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Q: What is the difference between exp(x) and ex.
Answer: it is the same. It is the exponential function. We will define it as a limit
of exph (1+h)x/h, which is an important function because it is the
"compoound interest rate function", which you should be familiar with if you interested
in finance. Here is the Wikipedia
entry. We use it in a more streamlined form and use the letter h, because in physics,
the Planck constant is denoted by h.
Nature seems not to like numbers smaller than say h=10-34, the physical reality starts
to change there. The interest rate formula appears in the movie
"The Bank",
where it is written as FutureValue = InitialValue (1+r)n, where r is the interest rate
and n is the number of years.
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Q: How do we determine whether a function is invertible from
A to B.
Answer: this will be easier in the future when we can differentiate,
for now, draw the graph of the function in the rectangle which has the interval A as a base and
the interval B as a side. The graph is the graph of a function if the vertical line test
is valid. Draw any vertical line. It should pass through exactly one point in the graph.
If also the horizontal line test is valid and every horizontal line intersects the
graph once, then the function is invertible.
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Q: How much work load do we expect?
Answer: It is a matter of fact that every math course requires a substantial amount of work.
Besides attending lectures, there is homework due every
class (5 problems each time). Take the homework seriously. It is 30 percent of the grade.
We keep the workload constant over
the semester and have self-contained handouts and worksheets for every lecture.
There are 2 midterms and one final exam.
