Synechism

by Dan Sloughter, Furman University

Chapter 1: Geometry of Rⁿ

Introduction to Rⁿ

Angles and the dot product

The cross product

Lines, planes, and hyperplanes

Linear and affine functions

Operations with matrices

Chapter 2: Functions from R to Rⁿ

Curves

Best affine approximations

Motion along a curve

Chapter 3: Functions from Rⁿ to R

Geometry, limits, and continuity

Directional derivatives and the gradient

Best affine approximations

Second-order approximations

Extreme values

Definite integrals

Change of variables in integrals

Chapter 4: Functions from R^m to Rⁿ

Geometry, limits, and continuity

Best affine approximations

Line integrals

Green's theorem

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.

Copyright © 1999, 2001 by Dan Sloughter

This work is licensed under a Creative Commons License.