What do I need to know to study calculus?

[The Rev]

What are the prerequisites?

In High School, we had Algebra I, Geometry, Algebra II (Intermediate Algebra), Trigonometry, and pre-calc classes, and you took them in that order. Do I only need the basics of Algebra, Euclidean Geometry and Trigonometry to start with calculus? Or are there other topics that would really help?

Also, if you know any good textbook recommendations for any of these areas, I would appreciate hearing them.

Thanks!



The Rev

 

[JFo]

Yes... algebra trig, and euclidean geometry are pretty much the major pre-reqs ( I consider pre-calc just a combination of the first two plus the transcendentals ln, e, log etc..)

Just to note, the better you are at algebra the easier time you'll have with calculus.

Texts:
The three classics are Spivak, Apostol, And Courant. They are also very challenging, but will really teach you the theory of calculus, not just how to use the formulas.

Just about all the others are considered cookbooks ie: they teach you the formulas, but not much of the theory.
-of the most recommended here is probably Stewart. If your not a math-wiz or you don't like a challenge, it might be best to start here and then move on to one of the three above.

edit: As far as a subject that would help, but is not necessary, would be logic (good for all math).

 

[phoenixthoth]

I think Stewart is just fine, especially with the appendix on "proofs of selected theorems." He still does epsilon-delta, doesn't he?

In conjunction with Stewart, you also should at least glance at the books by Hughes-Hallet, the Harvard folk responsible for "Calculus reform." I'll let the other people here point out the defeciencies in the reform approach.

In terms of prerequisites, you should be able to take a function and calculate a difference quotient:
(f(x+h)-f(x))/h and simplify it completely for, for starters, functions like

Sqrt[x], 1/x, x^2, x^3, 1/x^2, and -x^2-3x+1.

You should understand the difference between
x+1
and
(x^2-1)/(x-1).

You should be able to graph basic functions like
x^n (n integer), x^n (n rational), a x^2+b x+c, Trig[x] (Trig=one of the six circular functions from trigonometry), Exp[x], Log[x], and for an f listed above, something of the form a f[b x+c] + d.

You should be able to solve algebraic inequalities like
(x^2+4x+4)/(x-1) > 0.

There's I suspect more prerequisites but that's all the jumps out at me at this time.

As far as Spivak goes, my philosophy is to try out someone like Hemmingway before someone like that Russian dude who wrote War and Peace. But I would recommend trying Spivak, et al, but to not let yourself get too frustrated with the knowledge that those are some fairly hard core books.

 

[mathwonk]

the main prereq for cookbook calc is algebra. for honors calc logic is important.


i recommend an old old college algebra book. much better than any new "precalc" book.