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

1. What is the Pythagorean Theorem?

2. What is a function

3. How is the sine function defined?

4. What is the difference between units and dimensions?

5. What is a vector? What is the difference between a scalar and a vector?

6. What is a gradient? Is it a scalar or a vector? What dimensions does it have?

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?

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?

10. How is acceleration defined? What are its dimensions?

11. Is an object in perfect circular motion accelerated? Why or why not?

12. What does Newton's Second Law of Motion say, in English?

13. What is a conservation law? (What are some examples?)

14. What is a force? What are the dimensions of force?

15. What forces can act on water in a stream, a lake, an ocean, or underground?

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?

17. Conceptually, what is hydrostatic balance in a fluid?

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?

19. 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?

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