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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.
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