Geometrical Approach to Vector Analysis in Electromagnetics Education

A geometrical approach to teaching and learning vector calculus and analysis as applied to electromagnetic fields is proposed for junior-level undergraduate electromagnetics education. For undergraduate students, electromagnetics is typically the most challenging subject in the Electrical Engineering curriculum, and the most challenging component of the subject is the application of vector analysis to electromagnetic field theory and problem solving. According to the geometrical approach, the students are taught to “read” the figure and to “translate” this to equations at all times throughout the computation or derivation, instead of their “crunching” the formulas and numbers without even visualizing the structure. In performing vector manipulations, integrals, and derivatives, the students are taught to always deal with real geometrical entities and quantities (arrows, lengths, angles, points, lines, surfaces, volumes, etc.). They learn to “translate” the geometry and the electromagnetic physics attached to it into mathematical models (equations and symbolic or numerical values) using “first mathematical principles” instead of just “black-box” formulas as a computer would do. As opposed to the traditional formal algebraic approach to vector analysis in electromagnetics, which is very general but also very abstract and dry, the geometrical approach is problem-dependent but also much more intuitive and visual, and as such can do a great deal to increase students' understanding and appreciation of vector analysis and its application to electromagnetic theory and problem solving. This is confirmed by preliminary class testing and assessment of student learning, success, and satisfaction in the courses Electromagnetic Fields I and II at Colorado State University.