write this expression in Mathematica, and calculate the following quantity However, when I tried the following ...
0
votes
0answers
65 views

Why are the numerical and analytical evaluation of this integral not the same?

Since my integral and the way I used to solve it was so long, I put a .nb file here including all data which are needed. You can use it to try my question after reading the following details I had ...
18
votes
3answers
3k views

Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...
0
votes
1answer
43 views

Partial derivative on a Solve solution

Trying to solve a demand-supply equilibrium here and them find a partial derivative of the equilibrium with respect to the parameters. ...
2
votes
1answer
95 views

Fitting an integral function given a set of data points

I have a set of measures of the resistivity of a given material at different thicknesses and I'm trying to fit them using the Fuchs-Sondheimer model. My code is: ...
3
votes
3answers
186 views

Why such a big difference between results of Integrate and NIntegrate?

Studying an interesting article of Daniel Lichtblau, I consider a variation of an example from it, calculating an improper integral ...
0
votes
1answer
41 views

It would be possible to visualize the value of the integral together with the graph (in the same Manipulate command)

f[x_, y_] := x - 3 y Manipulate[RegionPlot[ 0 <= x <= a && 0 <= y <= b (1 - (x/a)), {x, 0, a + 2}, {y, 0, b + 2}], {a, 1, 20, 1}, {b, 1, 20, 1}] ...
2
votes
1answer
50 views

How to define derivative of function? [closed]

Could you help me, please? I'd like to evaluate the following expression: f' := 1/g[x] L[x_]:=L[x]=D[f[x]g[x], x] Thus, I'm ...
1
vote
1answer
148 views

Manipulate an integral with variable in limit of the solution of DDEs

I have the following problem: I solved DDEs with some parameters which have two solutions: r and s. Now, I need to calculate and ...
1
vote
1answer
53 views

Using VariationalD, getting derivative of Implicit Functions, derivative independent variables [closed]

Hey I am trying to solve this problem with wolfram: I figured using VariationalD was the way. However I can not figure out how this package works. It would be nice if someone could help me. I ...
5
votes
1answer
1k views

Change integration variable

Are there any automated procedures to change integration variables? For example by changing Sin[u]->x, I can change ...
0
votes
1answer
45 views

Derivative of predictor function

Given some data dat, we would like to generate a predictor function. Therefore we use ...
0
votes
0answers
57 views

How can I minimize this function?

I have a function, that is on the form $$ f(t,p) = c_1 t^{-\frac{4}{3}} + c_2 p^{-\frac{1}{2}} e^{-c_3 p} - c_4 p e^{c_5 p} t^{-2} + c_6 t^{-3} $$ where t and p are variables and $c_n$ are constants. ...
2
votes
0answers
60 views

How does Mathematica obtain this result?

FullSimplify[ Sqrt[2 π] InverseFourierTransform[1/(x^2 - a^2), x, p], Element[a, Reals]] Gives the output ...
1
vote
2answers
46 views

Plot an integral function for various values of the parameter

How can I plot the function F[x_,a_]:=Integrate[Abs[x - z]^(-1-2a), {z, -Infinity, -1}] + Integrate[Abs[x - z]^(-1-2a), {z, 1, Infinity}] for x in (-1,1) and a in (...
0
votes
1answer
134 views

Why is this integral divergent?

Integrate[DiracDelta[1 - y]*DiracDelta[y - 5], {y, 0, 10}] this is divergent integral but this ...
0
votes
1answer
73 views

How to calculate fractional differences of a timeseries?

I have a timeseries I am looking to transform with fractional differences per the following description: The idea being to retain the essence of stationarity of, say, a log transformed integer series ...
1
vote
0answers
66 views

Definite integral gets stuck in the calculation

$f=\frac{\sinh ^{-1}\left(e^{-2 k t} \sinh (6 k)\right)}{2 k}-2$ for $k=20$ I have: $\frac{df}{dt}=-\frac{e^{-20 t} \sinh (60)}{\sqrt{e^{-40 t} \sinh ^2(60)+1}}$ ...
1
vote
0answers
81 views

Limit gives wrong answer on both Mathematica 12.0 and Wolfram-Alpha

Limit[(Cos[x^2]/(x^2) - Cos[(x + 1)^2]/((x + 1)^2))/(1/(x^3)), x -> Infinity] Plot[(Cos[x^2]/(x^2) - Cos[(x + 1)^2]/((x + 1)^2))/(1/(x^3)), {x, 0, 1000}] The ...

1
2 3 4 5
74