Sturm Chain

The Sturm chain is kind of like a ladder with squares and numbers on it. Imagine you want to climb to the top of a really tall building, but the building has no stairs or elevator. So, you have to use this special ladder to get there. The ladder has different steps, each with a square and a number on it.

The first step of the ladder is a square with the number zero in it. The next step has a different square and a number in it, but it's not just any number - it's the solution to a special math problem called a differential equation. This solution tells us some really important things about the building you're climbing up.

Then, you climb up another step and get a new square with a different number in it. And so on, until you reach the top of the ladder. Each step of the ladder gives you a new solution to the same math problem, but each solution has different boundary conditions.

So, the Sturm chain is basically a way to find multiple solutions, each with unique properties, to a differential equation. And just like climbing up a ladder, you have to go step by step to get there.