Matlab的logo是怎么来的? L形区域上的波动方程的解

下面是mathworks的头儿Cleve Moler写的文章

"L形区域上波动方程的特征函数"

不过, 我打算稍后用Mathematica新增加的功能来计算这个结果, 我看到这里提到mathematica的文档中已经添加了解决类似问题的例子.

注意到这还只是线性的偏微分方程,如果问题复杂一些,可能要手动完成很多转换工作,才能实现求解.

Wolfram你要加油,努力吧

The MathWorks Logo is an Eigenfunction of the Wave Equation

By Cleve Moler, MathWorks

We hope you’ve seen it many times. It’s on the covers of our books. It’s on our business cards and stationery. It’s even on a “sponsor a highway” sign on Route 9 in Natick,Massachusetts. But, do you really know what the logo is?

I’m talking about the L-shaped membrane.We’ve used various pictures of it ever since The MathWorks was founded almost twenty years ago, but it only recently became the official company logo. I’d like to tell you about its mathematical background.

The wave equation is a fundamental model in mathematical physics that describes how a disturbance travels through matter. If t is time and x and y are spatial coordinates with the units chosen so that the wave propagation speed is equal to one, then the amplitude of a wave satisfies the partial differential equation

Periodic time behavior gives solutions of the form

The quantities λ are the eigenvalues and the corresponding functions v(x,y) are the eigenfunctions or modes of vibration. They are determined by the physical properties, the geometry, and the boundary conditions of each particular situation. Any solution to the wave equation can be expressed as a linear combination of these eigenfuncti