Chapter 7 Functions of Several Variables. Copyright © Houghton Mifflin Company. All rights reserved.7 | 2 Figure 7.1: Three-Dimensional Coordinate System.

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Presentation transcript:

Chapter 7 Functions of Several Variables

Copyright © Houghton Mifflin Company. All rights reserved.7 | 2 Figure 7.1: Three-Dimensional Coordinate System

Copyright © Houghton Mifflin Company. All rights reserved.7 | 3 Figure 7.4: Distance and Midpoint Formulas

Copyright © Houghton Mifflin Company. All rights reserved.7 | 4 Distance Formula in Space

Copyright © Houghton Mifflin Company. All rights reserved.7 | 5 Midpoint Formula in Space

Copyright © Houghton Mifflin Company. All rights reserved.7 | 6 Figure 7.6: Standard Equation of a Sphere

Copyright © Houghton Mifflin Company. All rights reserved.7 | 7 Figure 7.10: General Equation of a Plane

Copyright © Houghton Mifflin Company. All rights reserved.7 | 8 Figure 7.12: Planes Parallel to Coordinate Planes

Copyright © Houghton Mifflin Company. All rights reserved.7 | 9 Figure 7.13: Planes Parallel to Coordinate Axes

Copyright © Houghton Mifflin Company. All rights reserved.7 | 10 Figure 7.14

Copyright © Houghton Mifflin Company. All rights reserved.7 | 11 Elliptic Cone

Copyright © Houghton Mifflin Company. All rights reserved.7 | 12 Elliptic Paraboloid

Copyright © Houghton Mifflin Company. All rights reserved.7 | 13 Hyperbolic Paraboloid

Copyright © Houghton Mifflin Company. All rights reserved.7 | 14 Ellipsoid

Copyright © Houghton Mifflin Company. All rights reserved.7 | 15 Hyperboloid of One Sheet

Copyright © Houghton Mifflin Company. All rights reserved.7 | 16 Hyperboloid of Two Sheets

Copyright © Houghton Mifflin Company. All rights reserved.7 | 17 Definition of a Function of Two Variables

Copyright © Houghton Mifflin Company. All rights reserved.7 | 18 Figure 7.19: Contour Maps and Level Curves

Copyright © Houghton Mifflin Company. All rights reserved.7 | 19 Partial Derivatives of a Function of Two Variables

Copyright © Houghton Mifflin Company. All rights reserved.7 | 20 Notation for First Partial Derivatives

Copyright © Houghton Mifflin Company. All rights reserved.7 | 21 Figure 7.23: Graphical Interpretation of Partial Derivatives

Copyright © Houghton Mifflin Company. All rights reserved.7 | 22 Figure 7.26: Relative Extrema of a Function of Two Variables

Copyright © Houghton Mifflin Company. All rights reserved.7 | 23 Figure 7.28: First-Partials Test for Relative Extrema

Copyright © Houghton Mifflin Company. All rights reserved.7 | 24 Second-Partials Test for Relative Extrema

Copyright © Houghton Mifflin Company. All rights reserved.7 | 25 Figure 7.34: Finding a Maximum Value

Copyright © Houghton Mifflin Company. All rights reserved.7 | 26 Method of Lagrange Multipliers

Copyright © Houghton Mifflin Company. All rights reserved.7 | 27 Figure 7.37: Measuring the Accuracy of a Mathematical Model

Copyright © Houghton Mifflin Company. All rights reserved.7 | 28 Figure 7.38: Sum of the Squared Errors

Copyright © Houghton Mifflin Company. All rights reserved.7 | 29 Definition of the Sum of the Squared Errors

Copyright © Houghton Mifflin Company. All rights reserved.7 | 30 The Least Squares Regression Line

Copyright © Houghton Mifflin Company. All rights reserved.7 | 31 Least Squares Regression Quadratic

Copyright © Houghton Mifflin Company. All rights reserved.7 | 32 Determining Area in the Plane by Double Integrals

Copyright © Houghton Mifflin Company. All rights reserved.7 | 33 Figure 7.48: Volume of a Solid Region

Copyright © Houghton Mifflin Company. All rights reserved.7 | 34 Determining Volume by Double Integrals

Copyright © Houghton Mifflin Company. All rights reserved.7 | 35 Guidelines for Finding the Volume of a Solid

Copyright © Houghton Mifflin Company. All rights reserved.7 | 36 Average Value of a Function over a Region

Copyright © Houghton Mifflin Company. All rights reserved.7 | 37 Algebra Summary: Solving Systems of Equations