Don't look at other videos until you've internalized the first sentence. Think long and hard about what that sentence means : differential equations allow you to find any function that you can make enough "what happens when it moves" observations about. Enough usually means one.
For instance you can find Newton's equations from the statement that "falling things keep going linearly faster" (because they're the simplest function that satisfies that differential equation).
On the more complex side, Google's pagerank is also the solution to a differential equation. Very technically it sort-of kind-of qualifies as a first-order one, just not in the real number space.
There's a separate branch of "differential equations" (let's call it "the physics branch") that studies how to work it with discrete time intervals rather than continuous ones, which is also interesting and useful.
Don't look at other videos until you've internalized the first sentence. Think long and hard about what that sentence means : differential equations allow you to find any function that you can make enough "what happens when it moves" observations about. Enough usually means one.
For instance you can find Newton's equations from the statement that "falling things keep going linearly faster" (because they're the simplest function that satisfies that differential equation).
On the more complex side, Google's pagerank is also the solution to a differential equation. Very technically it sort-of kind-of qualifies as a first-order one, just not in the real number space.
There's a separate branch of "differential equations" (let's call it "the physics branch") that studies how to work it with discrete time intervals rather than continuous ones, which is also interesting and useful.