Advanced Calculus using Mathematica

Advanced Calculus using Mathematica: NoteBook Edition is a complete text on calculus of several variables written in Mathematica NoteBooks.

Building Vector Geometry Skills

Our development of the interaction between linear and nonlinear equations and graphs is based on vector algebra and geometry. Basic vector geometry and algebra is not only a helpful way to understand the equations of calculus, it is a powerful tool in many parts of math, science, and engineering. We urge our reader to develop a working lexicon (or “translation dictionary”) that contains the equivalent “words” of the two languages. This keeps being useful throughout the course, such as in a description of motion on a sphere.

Vector geometry can be hard to teach and learn at first. The instructor draws a picture and writes a formula. The students understand the picture and understand the computation, but don’t see how the transformation from one to the other works. These transformations are “trivial” or “obvious” to the instructor, but obscure to the beginner. By having students create a translation dictionary (lexicon) between geometry and algebra and apply it step-by-step in solution of vector geometry problems, this transformation becomes clearer. Eventually the best students consider it “trivial.”