New answers tagged

0 votes

Fitting data for an implicit function with two parameters

Didn't know how to accept your own answer until now... Here a simple approach to solve the implicit problem using "NMinimize" ...
Ulrich Neumann's user avatar
0 votes

Conformal Mapping Function and Scaling Factor

Not sure if it helps, but Ivanov and Trubetskov's Handbook did have a mapping for a rectangle. This code plots it with a strip in the center: (but you perhaps want an empty waveguide) ...
Jos Bergervoet's user avatar
6 votes
Accepted

How to find a closed-form expression for this integral depending on parameter?

A change of variables can help: ...
chuy's user avatar
  • 11.2k
0 votes

Define a function whose variable is differential operator

This method works when the f[x] template is a polynomial with constant coefficients. The method can be extended to other polynomials. The constant coefficient case ...
LouisB's user avatar
  • 12.3k
1 vote

Define a function whose variable is differential operator

We define an operator, that takes a polynomial in x and replaces every x by a derivative operator that acts on the variable x. To prevent that the operator is evaluated too early, we need "Hold&...
Daniel Huber's user avatar
  • 49.9k
0 votes

How to improve the following code to get rid of the warning messages?

Try inverse problem X = Values@ DSolve[{ (y ^2 - 1) == x'[y] (2*x[y]*y ) , x[1] == 2}, x , y][[1,1]] Plot[X[y], {y, 0, 5}]
Ulrich Neumann's user avatar
5 votes
Accepted

How to improve the following code to get rid of the warning messages?

\begin{align*} y^{\prime} & =f\left( x,y\right) \\ & =\frac{2xy}{y^{2}-1}\\ y\left( 2\right) & =1 \end{align*} We see at $y=1,x=2$ the $f\left( x,y\right) $ is not defined. Hence ...
Nasser's user avatar
  • 142k
1 vote

Numerical integral does not agree with analytic integral

There is a workaround. Let us put J[t_] := Integrate[Exp[-a*Cos[b + x]]*Sin[b + x], {x, 0, t}, Assumptions -> t >= 0 && t <= 2*Pi] Then ...
user64494's user avatar
  • 25.7k
3 votes
Accepted

Numerical integral does not agree with analytic integral

Not a Mathematica answer per se, but just in case its useful, I'll expand on my comment under the question. Let's write the original integral as $\int_0^{2 \pi } u(t) \, \mathrm{d}t$ where $u(t)=t \...
chuy's user avatar
  • 11.2k
4 votes
Accepted

Numerical Solution for a Non-Linear Functional Fractional Differential Equation (FFDE)

This is fractional delayed differential equation (FDDE), therefore we can't use method described in my answer here. Instead of the Haar wavelets method we try to use implicit difference scheme ...
Alex Trounev's user avatar
  • 43.3k
0 votes

Problem with evaluation of integral

Maybe so: ...
Mariusz Iwaniuk's user avatar
1 vote

Setting up a double integral over a polar region

Thanks for the nice answers by @David G. Stork and @cvgmt Since IntegrateChangeVariables is a promising (but a recent) addition, I would like to add this workaround:...
Syed's user avatar
  • 48.3k
7 votes
Accepted

Setting up a double integral over a polar region

...
David G. Stork's user avatar
5 votes

Setting up a double integral over a polar region

Method-1 f[x_, y_] := 9 - x^2 - y^2; reg = ParametricRegion[ r {Cos[t], Sin[t]}, {{t, 0, 2 π}, {r, 0, 1}}] Integrate[f[x, y], {x, y} ∈ reg] ...
cvgmt's user avatar
  • 68.9k
1 vote

Interpreting the output of double integral over a Circle

...
David G. Stork's user avatar
5 votes
Accepted

Interpreting the output of double integral over a Circle

Integrate[f[x, y], {x, y} ∈ Circle[]] 16 π is the line integrate https://en.wikipedia.org/wiki/Line_integral $$\int_{\...
cvgmt's user avatar
  • 68.9k
5 votes
Accepted

Using FindSequenceFunction to solve the integral of the product of Legendre polynomials and power functions

...
Bob Hanlon's user avatar
  • 155k
2 votes

Using FindSequenceFunction to solve the integral of the product of Legendre polynomials and power functions

Not using FindSequenceFunction: $$P_l(x)=\sum _{j=0}^{\infty } \sum _{k=0}^{\infty } \frac{2^{-j-k} (-x)^j (-l)_{j+k} (1+l)_{j+k}}{j! k! (j+k)!}$$ ...
Mariusz Iwaniuk's user avatar
1 vote

How to correctly calculate the sum of this series with Mathematica?

Numerically I also get the negative result. ...
Daniel Lichtblau's user avatar
4 votes
Accepted

How to integrate Legendre polynomials with parameters?

...
Bob Hanlon's user avatar
  • 155k
2 votes
Accepted

How to compute the $2n^{\text{th}}$-order derivative of a function

Another way to do this using HoldForm and ReleaseHold: ...
E. Chan-López's user avatar
1 vote

How to impose a change of variable in a differential equation?

If you want to do it with just plain substitution you can do this. ...
Bill Watts's user avatar
  • 8,167
2 votes

Find the range of Legendre polynomials

FunctionRange[{LegendreP[l, x], RealAbs[x] <= 1 && Element[l, Integers] && l > 0}, {x, l}, y, Method -> {"Reduced" -> True}] (...
lotus2019's user avatar
  • 2,091
3 votes

Why does this integral not converge?

If the sine function were not taken to an even power, its alternation of sign would give a convergent (though not absolutely convergent) integral. But, with that even power, the parts of the integral ...
paul garrett's user avatar
4 votes
Accepted

Why does this integral not converge?

You can first do the integral symbolically: Integrate[Sin[x*1/2]^4/x^1, x] which gives you: ...
SHuisman's user avatar
  • 3,260
3 votes

Mathematica cannot solve this complicated integration

This integral can be expressed by Leaky Aquifer function or Generalization of the Incomplete Gamma function. Let's consider: ...
Mariusz Iwaniuk's user avatar
0 votes

Mathematica cannot solve this complicated integration

There is one issue, capital "D" is differentiate. As a rule, avoid single capital letters as symbols in Mathematica (C, D, E, I, N). ...
Roland F's user avatar
  • 3,263
3 votes
Accepted

How to impose a change of variable in a differential equation?

...
Nasser's user avatar
  • 142k
1 vote

Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

Why not just solve the ODE symbolically by ...
bbgodfrey's user avatar
  • 61.3k
5 votes

Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

Yes, Mathematica is able to do that. ...
Ulrich Neumann's user avatar
0 votes

Is it possible to get rid of `Root` and have an explicit closed-form solution for the given equation?

This is possible for some values of the parameters. ...
user64494's user avatar
  • 25.7k
5 votes
Accepted

How to find the maximum and minimum values of a function

...
flinty's user avatar
  • 24.7k
0 votes
Accepted

Fitting data for an implicit function with two parameters

So we found our fit and now I will describe how if someone will face the same problem. First of all, we simplified our model to a polynomial of the 4th degree. ...
Karen Simonyan's user avatar
5 votes
Accepted

Speeding up minimization problem related to a minimal surface

Calculating the integral without any assumptions we obtain a ConditionalExpression which may not work quite seamlessly with ...
Artes's user avatar
  • 57.2k
1 vote

Why are the plot curves bumpy rather than smooth?

The function definition appears to be numerically unstable. Best would be to identify the cause of the problem and modify your function to avoid, if possible. E.g., using higher precision numbers or ...
tad's user avatar
  • 1,855
4 votes
Accepted

Maximize a function of $x$ and $y$ where $x^2 +y^2 \leq 1$

...
Bob Hanlon's user avatar
  • 155k
6 votes

Two integrals equal to Euler-Mascheroni constant not evaluating symbolically

It just means that Mathematica does not have these integrals in its database yet. One way to solve the first integral may be using Series: ...
azerbajdzan's user avatar
  • 13.3k
1 vote

In the given code, how can I ask Mathematica to replace the obtained points in function $g$ and plot it?

...
Bob Hanlon's user avatar
  • 155k
1 vote

In the given code, how can I ask Mathematica to replace the obtained points in function $g$ and plot it?

The result of the FindInstance is already a list of rules: ...
lericr's user avatar
  • 26.3k
1 vote

In the given code, how can I ask Mathematica to replace the obtained points in function $g$ and plot it?

Try Map[(-7 b^2)/(c + 2 d)^6 /. {b -> #[[1]], c -> #[[2]],d -> #[[3]]} &, points] (*{-0.0000330257, -3.44743*10^-6, -3.22685*10^-6}*)
Ulrich Neumann's user avatar
4 votes
Accepted

Strange analytical and numerical results during an integration of a complex integrand

Both integrals are improper because of two integrable singularities ...
user64494's user avatar
  • 25.7k
2 votes

Integrate InterpolatingFunction times polynomial

Another "exact" answer: ...
Goofy's user avatar
  • 2,542
5 votes
Accepted

Integrate InterpolatingFunction times polynomial

An "exact" result instead of an approximation by FunctionInterpolation: ...
Goofy's user avatar
  • 2,542
0 votes

Integrate InterpolatingFunction times polynomial

You may combine interpolating functions using "FunctionInterpolation". Here is an example: ...
Daniel Huber's user avatar
  • 49.9k
3 votes

How to compute this integral $\int_{-\frac c2}^{0} e^{-a \left(\frac{b x^3}{2}-\frac{x^2}{4}\right)} dx $?

You likely cannot get a nice closed form solution in terms of elementary and transcendental functions, but you can get a form expressed as an infinite sum and ...
flinty's user avatar
  • 24.7k
1 vote
Accepted

How can the sum of sequences be obtained in the given form?

Let us treat S[n] as the solution of the recurrence equation ...
user64494's user avatar
  • 25.7k
6 votes

Numeric integration and RegionDilation in higher dimensions

RegionDilation seems only work for simple region in higher dimensions. ...
cvgmt's user avatar
  • 68.9k
1 vote

Deriving a first-order condition and plotting it generates some outliers

Let me clean up your code a little bit, first: ...
AccidentalFourierTransform's user avatar

Top 50 recent answers are included