Chapter 7 Functions of Several Variables. Copyright © Houghton Mifflin Company. All rights...
Transcript of Chapter 7 Functions of Several Variables. Copyright © Houghton Mifflin Company. All rights...
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Chapter 7
Functions of Several Variables
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Figure 7.1: Three-Dimensional Coordinate System
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Figure 7.4: Distance andMidpoint Formulas
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Distance Formula in Space
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Midpoint Formula in Space
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Figure 7.6: Standard Equationof a Sphere
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Figure 7.10: General Equationof a Plane
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Figure 7.12: Planes Parallelto Coordinate Planes
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Figure 7.13: Planes Parallelto Coordinate Axes
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Figure 7.14
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Elliptic Cone
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Elliptic Paraboloid
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Hyperbolic Paraboloid
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Ellipsoid
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Hyperboloid of One Sheet
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Hyperboloid of Two Sheets
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Definition of aFunction of Two Variables
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Figure 7.19: Contour Mapsand Level Curves
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Partial Derivatives of aFunction of Two Variables
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Notation for First Partial Derivatives
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Figure 7.23: Graphical Interpretationof Partial Derivatives
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Figure 7.26: Relative Extremaof a Function of Two Variables
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Figure 7.28: First-PartialsTest for Relative Extrema
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Second-Partials Testfor Relative Extrema
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Figure 7.34: Finding aMaximum Value
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Method of Lagrange Multipliers
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Figure 7.37: Measuring theAccuracy of a Mathematical Model
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Figure 7.38: Sum of theSquared Errors
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Definition of the Sumof the Squared Errors
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The Least SquaresRegression Line
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Least SquaresRegression Quadratic
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Determining Area in thePlane by Double Integrals
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Figure 7.48: Volume ofa Solid Region
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Determining Volumeby Double Integrals
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Guidelines for Findingthe Volume of a Solid
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Average Value of aFunction over a Region
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Algebra Summary:Solving Systems of Equations