12.2 Idea of a Line Integral Update

[nelong]

• [x] Look at prextext notation for Newtons (Preview Activity 12.2.1)

• [x] Make interact to replace calcplot3d applet?

• [x] Add convention (or some kind of identifier) to C_1+C_2 meaning (at start of 12.2.3)

• [x] CalcPlot3D applet is interesting, but either needs more guidance to students on how to use it or to be built into an activity

• [x] We use the phrase “piecewise smooth” but don’t really define it

• [x] Subsection 12.2.2, first paragraph: Would be better to motivate with single variable integration (area) rather than differentiation

• [x] Figure 12.2.2

• The vectors attached are pretty wild. Choose something tamer.

• Break into a series of figures: curve with vector field, curve with subdivisions (fix a small value of n so it’s not so complicated), and then a figure where zoomed in to the point where the field looks constant

• [x] Move the discussion of dot product being positive or negative to after the definition

• [x] Definition 12.2.3: Better to have n go to infinity or have max length go to zero?

• [x] Figure 12.2.4: Decrease vector density, watch label position

• [x] Figure 12.2.7: Move labels and move or reshape the purple curve

• [x] Overall, review subsection structure

• [x] Add a figure before properties of line integrals to make the discussion of adding line integrals easier to understand.

• [x] Last sentence of paragraph in 12.2.4: “rotate” vs work with or work against

• [x] In the summary:

• [x] 1st bullet change “is” to “can be represented by”

• [x] 2nd bullet has “increases” twice

• [x] Add subsection at end with content dependencies and notes to instructor

[nelong]

• [x] Add some context or a link to where students would have seen NESW and angles to specify vector directions (in the Preview Activity).
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[nelong]

A few things for Mitch to tell me how to do:

• [x] The compass rose image is not showing up. I haven't dug into what is different about that...
• [x] Do we need to talk about simple curves for the circulation in the last subsection
• [x] In the convention 12.2.13, I'm not sure how we want to do the layout of the sample curves but they are generated in the Cocalc project and in the repository
• [x] Should we relabel example 12.2.11 or just show the solution (not as a knowl)
• [x] Put a reference to the property of definite integrals used at the start of the properties of line integrals subsection
• [x] Add Webwork exercises (listed in the WebWork Exercises text document in repository)