## The puddle

• differentials
• assignment Differentials of Two Variables

assignment Homework

##### Differentials of Two Variables
AIMS Maxwell AIMS 21 Static Fields Winter 2021 Find the total differential of the following functions:
1. $y=3u^2 + 4\cos 3v$
2. $y=3uv$
3. $y=3u^2\cos wv$
4. $y=u\cos(3v^2-2)$
• assignment Zapping With d 1

assignment Homework

##### Zapping With d 1
Energy and Entropy Fall 2020 Energy and Entropy Fall 2021

Find the differential of each of the following expressions; zap each of the following with $d$:

1. $f=3x-5z^2+2xy$

2. $g=\frac{c^{1/2}b}{a^2}$

3. $h=\sin^2(\omega t)$

4. $j=a^x$

5. $k=5 \tan\left(\ln{\left(\frac{V_1}{V_2}\right)}\right)$

• group Gravitational Potential Energy

group Small Group Activity

60 min.

##### Gravitational Potential Energy

Students examine a plastic “surface” graph of the gravitational potential energy of an Earth-satellite system to explore the properties of gravitational potential energy for a spherically symmetric system.
• AIMS Maxwell AIMS 21 The depth of a puddle in millimeters is given by $h=\frac{1}{10} \bigl(1+\sin(\pi xy)\bigr)$ Your path through the puddle is given by $x=3t \qquad y=4t$ and your current position is $x=3$, $y=4$, with $x$ and $y$ also in millimeters, and $t$ in seconds.
1. At your current position, how fast is the depth of water through which you are walking changing per unit time?
2. At your current position, how fast is the depth of water through which you are walking changing per unit distance?
3. FOOD FOR THOUGHT (optional)
There is a walkway over the puddle at $x=10$. At your current position, how fast is the depth of water through which you are walking changing per unit distance towards the walkway.