We develop two almost straightforward way to compute the Fourier transform of $\exp(-cx^2)$, in the sense that any contour integration and the calculus of residues are not required at all. The first cool approach enables us to think about these elementary concepts much deeper, so I highly recommend to study this approach as long as you are familiar with ODE of first order.

ContinuityWe are restricting ourselves into $\mathbb{R}$ endowed with normal topology. Recall that a function is continuous i...

前言洛必达法则相比甚至不少高中生甚至初中生都听说过，知道怎么进行简单的应用。简单点说，处理$\frac{0}{0}$的函数时，对上下进行求导，可能会很大程度上简化计算。但是洛必达法则为什么能奏效? 能不能用严格的数理语言进行论证? 这是这篇文章需要解...