The Calculus of Functions of Several Variables

Copyright © 1997, 2001 by Dan Sloughter.

Calculus of Functions of Several Variables is freely redistributable under the terms of the GNU General Public License

as published by the Free Software Foundation. This work comes with ABSOLUTELY NO WARRANTY.

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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

 

 

 

 


 

 

Functions from R to Rn

 

 

 

 

 

Curves

 

 

 

 

Best affine approximations

 

 

 

 

 

Motion along a curve

 

 

 

 


 

 

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

 

 

 

 


 

 

Functions from Rm to Rn

 

 

 

 

 

Geometry, limits, and continuity

 

 

 

 

Best affine approximations

 

 

 

 

Line integrals

 

 

 

 

 

Green's theorem