Memorize Differential Calculus: Tips & Strategies

[The_Z_Factor]

I was wondering, since recently I've been studying differential calculus on my own, how to memorize all this? I don't have a teacher so I am sort of my own teacher and I understand most of the stuff but I don't memorize it well. I can do it all so easy when I am doing it and then the next day I wake up open the book and try to solve a problem and I remember some things but not all of it. Just about everytime it seems I have to go back in the book and review and I memorize it again, and do more problems.

So I am wondering how I could try to memorize all this stuff the first time through? Should I just take a load of notes and get a bunch of books and solve problem after problem after problem? I had a world history teacher who probably had the best yet hardest way to make us learn things. He would give us maybe 5 pages of notes and several pages of homework everyday for one subject. He basically carved this history crap into our brains by making us write everything down. I still haven't forgotten a single thing he taught us. But its different with math..you can't exactly write a page or 2 of notes on how to differentiate this type of equation. Or at least I cant.

What happens to me is that when I go over it I understand how to do it. Its like, I read it once and I can do any equation with that step. The only problem is, I have trouble memorizing the steps, or all the steps to figure multi-step problems out. For example I was just studying marginal analysis yesterday and I memorized it perfectly I thought. I wake up today and I came to this place I come to to study, and I forgot almost completely how to do a few things in it. Like said before, I had to review.

So what do you guys think would be the best way for me to memorize this? Notes? Doing loads of equations and just carving it into my brain?

 

[Kurdt]

I don't think anybody memorises all of it. What tends to happen is that you memorise things that you're working with lots very easily (since you're using the methods all the time) and other things you have to use a book to reference. What is important is not memorising how to do things but recognising when things need to be applied. If you don't know how to apply it at that instant then you can always look it up in your favourite book. I will say that doing lots of examples should help embed things into your mind. Like I said, the things you use lots are the ones you remember most.

So I wouldn't worry that you can't remember everything, just make sure you can recognise the principles involved which you can then look up if need be.

 

[The_Z_Factor]

Funny thing is, that's sort of what I have a problem with. Like the other day I was doing I believe sketching a graph using functions and the derivatives of those functions by finding the points and the slopes of each point using a cubic polynomial. The next day I had a problem asking for that and I did it completely wrong because I had forgotten some of the stages used to solve them. What you were supposed to do according to my book is solve the functions of x for the points, and then the derivatives for the same x value, for the slope. I forgot to get the points, and I got confused. I knew what I was supposed to do, but I forgot each step in which to solve it, and of course got the answer wrong haha.

But, thank you for the advice, that helps me a lot because I was trying to make myself memorize each bit re-reading each section of the book over and over again, as if it was a requirement. Now I feel I shouldn't do that anymore but instead memorize the applications or the certain types of problems so I know what to look up for the answer, and I'll already know how to solve it. Thanks much.

 

[HallsofIvy]

You learn by doing. Do as many of the exercises as you can. Work through the examples in the text yourself, preferablly before reading through them.

 

[notagenius]

i suspect a lot of schools cover calc and ODEs in about 70 weeks. a bit less than 15 pages per week.

i take notes while reading; this is necessary as some of my books are borrowed. you could also try some video lectures to add an audio-visual component.

 

[The_Z_Factor]

i suspect a lot of schools cover calc and ODEs in about 70 weeks. a bit less than 15 pages per week.

i take notes while reading; this is necessary as some of my books are borrowed. you could also try some video lectures to add an audio-visual component.

I don't even know what an ODE is..

But I'm studying high school calculus. I guess right now it'd be in the "Pre-Calculus" section of high school study. I think..high school has what..36 weeks? 2 semesters 18 weeks a piece, in my district at least.

 

[Invictious]

'Memorizing' in math = Fail.
I know because my friends around me have always done that, and they never did too well on their tests. There is no easy way out, you have to keep on doing exercises until it becomes second nature.
Of course, learning how things are derived helps immensely, thought not necessary, since you just know how things work.

After you finish the exercises, do them again!
or go online and look for more.

 

[mathwonk]

my favorite way to learn is to lecture to others, and to write up the material in detail.