17.1 Chapter Introduction

In this final chapter, we study three generalizations of the Fundamental Theorem of Calculus, known as Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. This is a culmination of our efforts to extend the ideas of single-variable calculus to the multivariable setting. However, vector analysis is not so much an endpoint as a gateway to a host of applications, not only in the traditional domains of physics and engineering, but also in biological, earth, and environmental sciences, where an understanding of fluid and aerodynamics, and continuous matter is required.

Fluid flows, such as this water vortex, are analyzed using the fundamental theorems of vector analysis.