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. In principle the prerequisites for ERTH 430 help ensure that you're already acquainted with them. However, to learn
more about your comfort level, test yourself by trying to answer the questions
as best you can. Your answers can help us identify and fill any holes in your
knowledge before we really need that knowledge in class!
- What is the Pythagorean Theorem?
- What is a function?
- How is the sine function defined?
- What is the difference between units and dimensions?
- What is a vector? What is the difference between
a scalar and a vector?
- What is a gradient? Is it a scalar or a vector?
What dimensions does it have?
- 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?
- 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?
- What is a radian?
- How is acceleration defined? What are its dimensions?
- Is an object in perfect circular motion accelerated?
Why or why not?
- What does Newton's Second Law of Motion say, in
- What is a conservation law? (What are some examples?)
- What is a force? What are the dimensions of force?
- What forces can act on water in a stream, a lake, an ocean, or underground?
- 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?
- Conceptually, what is hydrostatic balance in a fluid?
- 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?
- 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?
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