All You Need To Know About Bessel Functions

Those were the days when an astronomer could still make substantial contributions to mathematics! Bessel functions, first introduced by the German astronomer Friedrich Bessel in the early 19th century, are …


Integration by Differentiation

We all have a foundational understanding from high school that integration is the opposite of differentiation, as it's the inverse operation. That's an accurate notion. But there's a lesser-known aspect …

July 16, 2023

NumPy: Understanding Meshed Grids

When I'm teaching my courses about scientific Python, students often have a hard time understanding the concept of meshed grids in NumPy and what's the difference between the various options. …

July 9, 2023

Solve math homework with Python

Since my days as a physics student, I have been dreaming about replacing tedious pencil and paper calculations completely by computer algebra, ideally in Python. This is the first part …

July 2, 2023

The Method of Manufactured Solutions

Constructing Unknowable Numerical Solutions for Precise Comparisons

When solving numerical problems like partial differential equations, knowing how accurate your solution is is always important. But how can you know if you don’t have the exact solution for …

June 25, 2023