The questions below ask about mathematical and physical ideas,
entities, and relations that are likely to come up in ERTH 430. You might feel confident about
answering some of these questions, less confident about others.
Don't try to answer any of these questions. Instead, for each
question please rate your level of confidence that you could answer
the question well if you tried. (For each question, circle the most appropriate
choice provided.)
First, though, what is the month and day (not year) of your
birthday? ____________
- What is the Pythagorean Theorem?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is a function?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- How is the sine function defined?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is the difference between units and dimensions?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is a vector? What is the difference between
a scalar and a vector?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is a gradient? Is it a scalar or a vector?
What dimensions does it have?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is the definition of the derivative of a
function, f, with respect to an independent variable, x?
(Use English or math notation, defining the meaning of any new symbols you
introduce.) What is the meaning of the derivative? What dimensions does the
derivative of a function, f, have?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is the definition of the integral of a function,
f, with respect to an independent variable, x? What is the
meaning of the integral? What dimensions does the integral of a function,
f, have?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is a radian?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- How is acceleration defined? What are its dimensions?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- Is an object in perfect circular motion accelerated?
Why or why not?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What does Newton's Second Law of Motion say, in
English?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is a conservation law? (What are some examples?)
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What is a force? What are the dimensions of force?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What forces can act on water in a stream, a lake, an ocean, or underground?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- What two (or perhaps three) mechanisms can change the temperature
of a blob of water in a stream, a lake, or an ocean, or underground?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- Conceptually, what is hydrostatic balance in a fluid?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- Do you feel prepared to say much about some of the following
other mathematical ideas and entities: finite vs. infinitesimal differences;
field variables; partial derivatives?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
- The figure below shows a graph of the horizontal position
of a piece of chalk on the blackboard, relative to the left-hand edge of the
board, as a function of time. The positive direction is defined to be to the
right.
- At what point(s) is the chalk moving fastest? Can you
tell how fast? At what point(s) is it moving the slowest? Can you tell
how slow?
- At what point(s) is the object accelerating? In what
direction(s) is it accelerating, if any?
- Sketch the derivative of this curve with respect to
time, as a function of time. What is the physical meaning of graph you've
drawn?
- Sketch the second derivative of this curve with respect
to time, as a function of time. What is the physical meaning?
a. Very confident |
b. Somewhat confident |
c. Not very confident |
d. Not much of a clue |
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