Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

I’ve started recreating many of my numerical model tutorials for introductory physics. In the beginning, I had students use spreadsheets to create models. Of course, spreadsheets aren’t very good for ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...