Normal 0 false false false Calculus hasnrs"t changed, but readers have. They have been raised on technology, immediacy, and the desire for relevance, and they come to calculus with varied mathematical backgrounds.Thomasrs" Calculus, Twelfth Edition, reaches todayrs"s readers by developing conceptual understanding while maintaining a consistent level of rigor; offering the right mix of relevant applications, conceptual exercises, and skills practice; and incorporating current learning and teaching technology. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and increased clarity and precision. KEY TOPICS:Functions; Limits and Continuity; Differentiation; Applications of Derivatives; Integration; Applications of Definite Integrals; Transcendental Functions; Techniques of Integration; First-Order Differential Equations; Infinite Sequences and Series; 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 MARKET: For all readers interested in Calculus.

**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*.

**George B. Thomas, Jr.** (late) of the Massachusetts Institute of Technology, was a professor of mathematics for thirty-eight years; he served as the executive officer of the department for ten years and as graduate registration officer for five years. Thomas held a spot on the board of governors of the Mathematical Association of America and on the executive committee of the mathematics division of the American Society for Engineering Education. His book,

*Calculus and Analytic Geometry*, was first published in 1951 and has since gone through multiple revisions. The text is now in its twelfth edition and continues to guide students through their calculus courses. He also co-authored monographs on mathematics, including the text

*Probability and Statistics*.

**11. Parametric Equations and Polar Coordinates**

11.1 Parametrizations of Plane Curves

11.2 Calculus with Parametric Curves

11.3 Polar Coordinates

11.4 Graphing in Polar Coordinates

11.5 Areas and Lengths in Polar Coordinates

11.6 Conic Sections

11.7 Conics in Polar Coordinates

**12. Vectors and the Geometry of Space**

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

12.6 Cylinders and Quadric Surfaces

**13. Vector-Valued Functions and Motion in Space**

13.1 Curves in Space and Their Tangents

13.2 Integrals of Vector Functions; Projectile Motion

13.3 Arc Length in Space

13.4 Curvature and Normal Vectors of a Curve

13.5 Tangential and Normal Components of Acceleration

13.6 Velocity and Acceleration in Polar Coordinates

**14. Partial Derivatives**

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

14.9 Taylor's Formula for Two Variables

14.10 Partial Derivatives with Constrained Variables

**15. Multiple Integrals**

15.1 Double and Iterated Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Area by Double Integration

15.4 Double Integrals in Polar Form

15.5 Triple Integrals in Rectangular Coordinates

15.6 Moments and Centers of Mass

15.7 Triple Integrals in Cylindrical and Spherical Coordinates

15.8 Substitutions in Multiple Integrals

**16. Integration in Vector Fields**

16.1 Line Integrals

16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux

16.3 Path Independence, Conservative Fields, and Potential Functions

16.4 Green's Theorem in the Plane

16.5 Surfaces and Area

16.6 Surface Integrals

16.7 Stokes' Theorem

16.8 The Divergence Theorem and a Unified Theory

**17. Second-Order Differential Equations (online)**

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications

17.4 Euler Equations

17.5 Power-Series Solutions