# Differences

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courses:order20:eeorder20:eembdiff 2018/08/20 09:21 | courses:order20:eeorder20:eembdiff 2019/03/22 11:30 current | ||
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* QUIZ/Derivatives pretest (10 min) | * QUIZ/Derivatives pretest (10 min) | ||

- | * [[..:..:lecture:inlec:indiff1d|Differentials of 1D Functions]] (Lecture: 10 min) | ||

- | * [[..:..:..:activities:guides:ee|Total Differentials on a Surface]] (SGA - 10 min) | ||

- | * [[..:..:lecture:inlec:indiffzap|How to zap with d]] (Lecture: 10 min) | ||

- | * [[..:..:..:activities:guides:inzapd|Evaluating Total Differentials]] (SGA - 10 min) | ||

- | * New Surfaces activity - Covariation in Thermal Systems (SGA - 10 min) | + | ====Lecture: Differentials of 1D Functions (Lec - 20 min)==== |

+ | Main ideas | ||

- | {{page>courses:hw20:eehw:eembdiff}} | + | * Previewing the Math Bits theme of Variables and Representations |

+ | * Teaching differentials, small changes, and zapping with d | ||

+ | | ||

+ | ==Lecture (30 minutes)== | ||

+ | | ||

+ | Ask students to make a sketch of f = 7x<sup>2</sup> on the big white board. | ||

+ | | ||

+ | What are the variables of interest? One idea here is to note that x is not the only variable here: f is also a variable from a physics perspective. | ||

+ | | ||

+ | What representations do we have for this relationship? The symbolic equation is one, and the graph is another. | ||

+ | | ||

+ | Introduce the differential quantities df and dx as small changes in f and x, respectively. Ask students to add df and dx to their graphs. | ||

+ | | ||

+ | Then, ask students how df and dx are related to each other. Students should be able to articulate that this is a derivative. | ||

+ | | ||

+ | Is the relationship the same if we choose a different point on the graph (a different initial x)? | ||

+ | | ||

+ | Then relate df and dx using the symbolic representation: df = 14xdx. | ||

+ | | ||

+ | : The following two steps can be replaced by other activities on the relevant Hour page. | ||

+ | * Give the students f = 5x<sup>2</sup>y<sup>3</sup>. What are the variables? What representations do we have (if time, hand out surfaces and have students make sketches similar to the above)? What does a differential relationship look like? For this last one, use the generic form df = A dx + B dy, and talk about the fact that this is another representation. | ||

+ | * Do some specific examples of using the zapping with d strategy (see [[http://physics.oregonstate.edu/BridgeBook/book/math/zap|Zapping with d]]). | ||

+ | | ||

+ | ====Activity: Total Differentials on a Surface==== | ||

+ | [[..:..:activities:eeact:eembdiffsurf|Link to Total Differentials on a Surface Activity]] | ||

+ | | ||

+ | **Activity Highlights** | ||

+ | {{page>activities:content:highlights:eembdiffsurf}} | ||

+ | | ||

+ | ====Activity: Evaluating Total Differentials==== | ||

+ | [[..:..:activities:inact:inzapd|Link to Evaluating Total Differentials Activity]] | ||

+ | | ||

+ | **Activity Highlights** | ||

+ | {{page>activities:content:highlights:eembdiffsurf}} | ||

+ | | ||

+ | | ||

+ | ====Activity: Covariation in Thermal Systems==== | ||

+ | [[..:..:activities:eeact:eesurfcovariation|Link to Covariation in Thermal Systems Activity]] | ||

+ | | ||

+ | **Activity Highlights** | ||

+ | {{page>activities:content:highlights:eesurfcovariation}} | ||

+ | | ||

+ | | ||

+ | ===== Homework for Energy and Entropy ===== | ||

+ | {{page>courses:hw20:eehw:eembdiff&noheader}} | ||

{{page>wiki:footers:courses:eehourfooter}} | {{page>wiki:footers:courses:eehourfooter}} | ||