# Differences

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courses:order20:eeorder20:eembdiff 2018/08/19 09:38 courses:order20:eeorder20:eembdiff 2019/03/22 11:30 current
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-====== Title ======+====== Differentials ======
{{page>courses:prereq20:eepre:eembdiff}} {{page>courses:prereq20:eepre:eembdiff}}
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* QUIZ/Derivatives pretest (10 min)   * QUIZ/Derivatives pretest (10 min)
-  * [[..:..:lecture:inlec:indiffzap|Zapping with d]] (Lecture: 20 min)
-  * [[..:..:activities:guides:inzapd|Evaluating Total Differentials]] (SGA - 10 min)
-  * New Surfaces activity - Covariation in Thermal Systems+====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>wiki:footers:courses:eehourfooter}} {{page>wiki:footers:courses:eehourfooter}}

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