The course 32B treats topics related to integration in several variables, culminating in the theorems of Green, Gauss and Stokes. Each of these theorems asserts that an integral over some domain is equal to an integral over the boundary of the domain. These theorems are generalizations of the fundamental theorem of calculus, which corresponds to the case where the domain is an interval on the real line. The theorems play an important role in electrostatics, fluid mechanics, and other areas in engineering and physics where conservative vector fields play a role. The laboratory courses 32AL and 32BL are based on the mathematical software package Maple, housed on PC's in the PIC lab with pentium processors.
Maple routines enable students to see geometric objects, quickly and easily.
In addition, the software enables students to solve associated problems, such as to find the roots of systems of equations. Enrollments in the lab courses are restricted, depending on the availability of computers in the PIC lab. Recent enrollment statistics for 32A and 32B are given in the following tables. In addition, parallel honors sections 32AH and 32BH were given in the Winter and Spring Quarters of 1997 respectively, and these included about 20 students each.