1 vote
121 views

### Can I take the Fourier transform of a PDE in both sides? [duplicate]

I want to know if it is possible to use a PDE in the function FourierTransform instead of a function. Consider for example the simple case for the heat equation ...
98 views

### FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
74 views

### How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...
• 429
1 vote
49 views

### Fourier transform of an equation [duplicate]

I have the following equation: $$m \frac{d^2 x}{dt^2} = -Kx - \alpha \frac{dx}{dt} + f(t)$$ Which I introduced into Mathematica as: ...
• 153
2k views

### Numerically solve the initial value problem for the 1-D wave equation

I want to solve the standard 1-dimensional wave equation $y_{xx}=y_{tt}$ using NDSolve (for $y(x,t)$) with the following conditions: ...
• 313
2k views

### Bilateral Laplace Transform

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
• 967
3k views

### Obtaining the Fourier transform of an operator

We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is $$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega}$$ and ...
• 41
406 views

### Prove linearity of integration [duplicate]

I'd like to prove the linearity of integration over one real variable ($x$). Integrate[f[x] + b g[x], x] == Integrate[f[x],x] + b Integrate[g[x],x] which I was ...
• 41.2k
428 views

### Problems with DSolve and NDSolve for Dirichlet problem on an annulus

To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro ...
• 26.3k
1k views

### Solving the heat equation on the semi-infinite rod

Cross posted in scicomp.SE. I want to test the solution which is given below is right by Mathematica. Please look the post in mathstackexhange or Please look below. Question: Solve the ...
• 543
1k views

### Solve PDE with DiracDelta function

This question is related to Analytic solution of dynamic Euler–Bernoulli beam equation with compatibility condition. I think it is more appropriate to open another question on this topic. In the ...
• 2,571
403 views

### Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
• 137k
182 views

### LaplaceTransform works well with x[t], but doesn't recognize x[1][t], how to make it works for x[1][t]?

Bug introduced in 12.2(?), persisting through 14.0 or later. When I am solving odes using LaplaceTransform, I found that LaplaceTransform works well with u[t] or y[...
• 1,323
272 views

### Derivative of real antisymmetric matrix in mathematica

Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
• 1,225