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Full Description
Calculuscourses 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.
Contents
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 PROJECTS 13 A FUNDAMENTAL TOOL: VECTORS 13.1 DISPLACEMENT VECTORS 13.2 PARTIAL DERIVATIVE 14.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY 14.3 LOCAL LINEARITY AND THE DIFFERENTIAL 14.4 GRADIENTS AND DIRECTIONAL 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 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 PARAMETERIZED SURFACES REVIEW PROBLEMS PROJECTS APPENDIX A ROOTS, ACCURACY,
