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# Short Activity 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

• Curvilinear Coordinates: Introduces curvilinear coordinate systems including the associated basis vectors and integration measures on curves, surfaces, and volumes.
• Geometry of Scalar Fields: Develops students' geometrical understanding of scalar fields in the context of electrostatic potentials.
• Geometry of Vector Fields: Develops students' geometrical understanding of vector fields in the context of electric and magnetic fields.
• Power Series Sequence: Introduces 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: Activities with similar geometries help students learn how to solve a hard activity by breaking it into several steps. (A Master's Thesis about the Ring Sequence)
• Gauss's Law (Integral Form): Students 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 (Integral Form): Students 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: Students explore the relationship between the integral and 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: Helps students derive the boundary conditions for electromagnetic fields across charged surfaces or surface currents.

### Quantum Mechanics Sequences

• Visualizing Complex Numbers: Use a sequence of activities to develop representations of complex numbers and functions in the context of spin-1/2 systems
• Quantum Operators Sequence: Use a sequence of activities to help students understand allegorically what does (and does NOT) go on inside a quantum measuring device.
• QM Ring Sequence: Use a sequence of activities to help students understand what questions can be asked about a particle confined to a ring in different representations.
• Ring-Sphere-Atom Sequence: Use a sequence of activities to help students gain skills for working with quantum systems that progressively increase in dimension and complexity.

### Thermo And Stat Mech Sequences

• Name the Experiment: Use of sequence of activities to connect thermodynamic derivatives with experiments

## Overarching Sequences: Under Construction

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

## Short Sequences: Under Construction

### E & M Sequences

• 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

### Thermo And Stat Mech Sequences

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