The Static Vector Field Paradigm continues the discussion of E&M from the Symmetries & Idealizations Paradigm, focusing on electric fields, magnetic fields, and the magnetic vector potential. This course uses a variety of pedagogical techniques (small group activities, computer visualization, kinesthetic activities, and lecture/discussion) to help students build a multifaceted understanding of these ideas. This course emphasizes extending the integral versions of Maxwell's equations (learned in introductory physics) to the local, differential versions; visualizing vector-valued functions in three dimensions using the computer algebra software Maple; and extending the techniques of vector calculus from rectangular to cylindrical and spherical coordinates. (Catalog Description)
For students to build conceptual and geometric understanding of current density, magnetic field, and magnetic vector potential and a formal understanding of the relationships between them (using vector calculus)
For students to understand divergence and curl - formally and geometrically - and the Divergence Theorem and Stoke's Theorem formally and geometrically
To derive the differential form of Maxwell's equations from the integral form and for students to have link their conceptual understanding with the formalism of Maxwell's equations
For students to understand Gauss' Law and Ampere's Law and how to make explicit symmetry arguments.
For students to understand the continuity of electric and magnetic fields across charge/current boundaries.
For students to understand how energy is stored in electric and magnetic fields, and be able to calculate the energy from sources, fields and potentials.
For students to come to understand that sources, fields, and potentials are different constructs that address the same phenomena, but are useful in different ways.
Sample Syllabus
Fall 2008
Textbook: The Geometry of Vector Calculus—-an introduction to vector calculus, with applications to electromagnetism. One of the Tables of Contents for this online interactive textbook has been specifically designed for this course.