Textbook

# Calculus: Multivariable, 6th Edition

## Description

Calculus: Multivariable, 6th Edition continues the effort to promote courses in which understanding and computation reinforce each other. The 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics. In addition, new problems on the mathematics of sustainability and new case studies on calculus in medicine by David E. Sloane, MD have been added. WileyPLUS sold separately from text.
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12 FUNCTIONS OF SEVERAL VARIABLES

12.1 FUNCTIONS OF TWO VARIABLES

12.2 GRAPHS AND SURFACES

12.3 CONTOUR DIAGRAMS

12.4 LINEAR FUNCTIONS

12.5 FUNCTIONS OF THREE VARIABLES

12.6 LIMITS AND CONTINUITY

REVIEW PROBLEMS

PROJECTS

13 A FUNDAMENTAL TOOL: VECTORS

13.1 DISPLACEMENT VECTORS

13.2 VECTORS IN GENERAL

13.3 THE DOT PRODUCT

13.4 THE CROSS PRODUCT

REVIEW PROBLEMS

PROJECTS

14 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES

14.1 THE PARTIAL DERIVATIVE

14.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY

14.3 LOCAL LINEARITY AND THE DIFFERENTIAL

14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE

14.5 GRADIENTS AND DIRECTIONAL DERIVATIVES IN SPACE

14.6 THE CHAIN RULE

14.7 SECOND-ORDER PARTIAL DERIVATIVES

14.8 DIFFERENTIABILITY

REVIEW PROBLEMS

PROJECTS

15 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA

15.1 CRITICAL POINTS: LOCAL EXTREMA AND SADDLE POINTS

15.2 OPTIMIZATION

15.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS

REVIEW PROBLEMS

PROJECTS

16 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES

16.1 THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES

16.2 ITERATED INTEGRALS

16.3 TRIPLE INTEGRALS

16.4 DOUBLE INTEGRALS IN POLAR COORDINATES

16.5 INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES

16.6 APPLICATIONS OF INTEGRATION TO PROBABILITY

REVIEW PROBLEMS

PROJECTS

17 PARAMETERIZATION AND VECTOR FIELDS

17.1 PARAMETERIZED CURVES

17.2 MOTION, VELOCITY, AND ACCELERATION

17.3 VECTOR FIELDS

17.4 THE FLOW OF A VECTOR FIELD

REVIEW PROBLEMS

PROJECTS

18 LINE INTEGRALS

18.1 THE IDEA OF A LINE INTEGRAL

18.2 COMPUTING LINE INTEGRALS OVER PARAMETERIZED CURVES

18.3 GRADIENT FIELDS AND PATH-INDEPENDENT FIELDS

18.4 PATH-DEPENDENT VECTOR FIELDS AND GREEN’S THEOREM

REVIEW PROBLEMS

PROJECTS

19 FLUX INTEGRALS AND DIVERGENCE

19.1 THE IDEA OF A FLUX INTEGRAL

19.2 FLUX INTEGRALS FOR GRAPHS, CYLINDERS, AND SPHERES

19.3 THE DIVERGENCE OF A VECTOR FIELD

19.4 THE DIVERGENCE THEOREM

REVIEW PROBLEMS

PROJECTS

20 THE CURL AND STOKES’ THEOREM

20.1 THE CURL OF A VECTOR FIELD

20.2 STOKES’ THEOREM

20.3 THE THREE FUNDAMENTAL THEOREMS

REVIEW PROBLEMS

PROJECTS

21 PARAMETERS, COORDINATES, AND INTEGRALS

21.1 COORDINATES AND PARAMETERIZED SURFACES

21.2 CHANGE OF COORDINATES IN A MULTIPLE INTEGRAL

21.3 FLUX INTEGRALS OVER PARAMETERIZED SURFACES

REVIEW PROBLEMS

PROJECTS

APPENDIX

A ROOTS, ACCURACY, AND BOUNDS

B COMPLEX NUMBERS

C NEWTON’S METHOD

D VECTORS IN THE PLANE

E DETERMINANTS

INDEX

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## New To This Edition

• New Strengthen Your Understanding problems at the end of every section. These problems ask students to reflect on what they have learned by deciding “What is wrong?” with a statement and to “Give an example” of an idea.
• Updated Data and Models: For example, Section 11.7 follows the current debate on Peak Oil Production, underscoring the importance of mathematics in understanding the world’s economic and social?problems.
• Drill Exercises build student skill and confidence.
• Online Problems available in WileyPLUS or WeBWorK, for example. Many problems are randomized, providing students with expanded opportunities for practice with immediate feedback.
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• Innovative and engaging problems. Under the approach called the “Rule of Four,” ideas are presented graphically, numerically, symbolically, and verbally, thereby encouraging students with a variety of learning styles to expand their knowledge.
• A Flexible Approach to Technology: Adaptable to courses having various levels of computer involvement, ranging from little or none to intensive. The book does not require any specific software or technology, though it has been used successfully with graphing calculators, graphing software, and computer algebra systems.
• Applied Problems for instructors wishing to emphasize the connection between calculus and other fields.
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Instructors Resources
Wiley Instructor Companion Site
Instructor's Solutions Manual, Multivariable
Instructor's Manual
AP Teacher's Guide
ConcepTests
ConcepTests PowerPoint Slides
Interactive Explorations Applets
Calculus Applets
Test Bank (Printable and Computerized)
Lecture Note PowerPoint slides
Focus on Theory supplement
Art PowerPoint slides
Image Gallery
Classroom Project Worksheets/Activities
ConceptTests
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Students Resources
Wiley Student Companion Site
Calculus Applets
Focus on Theory supplement
ConceptTests
Available Materials
by William G. McCallum, Deborah Hughes-Hallett, Andrew M. Gleason, David O. Lomen, David Lovelock, Jeff Tecosky-Feldman, Thomas W. Tucker, Daniel E. Flath, Joseph Thrash, Karen R Rhea, Andrew Pasquale, Sheldon P. Gordon, Douglas Quinney, Patti Frazer Lock
978-1-118-21738-2
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Purchase Options
Wiley E-Text
Calculus: Multivariable, 6th Edition
ISBN : 978-1-118-87663-3
512 pages
\$80.00

Loose-leaf
Calculus: Multivariable, 6th Edition Binder Ready Version
ISBN : 978-1-118-23378-8
512 pages