# The Calculus of Functions of Several Variables

by Dan Sloughter, Furman University

### Chapter 1: Geometry of \(\mathbb{R}^n\)

Introduction to \(\mathbb{R}^n\)

Lines, planes, and hyperplanes

### Chapter 2: Functions from \(\mathbb{R}\) to \(\mathbb{R}^n\)

### Chapter 3: Functions from \(\mathbb{R}^n\) to \(\mathbb{R}\)

Geometry, limits, and continuity

Directional derivatives and the gradient

Change of variables in definite integrals

### Chapter 4: Functions from \(\mathbb{R}^m\) to \(\mathbb{R}^n\)

Geometry, limits, and continuity

Answers for selected problems are available here.

A concatenated version (single download) is available here. This file is approximately 2.1 MB.

#### Send e-mail to Dan Sloughter to report any errors.

This work is licensed under a Creative Commons License.