文档介绍：STUDY GUIDE TO CALCULUS
This Student Study Guide panies the textbook Calculus by Gilbert Strang. It is correlated
section by section with the essential points of the text. The Guide contains ponents which
experience has shown are most helpful:
1. Model problems ments plete solutions.
2. Extra drill problems included with exercises for chapter review.
3. Read-through questions from the text with the blanks filled in.
4. Solutions to selected even-numbered problems in each section.
The Guide can be obtained from bookstores or by writing directly to Wellesley-Cambridge Press.
Our address is Box 812060, Wellesley MA 02181 (prepayment by check). The press also publishes two
other basic textbooks by Gilbert Strang: Introduction to Linear Algebra and Introduction to
Applied Mathematics. This Study Guide shares the same goal, to teach mathematics in an active
and purposeful way.
Velocity and Distance
The first step in calculus (in my opinion) is to begin working with junctions. The functions can
be described by formulas or by graphs. The first graphs to study are straight lines, and the functions
that go with them are linear: y = mx + b or (using other letters) f = vt + C. It takes practice to
connect the formula y - 4 = 7(x - 2) to the straight line with slope 7 going through the point (2,4).
You need to be able to rewrite that formula as y = 7x - 10. You also need to be able to find the
formula from the graph. Here is an example: Find the equations for these straight lines.
The first line goes down 2 and across 5. The slope is = -.4. The minus sign is because y
decreases as t increases - the slope of the graph is negative. The "starting pointn is y = 2 when
t = 0. The equation is y = 2 - .4t. Check that this gives y = 0 when t = 5, so the formula correctly
predicts that second point.
Problem 1: Find the equation for the second line. Comment: The points (0, b) and (a,O) are
given by letters not numb