ERTH 430: Fluid Dynamics in Earth Systems Confidence Survey: Math & Physics Diagnostic Questions (for class on Wednesday, 8/23/17) Dr. Dave Dempsey, Dept. of Earth & Climate Sciences, SFSU, Fall 2017

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? ____________

1. What is the Pythagorean Theorem?
 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

2. What is a function
 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

3. How is the sine function defined?
 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

4. What is the difference between units and dimensions?
 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

5. 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

6. 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

7. 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

8. 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

 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

10. How is acceleration defined? What are its dimensions?
 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. Conceptually, what is hydrostatic balance in a fluid?
 a. Very confident b. Somewhat confident c. Not very confident d. Not much of a clue

18. 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

19.

20. 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.

1. 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?
2. At what point(s) is the object accelerating? In what direction(s) is it accelerating, if any?
3. 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?
4. 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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