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Integration in One Dimension

Students entering into upper-division physics courses are typically familiar and comfortable with integration as taught in mathematics courses. In physics, there is additional language and interpretation which accompany integration. By reintroducing integration early in upper-division courses, many common student difficulties which arise in electricity and magnetism and other physics courses can be addressed. This sequence can serve as a quick reintroduction to integration and can likely be completed entirely in less than one hour.

Activities

  • Internal Energy of the "Derivative Machine" (Estimated time: ): This small group activity serves as an introduction to experimentally measuring an integral by determining the internal energy, $U$, of a nonlinear system at several locations. Students must choose a point of zero internal energy and then add up, incrementally, the force at each small change in distance by numerical integration.
  • 1D Rectangular Integration (Estimated time: ): This lecture introduces students to the language which physicists use with regard to integration. This includes the notion of integration as “chopping and adding” and “accumulation” as well as explanations of boundaries and functions as used in physics.
  • How what you're integrating isn't necessarily the parameter you want to vary after integrating. –Lecture or Homework primarily

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