This Sixth Edition of Calculus continues the effort to promote courses in which understanding and computation reinforce each other. Calculus: Multivariable 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.

Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of "sl(2), " both classical and quantum. Covering representations of "U(sl(2)), " quantum "sl(2), " the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals.

The classic subject of representations of "U(sl(2))" is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6"j"-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group "Ub-3.0 qb0(sl(2))" develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter "q" is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.

This book helps work more effectively and check solutions as you go along with the text! This "Student Solutions Manual" is designed to accompany Hughes Hallett's "Calculus: Single & Multivariable, 4th Edition". It contains solutions to every other odd numbered problem in the text for chapters 1-20. Striking a balance between concepts, modeling, and skills, "Calculus: Single & Multivariable, 4th Edition" is a highly acclaimed book that arms readers with an accessible introduction to calculus. It builds on the strengths from previous editions, presenting key concepts graphically, numerically, symbolically, and verbally. Guided by this innovative Rule of Four approach, the fourth edition examines new topics while providing readers with a strong conceptual understanding of the material.

Work more effectively and gauge your progress as you go along! This Student Study Guide is designed to accompany Hughes-Hallett's "Calculus: Single Variable, 4th Edition." It contains additional study aids for students that are tied directly to the text.

Now in its Fourth Edition, Hughes-Hallett's Calculus: Single Variable reflects the strong consensus within the mathematics community for a balance between contemporary and traditional ideas. Building on previous work, it brings together the best of both new and traditional curricula in an effort to meet the needs of instructors and students alike. The text exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that is easy to understand, and a flexible approach to technology.

Work more effectively and check solutions along the way! This Student Solutions Manual that is designed to accompany Hughes-Hallett's "Calculus: Single Variable, 4th Edition" contains solutions to every other odd-numbered problem in the text for chapters 1-11.

Now in its Fourth Edition, Calculus: Single Variable reflects the strong consensus within the mathematics community for a balance between contemporary and traditional ideas. Building on previous work, it brings together the best of both new and traditional curricula in an effort to meet the needs of instructors and students alike. The text exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that is easy to understand, and a flexible approach to technology.