Reference: GR 1
☐ Provide geometrical interpretations or physical examples for the gradient, divergence, and curl. Make a sketch or add a plot that you have made to illustrate these (point) derivatives.
☐ Provide geometrical interpretations or physical examples for the fundamental theorem for gradients, divergences, and curls.
☐ Write down Laplacian for an orthogonal coordinate system in terms of its scale factors. Verify this formula for cylindrical and spherical coordinates.
☐ Prove that the divergence of a radial inverse-square power vector field is consistent with a Dirac-delta point source or sink.
Week 3: Sep 2-4
Week 4: Sep 9-11 Electrostatics: Boundary conditions, work and energy, conductors
References GR 2
☐ Give the continuity conditions on the electric field and potential across interfaces.
☐ Show that the energy needed to set up a particular charge distribution given initial sources far away from each other can be obtained from the scalar potential.
☐ Provide the features of conductors that are relevant to determining the distribution of charges in them at electrostatic equilibrium.
☐ Briefly discuss how induced charges are set up on the surfaces of conductors in the presence of external electric fields.
☐ Prepare for a short quiz in the next on-site meeting.
Week 5/6: Sep 16-25 Electrostatics: Potentials
References GR 3
☐ Discuss the importance and advantages of formulating EM in terms of potentials (specifically for electrostatics).
☐ Give the relationship (Maxwell's equations) between the scalar potential and the electrostatic field.
☐ Enumerate the steps leading to a solution to Poisson's equation using Sturm-Liouville theorem techniques (separation of variables, eigenfunction expansion).
☐ Enumerate the steps leading to a solution to Poisson's equation using a Green's function solution.
☐ Use both techniques to solve a boundary value problem with fixed boundary conditions (you can choose your own example, in two or three dimensions).
Week 7: Sep 30 - Oct 1 Electrostatics: Multipole expansion
! One problem in the midterm will involve using multipole expansion techniques.
Midterms: 07 October 2026, in class. If suspended by UPD or LGU, next on-site class. Coverage is Griffiths Ch 1-3. Open paper notes.
Notebook: Due 14 October 2026, through Google Drive submission link (will be placed here soon). Coverage Weeks 1-6.
Faculty
- Francis Paraan