![]() ![]() Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.ĩ7817_14_ch14_p901-909.qk_97817_14_ch14_p901-909 11/8/10 1:26 PM, , 902,, CHAPTER 14,, PARTIAL DERIVATIVES,, Functions of Several Variables,, 14.1,, In this section we study functions of two or more variables from four points of view:, ■ verbally, (by a description in words), ■,, numerically,, (by a table of values),, ■,, algebraically,, (by an explicit formula),, ■,, visually,, (by a graph or level curves),, Functions of Two Variables, The temperature T at a point on the surface of the earth at any given time depends on the, longitude x and latitude y of the point. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s)., Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. May not be copied, scanned, or duplicated, in whole or in part. But, in the real world, physical, quantities often depend on two or more variables, so in this chapter we turn our attention to functions of, several variables and extend the basic ideas of differential calculus to such functions.,, 901,, Copyright 2010 Cengage Learning. Such surfaces are discussed, in Section 14.7.,, Photo by Stan Wagon, Macalester College,, So far we have dealt with the calculus of functions of a single variable. At this location in, southern Utah (Phipps Arch) you can, see a point that is a minimum in one, direction but a maximum in another, direction. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.ĩ7817_14_ch14_p901-909.qk_97817_14_ch14_p901-909 11/8/10 1:26 PM, , 14,, Partial Derivatives,, Graphs of functions of two variables are, surfaces that can take a variety of, shapes, including that of a saddle or, mountain pass. 97879_FM7eMV_FM7eMV_pi-xiv.qk_97879_FM7eMV_FM7eMV_pi-xiv 11/9/10 4:30 PM Page v,, CONTENTS,, 14,, Partial Derivatives,, 901,, 14.1,, Functions of Several Variables,, 14.2,, Limits and Continuity,, 14.3,, Partial Derivatives,, 14.4,, Tangent Planes and Linear Approximations,, 14.5,, The Chain Rule,, 14.6,, Directional Derivatives and the Gradient Vector,, 14.7,, Maximum and Minimum Values, N,, Discovery Project,, 916, 924,, N,, Quadratic Approximations and Critical Points,, Rocket Science,, 988,, Applied Project,, N,, Hydro-Turbine Optimization,, 995,, 997,, Double Integrals over Rectangles,, 15.2,, Iterated Integrals,, 15.3,, Double Integrals over General Regions,, 15.4,, Double Integrals in Polar Coordinates,, 15.5,, Applications of Double Integrals,, 15.6,, Surface Area,, 15.7,, Triple Integrals,, 998,, 1006, 1012, 1021,, 1027,, 1037, 1041,, Discovery Project,, N,, Volumes of Hyperspheres,, 1051,, Triple Integrals in Cylindrical Coordinates 1051, Discovery Project,, N,, The Intersection of Three Cylinders,, Triple Integrals in Spherical Coordinates, Applied Project,, 15.10,, 990,, 991,, 15.1,, 15.9,, 980,, 981,, N,, Multiple Integrals,, 15.8,, 957,, 980,, Applied Project,, Problems Plus,, 939,, 970,, Designing a Dumpster,, Lagrange Multipliers,, Review,, 15,, 902,, 948,, Applied Project,, 14.8,, v,, N,, Roller Derby,, Problems Plus,, 1057,, 1063,, Change of Variables in Multiple Integrals, Review,, 1056,, 1064,, 1073, 1077,, Copyright 2010 Cengage Learning.
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