" Undergraduate Electromagnetics : Discrete , Numeric , and Continuous

This paper describes a new approach to undergraduate electromagnetics that is based on spatial discretization and numeric computation. The initial coverage is limited to quasi-static, twodimensional, Cartesian geometries with no leakage flux, descriptive of many ideal lumped circuit elements with which the students are already familiar. The circuit behavior of resistors, capacitors, and inductors motivates the introduction, formulation and interpretation of the behavior of the electric and magnetic fields. The fields within the elements are expressed by Laplace’s equation in discretized form. This formulation provides the basis for numeric computations that exploit the power of modern PCs. In addition, PC-based software provides a rich graphic environment that enables students to display the solutions in a variety of visual modes. The simplicity of this approach allows students to focus upon the electromagnetic principles and to gain valuable experience in solving problems. In the simplest form, classroom and homework activities include spreadsheets, matrix solvers, and circuit analog simulations. More ambitious student activities are realized with a powerful, PC-based, interactive, electromagnetic computation engine that empowers students to experiment with the geometry and material properties of two-dimensional electromagnetic problems. As the students gain experience, the more traditional formulations of continuous differential and integral vector calculus are introduced to complete their preparation for advanced courses. This technologically intensive approach is particularly attractive since all of our students have laptops and most classrooms allow network access to all students. A variety of software packages (including Maple, Mathcad, Matlab, Excel, Pspice and VEM) further enhances this approach. Course details and software demonstrations are included in the presentation.