Class Summary for June 1, 1998
MAC 2311--Calculus I
We introduced the derivative in class. This is just a term for
the three-step process that we have been following. However, this process
describes an instantaneous rate of change in a more general sense than
we have applied it so far, hence we have a general term for the process.
We will see later on many more places where the derivative occurs: in economics,
biology, chemistry, physics, and other areas. We introduced the most common
notations for the derivative of a function r(t): r'(t) (Lagrange), dr/dt
(Leibniz), and the dot notation due to Newton, that is still used a lot
in physical science and engineering. We talked briefly about the derivative
as describing a rate of change of one quantity with respect to another;
this is important to remember because this allows us to recognize derivatives
when they occur in applications. Looking at the units also helps us to
establish some specific about the derivative: for example, velocity is
expressed in feet/sec, which tells us that velocity is a derivative of
distance (position) with respect to time, since the former is measured
in feet and the latter in seconds.
Next, we had a brief review for test 1, which will be Wednesday, June
3. The test will consist of two parts, an in-class and a take-home part:
the take-home part will be due on Friday, June 5. The topics for the test
are as follows (asterisks indicate topics that will be covered on the in-class
part as well as the take-home part):
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**Vectors: magnitude and direction, component form, and conversions between
the two.
-
**Vector operations (sum difference, scalar product, dot product)
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**perspectives on vector addition: geometric and algebraic
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**projections of vectors
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**Three-step process for finding the instantaneous velocity
-
parametric representations of curves. Some specific classes of curves that
you should be faniliar with are lines, circles and ellipses, and
representations of regular functions y=f(x).
-
average and instantaneous velocity
-
slope of a curve and the tangent line
-
**horizontal and vertical tangents (what do you look for?)
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applications of instantaneous velocity
Distributions:
No new distributions. Solutions to Homework
Set 4 (Maple file) will be emailed out and placed into course folder
as soon as they are available.
Assignment:
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