The Calculus of Functions of Several Variables by Dan Sloughter is available in pdf format for free. In your first exposure to calculus, the primary focus of your attention was on functions involving a single independent variable and a single dependent variable.
However, many of the functions of importance both within mathematics itself as well as in the application of mathematics to the rest of the world involve many variables simultaneously. This book covers introduction to Rn, angles and the dot product, the cross product, lines, planes, and hyperplanes, linear and affine functions, operations with matrices, and much more.
Table of Contents
- Geometry of Rn
- Functions from R to Rn
- Functions from Rn to R
- Functions from Rm to Rn
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