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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**: Develops students' geometrical understanding of scalar fields in the context of electrostatic potentials.

**Geometry of the Gradient:**Develops students' understanding of the geometry of the gradient to relate electrostatic potentials and electric fields.

**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 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:**Helps students develop a geometrical understanding of flux.

**Gauss's Law:**Helps 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:**Helps 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*.

**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.

### Vector Calculus Sequences

### Rotating Frames Sequences

### Special Relativity Sequences

### Thermo And Stat Mech Sequences

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

**The Partial Derivative Machine**: Use a sequence of activities to introduce students to partial derivatives in the context of physics

## Overarching Sequences: Under Construction

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

## Short Sequences: Under Construction

### E & M Sequences

- 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.

- Plane Wave Sequence: Use a sequence of activities to help students understand what is planar about plane waves.

- Scalar Integration in Curvilinear Coordinates Use a sequence of activities to introduce students to integration in various coordinates in order to determine the total charge in an area or volume

- Total Charge in Curvilinear Coordinates Use a sequence of activities to introduce students to finding total charge from charge densities in Cartesian, cylindrical, and spherical coordinates

- Integration in One Dimension Use a sequence of activities to introduce students to integration in the context of physics

- Internal Energy of a One Dimensional System Use a sequence of activities to introduce students to experimentally determining the internal energy of a nonlinear, one dimensional system

- 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

- Representations of Two-Dimensional Scalar Fields Use a sequence of activities to develop representations of scalar fields of two-dimensions

- Representations of Ordinary Derivatives Use a sequence of activities to develop representations of ordinary derivatives

- Superposition of Electrostatic Potentials due to Point Charges Use a sequence of activities to introduce the superposition principle in the context of electrostatic potentials due to point charges

- Curvilinear Coordinates Use a sequence of activities to introduce students to curvilinear coordinates including naming conventions and unit vectors

- Direct Integration to Determine Electrostatic Potential Use a sequence of activities to introduce students to using direct integration through finding the electrostatic potential due to a ring of charge