Question

Help with how to remember vector identities. Any tips?

Answer 1

practice them

Answer 2

Consolidation into long term memory, aka: memorization, is the same for just about anything. 1) Spaced repetition. 2) Self test. 3) Application. 4) Memory keys such as stories or other mnemonic devices. With math, derivation from one form to many can also be useful.

Answer 3

Oh, and anything visual is usually pretty helpful. 70% of sensory processing and memory is for vision. So it makes for a good way to get the most in. This is why people work things into drawings. While especially great for history, people have made picture stories of other things to remember other topics. Like those one where people use a picture of an eye next to 8 next to a rocket launching to mean I ate lunch.

Answer 4

I see. I was thinking of maybe a way to derive them. But thanks!

Answer 5

Deriving them is always good in math. The more you work them, the easier that part gets. Oh, and that uses several of the principals.

Memory consolidation is a process of linking different things in long term so that retrieval is easier. When you can wok A to B to C and C to A and so on, you are linking them all up and make them easier to remember. Even if you don't remember them all right off, you may develop a way to get them quickly, which is just as good... and sometimes better!

Answer 6

im sorry i don't really have any tips to remember them by i just think of them in order and practice them sorry

Answer 7

I dunno if it helps but I right them down on every homework problem that I need them for...if that means writing them down 4 times on the same piece of paper then I write it down all 4 times. Also if you have friends in the same class have a conversation with them about the identities have them tell you the formulas; you tell them the formula. People are generally good at recalling conversations.

Answer 8

oh my....that first right should be a write....I should not have left without checking....

Answer 9

@kantalope Ah yes, very true. With many concepts when you talk about them you have to break them down. In fact, working out how you would explain it to to say someone that was new to the concept is very good. It makes you clarify it in your thoughts. In fact, writing it down to simplify simplify it for explanation is a great way to make it more memorable.

Working from your explanation alone, can you get back to the whole topic?

There was a professor that was very fond of this because he found it was an easy way to convey even the most complex of ideas. Can't remember the name right now, but if he got someone to start a topic this way, he could usually finish the explanation for them. Even on topic he was not trained in, the simplicity of common language explanations would build up the topic to the point where he could see where it was going.

Answer 10

As it is said until now, repetition is one of the best ways to memorize them. In my case, I also use some physics insight. For example, when you try to remeber the identitity,
\[\nabla\times(\nabla\cdot f)=0\]I remember that f is a potential from a central force (generic case) and then the vector field generated by the gradient should be irrotational.

Practice them with "physical" cases should be the best, I think, but you can memorize them by simple repetition.

Answer 11

Alright thank you all :)