HN Theater @HNTheaterMonth

>My money is on the fact that their teacher was managing some other student doing something stupid.

But an ineffective teacher also happens in college where professors do not need to deal with any misbehaving adult students.

Surely many of us have experienced a college class (in USA) being taught by a TA that can barely speak English. Even though the students are all quiet and respectful, nobody understands the lecture.

In those situations, the advantages of on-site presence of the professor is overshadowed by the disadvantages of the ineffective teaching presentation.

That's why many Youtube mathematics videos have comments such as:

https://www.youtube.com/watch?v=ly4S0oi3Yz8

+ 261 thumbs up: "Your videos are what college should be like. And isn‘t."

⬐ chobytes

Wish I had access to 3B1B when I was just starting to learn this stuff. His expository style and graphics are such great sources of intuition.

⬐ nyc111

But, a differetial equation is not an equation, right? It’s a definition. Its solution is an equation. Do I understand this correctly?

⬐ randyrand

What "solving" means is a bit arbitrary.

Solving a differential equations typically means taking one of the sides and going down one order.

For example making a new equation 'temperature' = X from 'derivative of temperature' = X

⬐ GolDDranks

No, it's an equation. Equation is a statement that says that thing A is equal with thing B. The point is that thing A and thing B are often quite dissimilar in form. But since they are the same thing, and because math is deterministic, if you manipulate the both sides the same way (For example, multiply both sides with the same amount), it stays equal. (Plus sometimes you are allowed to manipulate them in different ways, because the axiomatic system you're in says that's allowed for some cases. Example: you are allowed to rewrite (AB)C as A(BC) if you know that the object you are manipulating is associative.) "Solving" an equation means manipulating it in a way that the other side becomes trivial in form. You maybe can't do that for many differential equations, but that doesn't make them less of equations.

⬐ potbelly83

Well technically a PDE is an operator between various function spaces.

⬐ nyc111

> Equation is a statement that says that thing A is equal with thing B.

But this describes an equality. I imagine an equation to be a proportionality written with standard units. Aren't they different? I mean an equality, an identity, a definition and an equation are different, even though most of the time they are indicated with the equality sign.

⬐ creatornator

I believe identities and definitions have different symbols by convention, either the equal-delta sign (definition [0]), or the triple-line equals sign (identity [1]).

[0] https://hsm.stackexchange.com/questions/5166/who-first-defin...

[1] https://www.quora.com/What-does-a-triple-equals-sign-mean

⬐ sunstone

Well I guess they would be equations that are partially differentiated from other equations?

⬐ IIAOPSW

Or as I used to call them, Particularly Difficult Equations.

You see, the trick to a PDE is to use the LOFL transform. The LOFL transform (Leap Of Fuggin Logic) moves your PDE into easy space. Easy space has the important property that all problems are trivial and or linear. Once you've solved you're PDE in easy space you just apply the inverse LOFL and you're done.

How do you take a LOFL transform you ask? That's left as an exercise for the reader.

⬐ thatoneuser

Better yet - I'll show you how to perform the LOFL. I'll show you with the most trivial example possible. It will have no applicability to any other problem you encounter and may in fact be the only problem solveable by the LOFL.

⬐ gundmc

Integral transformations are the "rest of the fucking owl"[1] of the STEM world.

[1] - https://i.kym-cdn.com/photos/images/original/000/572/078/d6d...

⬐ nsporillo

Interesting that you mention this as this is a topic I learned today in Numerical Linear Algebra: Krylov subspace methods.