Chapter 15 Vector Analysis. Copyright © Houghton Mifflin Company. All rights reserved.15-2 Definition of Vector Field.

Chapter 15

Vector Analysis

Copyright © Houghton Mifflin Company. All rights reserved. 15-2

Definition of Vector Field


Figure 15.1


Figure 15.2


Figure 15.3


Definition of Inverse Square Field


Definition of Conservative Vector Field


Theorem 15.1 Test for Conservative Vector Field in the Plane


Definition of Curl of a Vector Field


Theorem 15.2 Test for Conservative Vector Field in Space


Definition of Divergence of a Vector Field


Theorem 15.3 Relationship Between Divergence and Curl


Figure 15.8


Definition of Line Integral


Theorem 15.4 Evaluation of a Line Integral as a Definite Integral


Figure 15.12


Figure 15.13


Definition of Line Integral of a Vector Field


Theorem 15.5 Fundamental Theorem of Line Integrals


Figure 15.22


Theorem 15.6 Independence of Path and Conservative Vector Fields


Figure 15.23


Theorem 15.7 Equivalent Conditions


Figure 15.25


Figure 15.26


Theorem 15.8 Green's Theorem


Figure 15.27


Theorem 15.9 Line Integral for Area


Figure 15.34


Definition of Parametric Surface


Figure 15.35


Figure 15.40


Normal Vector to a Smooth Parametric Surface


Figure 15.42


Area of a Parametric Surface


Figure 15.44


Theorem 15.10 Evaluating a Surface Integral


Figure 15.50


Figure 15.51


Definition of Flux Integral


Theorem 15.11 Evaluating a Flux Integral


Summary of Line and Surface Integrals


Figure 15.54


Theorem 15.12 The Divergence Theorem


Figure 15.55


Figure 15.59


Figure 15.60


Figure 15.61


Figure 15.62 and Figure 15.63


Theorem 15.13 Stokes's Theorem


Figure 15.66


Figure 15.67


Summary of Integration Formulas

Chapter 15 Vector Analysis. Copyright © Houghton Mifflin Company. All rights reserved.15-2 Definition of Vector Field.

Documents

normal vector

flux integralsummary

divergence theoremfigure

spacedefinition of divergence

surface integralsfigure

greens theoremfigure

stokess theoremfigure

surface integralfigure