Expert: Scott A Wilson - 5/11/2009

Question
Hello, I'm in grade eight and I've been self-studying for
the past six months. I'm finishing up trigonometry and pre-
calculus and i'm hoping to begin calculus this summer. I
want to buy a calculus textbook, but i'm not sure what to
get. I've seen a preview of Stewart's textbook and for the
most part it seems great, but reviews say otherwise. But I
really like because it covers majority of calculus and I
need that because i don't want to buy more than one
textbook since they're pretty expensive. Would you recommend the Stewart's text for a self-studier such as
myself as a intro to calculus? Do I need any prior
knowledge of math other than algebra, geometry,
trigonometry. and pre-calculus before i start calculus?

Thank you in advance!

Answer
Contents of this Letter:
1) Need to Know
2) What you'll learn
3) The Book

1) Need to Know:
I don't know that much about books, but as long as the book is read
and the problems are done until you understand them, it would seem
OK.  As far as prior knowledge, it sounds like you have what you
need.  What I saw in calculus when I took it was you needed to know
is the following:

 be able to solve the quadratic equation

 know that y and f(x) are frequently used together,
 though not all the time

 the sum of angles in a triangle is 180°

 as caculus is gotten into, you'll need to know that
 sin = a/c   csc = c/a
 cos = b/c   sec = c/b
 tan = a/b   ctn = b/a
 so that you can interchange them with the following equations:
    sin²(x) + cos²(x) = 1
    tan²(x) + 1 = sec²(x)   { the last equation / cos²(x) }
    1 + ctn²(x) = csc²(x)   { the top equation / sin²(x) }

 Physics would also be useful, but it is not necessary.
 I only used a small part of my physics in mathematics and didn't
 really need to know it first, but it was useful that I did.

2) What you'll learn:
The basic thing you will learn first off is that the derivative is
the slope of a line.  If the line is x, the slope is 1.  If the
line is 3x², the slope is 6x.  If the line is 7x^3, the slope is
21x².  Basically, if the line is ax^n, the slope is anx^(n-1).

This paragraph is for a side on what you'll learn in the course.
It would also be useful to know basic physics of motion, but that
is not really that necessary.  There will be equations that deal
with distance, velocity, and motion.  What you will learn is that
if d(t) is the distance after time t, then v(t) is the velocity,
and a(t) is the accelartion.  The reason these will come up is
velocity is the derivatve of distance, and acceleration is the
derivatve of height in regards to falling objects.

From physics, it is known that acceleration is usually known as the
variable a.  Velocity is then the equation v=at, and distance is
s=at².  The reason s is used, is in calculus, d is reserved for
derivatives.  The derivative of s is s'(t) = ds/dt = v.  The
derivative of velocity = v'(t) = dv/dt = a.

This was learned after about a month or two when I took calculus.

The Book
What I learned in the second term or so was that the opposite of the
derivative is the integral, which I see on the cover of that book
(if I got the right one, that is).  I'm looking at a website called
http://www.amazon.com/Calculus-Stewarts-James-Stewart/dp/0495011606

When I was in college, books were expensive.  I always bought used
books when they were avaialable for the course.

If this is the right book, after browsing through it, there is a
lot of good stuff in it.  The pictures in are very good and give
me an idea of what is going to be talked about.

Summary
As long as you want to learn it and spend you're time studying it
( and possibly sending me an occasional question), you'll be sure
to understand it.  Each chapter is important and is very good to
know.  It looks like the first 9 chapters cover the basics and the
second 9 chapter (10-18) cover detail in various subjects.