**This text is designed for the multivariable component a three-semester or four-quarter calculus course (math, engineering, and science majors).**

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. **Thomas’ Calculus, Twelfth Edition**, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, and improved conceptual flow.

*The full version of the text contains Chapters 1-16. * *A separate version covers Single Variable topics (Chapters 1-11). This Multivariable version of the text contains Chapters 11-16. MyMathLab access is not included with this ISBN.*

*"synopsis" may belong to another edition of this title.*

Calculus hasn't changed, but readers have. Today's readers have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds.**Thomas' Calculus, Twelfth Edition**, helps readers successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and MyMathLab®, the best in technology for learning and teaching.

**KEY TOPICS**: Parametric Equations and Polar Coordinates; Vectors and the Geometry of Space; Vector-Valued Functions and Motion in Space; Partial Derivatives; Multiple Integrals; Integration in Vector Fields; Second-Order Differential Equations

**Joel Hass** received his PhD from the University of California—Berkeley. He is currently a professor of mathematics at the University of California—Davis. He has coauthored six widely used calculus texts as well as two calculus study guides. He is currently on the editorial board of *Geometriae Dedicata* and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.

**Maurice D. Weir** holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the *University Calculus *series and the twelfth edition of *Thomas’ Calculus*.

*"About this title" may belong to another edition of this title.*

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