Understanding vs. Memorization: Approaches to Success in Calculus

[lLovePhysics]

How to succeed in Calculus??

I've started Calculus and aced my first review exam of precalc. However, we are now studying the continuity of limits right now and we have learned quite a few theorems and rules already. Do these need to be memorized or is there a way to "understand" or "derive" these rules/theorems so it you can understand it conceptually instead of just analytically. As I flip through my text, there seems to be more complicated theorems and laws. Do you seriously need to memorize these or will they come naturally and be embedded in your brain?

Are these equations like Physics equations where they can all be understood conceptually? For example, you can explain the equation F=ma in so many different ways so that you can understand its true meaning. Is it like that in Calculus where you can find relationships etc.? What are the best ways to approach theorems, laws, and whatnot? Thanks.

I do not support rote memorization in math or Physics and I love understanding these instead of just memorizing the functions which mean nothing if you do not understand what they "symbolize."

 

[Dick]

Math is the same as physics in the sense that there are very few things that you need to memorize. As you understand more and more you will memorize less and less. As you say the concepts will become "embedded in your brain" and you will find it easy to derive the formulas if you need them.

 

[PowerIso]

I wouldn't worry to much about proofs and theorems in calculus 1. There are a few main ones that you might want to keep in mind. Some examples are the Squeeze theorem, Mean Value theorems, Fundamental Theorem of Calculus, Limit of Riemann Sum. Some other theorems are pretty much the same as others but applied to a different case or extended.

You'll learn to derive the formulas given to you if you want to, but sometimes it's easier to memorize it. The more you do it, the more it'll come to you.

 

[lLovePhysics]

I see. I guess I will just memorize things for now and try to understand why they are true if possible. From my experiences, when you step into any new subject it seems totally new and complex but then later it becomes a piece of pie (with hardwork, that is). Hoepfully, Calculus will be the same! :]

 

[Dick]

It will be. For all of the theorems PowerIso mentioned, I don't even remember a formula, I just remember a picture. In fact, sometimes I don't even remember the correct name. But I do remember the content.

 

[PowerIso]

It'll be easier. I'm also assuming you have very little experience in formal proof writing. I would advise you to pay attention to the methods used in the proofs that are presented. Also, a lot of these theorems can be shown by geometry, so knowing the formal definitions are not important at first. I would advise you to remember the definition of a limit and derivative if you plan to major in mathematics. Otherwise, it'll be fairly straightforward.

 

[learningphysics]

I see. I guess I will just memorize things for now and try to understand why they are true if possible. From my experiences, when you step into any new subject it seems totally new and complex but then later it becomes a piece of pie (with hardwork, that is). Hoepfully, Calculus will be the same! :]

Yup, calculus is exactly like that. As you practice it will become more and more natural to you.

 

[rootX]

If teacher assigns like q#2,3,5,7,15 from say chapter 2,
you do all the questions say >100 ...

(That's my way... lol, but I am now wondering if its good enough..)

 

[bob1182006]

When doing a lot of problems to make sure you know the material, at first do write them out and stuff, but after a while you can just do it in your mind (for this problem I would do ... and ... and the answer should be *) and if you get stuck then you should write it out. This way you can do say every problem in the end of your chapter in a few minutes instead of a half hour? writing everything out...