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How to Find Potential Functions? A 10 Minute Introduction

Definition/Summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Equations $$\nabla \phi(x,y,z) = \vec F(x,y,z)$$ $$\nabla \times \vec F(x,y,z) = \vec 0$$ Extended explanation Suppose we are given a vector field ##\vec F(x,y,z)=\langle f(x,y,z),g(x,y,z),h(x,y,z)\rangle## that has a potential function ##\phi## and we wish to recover the potential…

Demystifying Parameterization and Surface Integrals

Introduction This article will attempt to take the mystery out of setting up surface integrals. It will explain the basic ideas underlying surface integration and show you how to parameterize surfaces to set up the corresponding integrals efficiently. You will need to have had or be taking ##3D## calculus covering multiple integrals to get the…