### Chapter 7 - Palm Beach State College

Chapter 7
Functions of
Several Variables
Figure 7.1: Three-Dimensional
Coordinate System
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Figure 7.4: Distance and
Midpoint Formulas
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Distance Formula in Space
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Midpoint Formula in Space
7|5
Figure 7.6: Standard Equation
of a Sphere
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Figure 7.10: General Equation
of a Plane
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Figure 7.12: Planes Parallel
to Coordinate Planes
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Figure 7.13: Planes Parallel
to 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 a
Function of Two Variables
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Figure 7.19: Contour Maps
and Level Curves
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Partial Derivatives of a
Function of Two Variables
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Notation for First Partial Derivatives
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Figure 7.23: Graphical Interpretation
of Partial Derivatives
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Figure 7.26: Relative Extrema
of a Function of Two Variables
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Figure 7.28: First-Partials
Test for Relative Extrema
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Second-Partials Test
for Relative Extrema
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Figure 7.34: Finding a
Maximum Value
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Method of Lagrange Multipliers
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Figure 7.37: Measuring the
Accuracy of a Mathematical Model
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Figure 7.38: Sum of the
Squared Errors
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Definition of the Sum
of the Squared Errors
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The Least Squares
Regression Line
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Least Squares
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Determining Area in the
Plane by Double Integrals
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Figure 7.48: Volume of
a Solid Region
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Determining Volume
by Double Integrals
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Guidelines for Finding
the Volume of a Solid