Important Posts of This Blog

This post collects the top 5 most popular content according to Google Search Console.

analytic continuation of zeta function…

In the post A Step-by-step of the Analytic Continuation of the Riemann Zeta Function, we did what the title said. There is no hype, myth or $1+2+3+\dots=-\frac{1}{12}$, but serious mathematics in the era of Riemann and before.

irreducible representations of so(3)…

The group $SO(3)$ is one of the most “realistic” Lie groups, as it describes all 3D rotations in real world. In the post Irreducible Representations of SO(3) and the Laplacian, we compute all of its irreducible representations, using the theory of Laplacian and harmonic polynomials. This is indeed not an easy job, as it shows the “hard” side of linear algebra.

fourier transform of sinx/x…

The Fourier transforms of $\frac{\sin x}{x}$ and $\left(\frac{\sin{x}}{x}\right)^2$ are important but not easy to compute. In this post The Fourier transform of sinx/x and (sinx/x)^2 and more we did the computation by extensively using contour integration. Along the journey, we also review important concepts in complex analysis.

fréchet derivative…

Fréchet derivative generalises the concept of derivative into any topological vector spaces, the dimension being arbitrary. The most important thing is, derivative should oftentimes be understood as a linear operator instead of a number or a matrix, as is shown in the post A Brief Introduction to Fréchet Derivative.

fourier transform of e^-ax^2…

In this post The Fourier Transform of exp(-cx^2) and Its Convolution, we compute the Fourier transform of $\exp(-cx^2)$ using two ways, differential equation and Gaussian integral. We also find the convolution quite easy to be computed if we utilise Fourier transform.