This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows.

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**William Briggs **has been on the mathematics faculty at the University of Colorado at Denver for twenty-three years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, *Using and Understanding Mathematics; *an undergraduate problem solving book, *Ants, Bikes, and Clocks; *and two tutorial monographs, *The Multigrid Tutorial *and *The DFT: An Owner’s Manual for the Discrete Fourier Transform. *He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President’s Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.

**Lyle Cochran **is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and, since 1995, at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the *Instructor’s Mathematica Manual *for *Linear Algebra and Its Applications *by David C. Lay and the *Mathematica Technology Resource Manual *for *Thomas’ Calculus. *He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth University.

**Bernard Gillett** is a Senior Instructor at the University of Colorado at Boulder; his primary focus is undergraduate education. He has taught a wide variety of mathematics courses over a twenty-year career, receiving five teaching awards in that time. Bernard authored a software package for algebra, trigonometry, and precalculus; the Student’s Guide and Solutions Manual and the Instructor’s Guide and Solutions Manual for

*Using and Understanding Mathematics *by Briggs and Bennett; and the Instructor’s Resource Guide and Test Bank for

*Calculus *and

*Calculus: Early Transcendentals *by Briggs, Cochran, and Gillett. Bernard is also an avid rock climber and has published four climbing guides for the mountains in and surrounding Rocky Mountain National Park.

**8. Sequences and Infinite Series**

8.1 An overview

8.2 Sequences

8.3 Infinite series

8.4 The Divergence and Integral Tests

8.5 The Ratio, Root, and Comparison Tests

8.6 Alternating series

**9. Power Series**

9.1 Approximating functions with polynomials

9.2 Properties of Power series

9.3 Taylor series

9.4 Working with Taylor series

**10. Parametric and Polar Curves **

10.1 Parametric equations

10.2 Polar coordinates

10.3 Calculus in polar coordinates

10.4 Conic sections

**11. Vectors and Vector-Valued Functions**

11.1 Vectors in the plane

11.2 Vectors in three dimensions

11.3 Dot products

11.4 Cross products

11.5 Lines and curves in space

11.6 Calculus of vector-valued functions

11.7 Motion in space

11.8 Length of curves

11.9 Curvature and normal vectors

**12. Functions of Several Variables**

12.1 Planes and surfaces

12.2 Graphs and level curves

12.3 Limits and continuity

12.4 Partial derivatives

12.5 The Chain Rule

12.6 Directional derivatives and the gradient

12.7 Tangent planes and linear approximation

12.8 Maximum/minimum problems

12.9 Lagrange multipliers

**13. Multiple Integration**

13.1 Double integrals over rectangular regions

13.2 Double integrals over general regions

13.3 Double integrals in polar coordinates

13.4 Triple integrals

13.5 Triple integrals in cylindrical and spherical coordinates

13.6 Integrals for mass calculations

13.7 Change of variables in multiple integrals

**14. Vector Calculus**

14.1 Vector fields

14.2 Line integrals

14.3 Conservative vector fields

14.4 Green’s theorem

14.5 Divergence and curl

14.6 Surface integrals

14.6 Stokes’ theorem

14.8 Divergence theorem