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 …
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. …
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 …
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 …