University Calculus, Early Transcendentals, Multivariable

9. Infinite Sequences and Series

9.1 Sequences

9.2 Infinite Series

9.3 The Integral Test

9.4 Comparison Tests

9.5 The Ratio and Root Tests

9.6 Alternating Series, Absolute and Conditional Convergence

9.7 Power Series

9.8 Taylor and Maclaurin Series

9.9 Convergence of Taylor Series

9.10 The Binomial Series and Applications of Taylor Series

10. Parametric Equations and Polar Coordinates

10.1 Parametrizations of Plane Curves

10.2 Calculus with Parametric Curves

10.3 Polar Coordinates

10.4 Graphing in Polar Coordinates

10.5 Areas and Lengths in Polar Coordinates

10.6 Conics in Polar Coordinates

11. Vectors and the Geometry of Space

11.1 Three-Dimensional Coordinate Systems

11.2 Vectors

11.3 The Dot Product

11.4 The Cross Product

11.5 Lines and Planes in Space

11.6 Cylinders and Quadric Surfaces

12. Vector-Valued Functions and Motion in Space

12.1 Curves in Space and Their Tangents

12.2 Integrals of Vector Functions; Projectile Motion

12.3 Arc Length in Space

12.4 Curvature and Normal Vectors of a Curve

12.5 Tangential and Normal Components of Acceleration

12.6 Velocity and Acceleration in Polar Coordinates

13. Partial Derivatives

13.1 Functions of Several Variables

13.2 Limits and Continuity in Higher Dimensions

13.3 Partial Derivatives

13.4 The Chain Rule

13.5 Directional Derivatives and Gradient Vectors

13.6 Tangent Planes and Differentials

13.7 Extreme Values and Saddle Points

13.8 Lagrange Multipliers

14. Multiple Integrals

14.1 Double and Iterated Integrals over Rectangles

14.2 Double Integrals over General Regions

14.3 Area by Double Integration

14.4 Double Integrals in Polar Form

14.5 Triple Integrals in Rectangular Coordinates

14.6 Moments and Centers of Mass

14.7 Triple Integrals in Cylindrical and Spherical Coordinates

14.8 Substitutions in Multiple Integrals

15. Integration in Vector Fields

15.1 Line Integrals

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

15.3 Path Independence, Conservative Fields, and Potential Functions

15.4 Green's Theorem in the Plane

15.5 Surfaces and Area

15.6 Surface Integrals

15.7 Stokes' Theorem

15.8 The Divergence Theorem and a Unified Theory

16. First-Order Differential Equations (Online)

16.1 Solutions, Slope Fields, and Euler's Method

16.2 First-Order Linear Equations

16.3 Applications

16.4 Graphical Solutions of Autonomous Equations

16.5 Systems of Equations and Phase Planes

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

• The exercises are known for their breadth and quality, with carefully constructed exercise sets that progress from skills problems to applied and theoretical problems. The text contains more than 3,700 exercises in all.
  • End-of-chapter exercises feature review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises.
• Figures are conceived and rendered to support conceptual reasoning and provide insight for students. They are also consistently captioned to aid understanding.
• The flexible table of contents divides complex topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students. For example, the precise definition of the limit is contained in its own section and may be skipped.
• Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.
• A robust MyMathLab course contains more than 7,000 assignable exercises, a complete e-book, and built-in tutorials so students can get help whenever they need it.
• A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.

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.

Your opinions count

Be the first to review this product. Write your review now.