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.

9. Sequences and Infinite Series

9.1 An overview

9.2 Sequences

9.3 Infinite series

9.4 The Divergence and Integral Tests

9.5 The Ratio, Root, and Comparison Tests

9.6 Alternating series

10. Power Series

10.1 Approximating functions with polynomials

10.2 Properties of Power series

10.3 Taylor series

10.4 Working with Taylor series

11. Parametric and Polar Curves

11.1 Parametric equations

11.2 Polar coordinates

11.3 Calculus in polar coordinates

11.4 Conic sections

12. Vectors and Vector-Valued Functions

12.1 Vectors in the plane

12.2 Vectors in three dimensions

12.3 Dot products

12.4 Cross products

12.5 Lines and curves in space

12.6 Calculus of vector-valued functions

12.7 Motion in space

12.8 Length of curves

12.9 Curvature and normal vectors

13. Functions of Several Variables

13.1 Planes and surfaces

13.2 Graphs and level curves

13.3 Limits and continuity

13.4 Partial derivatives

13.5 The Chain Rule

13.6 Directional derivatives and the gradient

13.7 Tangent planes and linear approximation

13.8 Maximum/minimum problems

13.9 Lagrange multipliers

14. Multiple Integration

14.1 Double integrals over rectangular regions

14.2 Double integrals over general regions

14.3 Double integrals in polar coordinates

14.4 Triple integrals

14.5 Triple integrals in cylindrical and spherical coordinates

14.6 Integrals for mass calculations

14.7 Change of variables in multiple integrals

15. Vector Calculus

15.1 Vector fields

15.2 Line integrals

15.3 Conservative vector fields

15.4 Green’s theorem

15.5 Divergence and curl

15.6 Surface integrals

15.6 Stokes’ theorem

15.8 Divergence theorem

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