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Chapter 24: Reducing a Surface Integral to a Multiple Integral and the Jacobian

Introduction

Surface integrals are of greatest importance from their power in representing important physical concepts, such as flow of a material or charge, or flux of electric or magnetic fields. We also want to be able to compute them and we show here how this is done.

Topics

24.1 Conceptual Discussion and Main Result

24.2 Implications for Integrals over Area in the Plane: the Jacobian

24.3 Generalizations to Higher Dimensions

24.4 Volume and Surface Integrals as Single Ordinary Integrals