Some nice review tutorials from Harvey Mudd College

Hour 1: Electric Potential

• QUIZ
• Coulomb's Law

Hours 2-3: Potential Due to Point Charges

• Superposition
  • Small Group Activity: Visualizing Equipotential Surfaces
• Equipotential surfaces

Hour 4: Power Series This hour is likely to move to Energy and Entropy in the future.

• Power Series Approximations
  • Small Group Activity: Calculating Coefficients for a Power Series
• Properties of Power Series

Hour 5: The Distance between Two Points

• Vectors
  • Kinesthetic Activity: Star Trek
• Dot Products

Hour 6: Two Point Charges

• Dipoles
  • Small Group Activity: Electric Potential for 2 Point Charges (with Power Series)

Hour 7: Differential Vector Elements Math Bits??

• The Position Vector
• The dr Vector
  • Small Group Activity: Vector Differentials

Hour 8: Line Integrals Math Bits??

• QUIZ
• Line Integrals
  • Small Group Activity: Boysenberry Patch

Hours 9-10: Integrating Charge Densities Math Bits??

• Charge Density
  • Kinesthetic Activity: Acting Out Charge Densities
• Cross Product
  • Small Group Activity: Finding dA and dV
• Total Charge
  • Small Group Activity: Total Charge

Hours 11-12: Calculating Potentials

• Find the surface area of a cone
• SQBQ write $d\vec r$ in 3 different coordinate systems
• —— Old ——
• Potential Integrals
  • Small Group Activity: The Ring 1 (V)
• Approximating Integrals with Power Series
• Potential Due to Finite and Infinite Lines

Hours 13-14: Superposition of Electric Fields

• Electric Field Vectors
  • Small Group Activity: The Ring 2 (E)

Hour 15-16: Gradient Math Bits??

• QUIZ
• The Gradient
  • Surfaces Activity: The Hillside
  • Small Group Activity: Navigating a Hill
  • Kinesthetic Activity: Acting out the Gradient
• Directional Derivatives (Optional)
• Electric Field as Gradient

Hour 17: Flux

• Electric Flux
  • Kinesthetic Activity: The Concept of Flux
  • Small Group Activity: Calculating Flux
  • Mathematica Activity: Visualizing Electric Flux

Hour 18: Divergence Math Bits??

• The Divergence
  • Small Group Activity: Visualizing Divergence
• The Divergence Theorem
• Gauss's Law (Differential Form)

Hours 19-20: Gauss's Law

• Gauss's Law (Integral Form)
  • Small Group Activity: Using Gauss's Law

Hours 21-22: Conservative Fields

• What Fields Are Conservative?
  • Small Group Activity: Counting Paths
• Vector line integrals
• QUIZ
• Relating Work to Potential
  • Small Group Activity: Work
• Finding Potentials from Fields
  • Small Group Activity: The Murder Mystery Method

Hours 23-25: Solving Laplace's Equation

• Second Derivatives
• The Laplacian
• Conductors
• Separation of Variables
  • Small Group Activity: Boundary Value Problem (New activity)
  • Computer Activity: Relaxation Technique (Optional/Computation course)

Hour 26: Energy

• Electrostatic Energy
  • Kinesthetic Activity: Energy of Discrete Charges

Hour 27: Curl Math Bits??

• The Curl as Circulation
  • Small Group Activity: Visualizing Curl
• The Curl in Curvilinear Coordinates

Hour 28: Current

• Electric Current
• Current Density
  • Kinesthetic Activity: Acting Out Current Density

Hours 29-30: Vector Potentials

• QUIZ
• What Is Vector Potential?
  • Small Group Activity: The Ring 3 (A)

Hours 31-32: Magnetic Fields

• The Biot-Savart Law
  • Small Group Activity: The Ring 4 (B)

Hour 33: Ampère's Law

• Symmetry Arguments
  • Small Group Activity: Ampère's Law

Hour 34: Stokes' Theorem

• Curl Revisited
• Stokes' Theorem
  • Small Group Activity: Where Is the Current? We need a new activity

Hour 35: Review

Note that this is now covered in Waves and Oscillations, and also in Periodic Systems

• Prerequisite Ideas
• Reading: GVC § Step Functions–The Dirac Delta Function and Densities
• Step Functions
• Delta Functions
• Homework

These feel like they go really well early in the Capstone to set up E and B fields in matter.

• Prerequisite Ideas
• Continuity of the Electric Field at Boundaries (SGA )
• Continuity of the Magnetic Field at Boundaries (SGA)

• Prerequisite Ideas
• Reading: GVC § Product Rules–Integration by Parts
• Product Rules (lecture)
• Integration by Parts (lecture)

• Prerequisite Ideas
• Energy for Continuous Distributions (lecture)
• Homework