A Brief Introduction

Undergraduate calculus progresses from differentiation and integration of functions on the real line to functions in the plane and in 3-space. Then one encounters vectorvalued functions and learns about integrals on curves and surfaces. Real analysis extends differential and integral calculus from $$ \mathbb{R}^3 to \mathbb{R}^n$$ . This book is about the extension of calculus from curves and surfaces to higher dimensions.