Learning Calculus: What's the Right Order?

[CuriousBanker]

I bought Spivaks book on calculus, and also "how to prove it". I am just doing this for fun, not for school.

On an old thread I remember reading I should learn to do proofs first before moving on to Spivak. I won't be doing this for a few months because I am busy studying for CFA exam, but I just flipped through how to prove it, and on page 2 it starts talking about intergers. I don't know what an interger is (Well I know its the area under a curve but that's about it). Should I read Spivak first?

 

[A. Bahat]

Do you mean "integral" (as in area under a curve) or "integer" (as in 0,1,-1,2,-2,...)?

 

[Feodalherren]

Kinda worries me if you're moving on to calculus without knowing what an integer is :p.

 

[micromass]

If you don't know what an integer is, then I think that Spivak will be a bit too difficult for you.

Why don't you first get a good book like "basic mathematics" by Lang and work through that?

 

[CuriousBanker]

I meant integral not interger. Whoops

 

[johnqwertyful]

I meant integral not interger. Whoops

An integral is a limit of Riemann sums. A Riemann sum is a height x width. Let's say you want to find the area under x^2 from 0 to 2.. A very crude estimate would be 4x2 (a single box). If you do two boxes, width 1, you get 1x1+4x1=5. A better estimate. Then 3, 4, 5, and so on. An INTEGRAL is where you take the limit as the number of boxes approaches infinity.

You get a cool theorem called the Fundamental Theorem of Calculus that helps you evaluate them.

 

[Kaldanis]

I bought the Spivak book just before I started Calculus I so that I could 'prepare'. Huge mistake. I understood very little and to be quite honest, it made me fear what was about to come. I'm now taking Calc III and still won't go back to Spivak because of my earlier experiences with it.

If you're just starting then I think it may be a bit too difficult to use as a learning tool. I'm using a book called Calculus Early Transcendentals (Stewart) and it's quite good.