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## Short Sequences

In many cases, we use several activities in a carefully structured sequence, to help students see how information ties together. This is a major task for beginning upper-division learners. Short sequences are  3 or 4 activities that are used together to explore a particular topic from several different viewpoints.

### E & M Sequences

• Representations of Scalar Fields: Use a sequence of activities to develop students' geometrical understanding of scalar fields in the context of electrostatic potentials
• Geometry of the Gradient: Use a sequence of activities to develop student understanding of the geometry of the gradient to relate electrostatic potentials and electric fields
• Geometry of Vector Fields: Use a sequence of activities to develop students' geometrical understanding of vector fields in the context of electric and magnetic fields
• Power Series Sequence: Use a sequence of activities to introduce students to making approximations with power series expansions and help students exploit power series ideas to visualize the electrostatic potential due to a pair of charges. The final activity of this sequence is the first activity in the ring sequence.
• Ring Sequence: Use a sequence of activities with similar geometries to help students learn how to solve a hard activity by breaking it into several steps. (A Master's Thesis about the Ring Sequence)
• The Geometry of Flux: Use a sequence of activities to help students develop a geometrical understanding of flux.
• Gauss's Law: Use a sequence of activities to help students understand how to use the integral form of Gauss's law to find electric fields in situations with high symmetry. These activities have a special emphasis on helping students make clean, coherent symmetry arguments using Proof by Contradiction.
• Ampere's Law: Use a sequence of activities to help students understand how to use the integral form of Ampere's law to find magnetic fields in situations with high symmetry. These activities have a special emphasis on helping students make clean, coherent symmetry arguments and to use Proof by Contradiction.
• The Differential Form of Maxwell's Equations: Use a sequence of activities to help students understand the differential versions of Maxwell's equations. Included are activities that address the geometric interpretations of flux, divergence, and curl and also derivations of the Divergence theorem, Stokes' theorem, and using these theorems to derive the differential versions of Maxwell's equations from the integral versions.
• Boundary Conditions: Use a sequence of activities to help students derive the boundary conditions for electromagnetic fields across charged surfaces or surface currents.
• Plane Wave Sequence: Use a sequence of activities to help students understand what is planar about plane waves.
• Flux Integration Use a sequence of activities to develop student skills to perform integration involving various forms of flux prior to the introduction of Gauss's law
• Curvilinear Coordinates Use a sequence of activities to introduce students to curvilinear coordinates including naming conventions and unit vectors

## Overarching Sequences

Some sequences (or stories or themes) occur over several Paradigms and Capstone courses:

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