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courses:order20:eeorder20:eembdiff 2018/08/31 13:38 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:indiffzap|Differentials of 1D Functions]] (Lec - 20 min) 
-  * [[..:..:..:activities:guides:eembdiffsurf|Total Differentials on a Surface]] (SGA - 10 min) 
-  * [[..:..:..:activities:guides:inzapd|Evaluating Total Differentials]] (SGA - 10 min) 
-  * New Surfaces activity - [[..:..:..:activities:guides:eesurfcovariation|Covariation in Thermal Systems]] (SGA - 10 min)+====Lecture: Differentials of 1D Functions (Lec - 20 min)==== 
 +Main ideas 
 + 
 +  * 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 ===== ===== Homework for Energy and Entropy =====

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