The subject is traditionally called Calculus of Several Variables , Vector Calculus , or Multivariable Calculus . Green's, Stokes', and Divergence Theorems. We have tried to modernize the course, in part by introducing the mathematical software system Mathematica as a powerful tool. To elaborate, we describe some benefits that follow from introducing Mathematica. First, the traditional multivariable calculus course has a tremendous geometric component.
Students struggle to handle it.
Unless they are endowed with artistic gifts or uncanny geometric insight, they may fail to depict and understand the geometric constructs. Often, they rely on illustrations in their text or prepared by their instructor. Providing a software system like Mathematica enables all students to draw, manipulate, and analyze the geometric shapes of multivariable calculus. Second, most of the numbers, formulas, and equations found in standard problems are highly contrived to make the computations tractable. This places an enormous limitation on the faculty member trying to present meaningful applications, and lends an air of untruthfulness to the course.