Textbook

# Calculus: Multivariable, Enhanced eText, 7th Edition

For Instructors

## Description

With Wiley’s Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including:

• Embedded Example Videos
• Built-In Assessments
• Interactive Exploration applets
• Searchable Appendices & chapter summary reviews

Calculus: Multivariable, 7e
continues the effort to promote courses in which understanding and computation reinforce each other. The 7th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secdondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. The program includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields. Calculus: Multivariable, 7e will include Wiley's seamlessly integrated adaptive WileyPLUS ORION program, covering content from refresher Algebra and Trigonometry through Multi-Variable Calculus. Calculus: Multivariable, 7e is the first adaptive calculus program in the market.
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12. Functions of Several Variables 651
12.1 Functions of Two Variables 652
12.2 Graphs and Surfaces 660
12.3 Contour Diagrams 668
12.4 Linear Functions 682
12.5 Functions of Three Variables 689
12.6 Limits and Continuity 695
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13. A Fundamental Tool: Vectors 701
13.1 Displacement Vectors 702
13.2 Vectors in General 710
13.3 The Dot Product 718
13.4 The Cross Product 728
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14. Differentiating Functions of Several Variables 739
14.1 The Partial Derivative 740
14.2 Computing Partial Derivatives Algebraically 748
14.3 Local Linearity and the Differential 753
14.4 Gradients and Directional Derivatives in the Plane 762
14.5 Gradients and Directional Derivatives in Space 772
14.6 The Chain Rule 780
14.7 Second-Order Partial Derivatives 790
14.8 Differentiability 799
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15. Optimization: Local and Global Extreme 805
15.1 Critical Points: Local Extreme and Saddle Points 806
15.2 Optimization 815
15.3 Constrained Optimization: Lagrange Multipliers 825
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16. Integrating Functions of Several Variables 839
16.1 The Definite Integral of a Function of Two Variables 840
16.2 Iterated Integrals 847
16.3 Triple Integrals 857
16.4 Double Integrals in Polar Coordinates 864
16.5 Integrals in Cylindrical and Spherical Coordinates 869
16.6 Applications of Integration to Probability 878
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17. Parameterization and Vector Fields 885
17.1 Parameterized Curves 886
17.2 Motion, Velocity, and Acceleration 896
17.3 Vector Fields 905
17.4 The Flow of a Vector Field 913
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18. Line Integrals 921
18.1 The Idea of a Line Integral 922
18.2 Computing Line Integrals Over Parameterized Curves 931
18.3 Gradient Fields and Path-Independent Fields 939
18.4 Path-Dependent Vector Fields and Green's Theorem 949
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19. Flux Integrals and Divergence 961
19.1 The Idea of a Flux Integral 962
19.2 Flux Integrals for Graphs, Cylinders, and Spheres 973
19.3 The Divergence of a Vector Fields 982
19.4 The Divergence Theorem 991
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20. The Curl and Stokes' Theorem 999
20.1 The Curl of a Vector Fields 1000
20.2 Stokes' Theorem 1008
20.3 The Three Fundamental Theorems 1015
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21. Parameters, Coordinates, and Integrals 1021
21.1 Coordinates and Parameterized Surfaces 1022
21.2 Change of Corrdinates in a Multiple Integral 1033
21.3 Flux Integrals Over Parameterized Surfaces 1038
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## The Wiley Advantage

Calculus: Multivariable, 7e continues using the "Rule of Four" approach created by the Consortium where ideas are presented graphically, numerically, symbolically and verbally, thereby ancouraging student with a variety of learning styles to expand their knowledge.
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