Multivariable Calculus
Updated 2020 by Don Shimamoto, Swarthmore College.
Covers the standard material for a one-semester course in multivariable calculus. Topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. 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. The book is written to get to the exercises as quickly as possible.