1. Chapter 7 Functions of Several Variables

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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