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.
3,666
questions
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
0answers
55 views
How to perform brute force method with Knapsack /0-1 money-changing problem, with the following table of potential knapsack items
This is the listing item with 400 as Knapsack size...
...
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
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 ...
