Description

This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves/ differentiability and partial derivatives/ multiple integrals/ vector fields/ line and surface integrals/ and the theorems of Green/ Stokes/ and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable/ real-valued functions of many variables/ and finally the general case of vector-valued functions of many variables. As is always the case/ the most productive way for students to learn is by doing problems/ and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result/ there is a priority placed on understanding why things are true and a recognition that/ when details are sketched or omitted/ that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful/ but not required.