DescriptionCalculus: 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.
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
13 A FUNDAMENTAL TOOL: VECTORS
13.1 DISPLACEMENT VECTORS
13.2 VECTORS IN GENERAL
13.3 THE DOT PRODUCT
13.4 THE CROSS PRODUCT
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
15 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA
15.1 CRITICAL POINTS: LOCAL EXTREMA AND SADDLE POINTS
15.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS
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
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
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
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
20 THE CURL AND STOKES’ THEOREM
20.1 THE CURL OF A VECTOR FIELD
20.2 STOKES’ THEOREM
20.3 THE THREE FUNDAMENTAL THEOREMS
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
A ROOTS, ACCURACY, AND BOUNDS
B COMPLEX NUMBERS
C NEWTON’S METHOD
D VECTORS IN THE PLANE
ANSWERS TO ODD-NUMBERED PROBLEMS
- 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.
- 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.