Recent content by kzhu

The definition of Fourier transform that I refer to is X(j\omega) = \int_{-\infty}^{+\infty}x(t) e^{-j\omega t}dt and the inverse x(t)=\frac{1}{2\pi} \int_{-\infty}^{+\infty} X(j\omega)e^{j\omega t} d\omega On a second thought, my question can read: Could someone provide a couple of...

Homework Statement The sufficient condition of the existence of the Fourier transform of a function is that the function is absolutely integrable. I have identified a function that is absolutely integrable, but not square-integrable f(t) = \frac{1}{\pi}\frac{1}{1+t^2}|t|^{\frac{-1}{2}}...

Thx for the discussion. I was able to derive these two expressions. The method is to use the recursive relation of associated legendre's function (m-n-1)P_{n+1}^m(x) + (2n+1)xP_n^m(x) - (m+n)P_{n-1}^m = 0. and get \frac{P_{n+1}^1}{\sin\theta} =...

Dear All, I am implementing the scattering of dielectric sphere under electromagnetic plane wave. The expression of the field contain \frac{P_n^1(\cos\theta)}{\sin\theta} and\sin\theta P_n^1'(\cos\theta), where the derivative is with respect to the argument. These two terms are giving me...

The graph at Wikipedia is a function of two variables f(x,y). If you take the gradient of this function (or a scalar field), it would be the 2-D vector as plotted on graph in the X-Y plane. The discussion of being perpendicular is in the X-Y plane but not the X-Y-Z space. So what is...

This is about finding the Green's function for the Laplacian operator under infinite boundary condition. Basically, 9.173 gives the relation between the Green's function and the unit excitation. In 3D, the unit excitation is assumed located at the center of a sphere. If you write out the...

My understanding is that once you have proved that the system is time invariant, i.e. h(t) = h(t-t0), you can safely drop t0 in the expression and simply state the impulse response is h(t).

On a second thought, would "distribution basis function" be a more descriptive name? I have also find the name "tempered function" difficult to grasp.

Thank you for the clarification.

What does "test" mean in distribution theory Dear all, I am recently exposed to the distribution theory. Why are "test" functions called "test" functions? What are they testing for? or What are they tested for? Why do we need to introduce the idea of distribution? It is merely for...

Personally, I recommend Habberman's book as an undergraduate textbook on PDE. The english is plain and the subjects are very application oriented. The author simply takes his time to explain the details, which makes it a standalone piece of work. My favorite chapter is on Sturm-Liouville's...