Calculus of Several Variables

Bol

The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.

Bol Partner

This text represents materials for the third semester of calculus, and is the product of one of several NSF-funded calculus curriculum projects, known also as the Oregon State Calculus Connections program. Calculus of a Single Variable , published in 1994, represented the first two semesters' work in calculus from this same program. These materials were also used by thousands of high school and college students in a preliminary edition. Like other reform calculus texts, this book assumes that the student has access to graphing calculators or computers, but it is not tied to any particular technology. The text also employs the rule of three (a watchword among reform-minded calculus instructors): functions are represented (1) algebraically (or symbolically; e.g., as an equation, like x = y+2 ); (2) numerically (e.g. as tables of values); and (3) graphically (e.g., as graphs ulines or figures plotted on axes).