Solving classical problems in physics using Python’s computer algebra package SymPy. — I have always tried to simplify tedious calculations using computer algebra systems like Mathematica or Maple. But my favorite one is SymPy, because it is a normal Python package that you can easily extend, customize and integrate into your own code. In this article, I will show how one can…

Applying findiff and SciPy To Quantum Mechanics — In one of my recent posts, I stated that all of science is just matrix multiplication. Today I will demonstrate that with an application to quantum mechanics. Quantum mechanics and its weird predictions have the reputation of being hard. I think it was Niels Bohr who said that nobody understands…

Your Daily Dose of Scientific Python — This is a quick follow-up to my recent article on taking derivatives using the FFT Fourier transform. As promised, I give the generalization from 1 to 𝑁 dimensions. The approach is quite the same, just the numpy functions are different and we have to use meshed grids. Daily Dose of Scientific Python Common and not-so-common problems solved with Numpy, Sympy, SciPy and matplotlib.medium.com

The Lagrangian way of doing interpolation — Wow, this is my 100th story! As a topic, I have chosen something about one of my favorite mathematicians… or should I say, physicists? I’m talking about Joseph-Louis Lagrange. It’s a well-known and plausible fact that for every 𝑁 different points in the plane, you can choose exactly one polynomial…

Your Daily Dose of Scientific Python — This is an amusing little problem that I found scribbled on some blackboard at my home institute. Without using a calculator, decide which of the following numbers is bigger:

Your Daily Dose of Scientific Python — In the last article, we have seen that using Fourier techniques, one can replace differentiation with multiplication. This fact can be exploited to solve partial differential equations numerically in a simple way. That’s what we are going to discuss today. Daily Dose of Scientific Python Common and not-so-common problems solved with Numpy, Sympy, SciPy and matplotlib.medium.com

Numerical differentiation with spectral methods — In the last article of this series, we have seen how one can use Fourier series to do differentiation without actually doing differentiation. Instead, the Fourier technique replaces differentiation with multiplication. In principle, this is great, but for all practical matters, the approach discussed in that article is not feasible…

How to replace derivatives by multiplication — Taking derivatives is rather easy. At least, if you do it by hand. Well, it may be cumbersome and tedious, but there is only a handful of rules, and all you need is time, pencil, and paper. For numerical work, the analytic rules are no longer helpful, instead, there is…

Your Daily Dose of Math, Science, and Python — In yesterday’s article, I discussed the Gauss algorithm which can be used to solve linear equation systems. But it can do more! It can also invert matrices! The gist of the Gauss algorithm is to convert a matrix 𝐴 into an identity matrix. All operations required are not only applied…