University 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 Thomas’ Calculus.

• 9. Infinite Sequences and Series9.1 Sequences9.2 Infinite Series9.3 The Integral Test9.4 Comparison Tests9.5 Absolute Convergence; The Ratio and Root Tests9.6 Alternating Series and Conditional Convergence9.7 Power Series9.8 Taylor and Maclaurin Series9.9 Convergence of Taylor Series9.10 The Binomial Series and Applications of Taylor Series  10. Parametric Equations and Polar Coordinates10.1 Parametrizations of Plane Curves10.2 Calculus with Parametric Curves10.3 Polar Coordinates10.4 Graphing in Polar Coordinates10.5 Areas and Lengths in Polar Coordinates10.6 Conics in Polar Coordinates  11. Vectors and the Geometry of Space11.1 Three-Dimensional Coordinate Systems11.2 Vectors11.3 The Dot Product11.4 The Cross Product11.5 Lines and Planes in Space11.6 Cylinders and Quadric Surfaces  12. Vector-Valued Functions and Motion in Space12.1 Curves in Space and Their Tangents12.2 Integrals of Vector Functions; Projectile Motion12.3 Arc Length in Space12.4 Curvature and Normal Vectors of a Curve12.5 Tangential and Normal Components of Acceleration12.6 Velocity and Acceleration in Polar Coordinates  13. Partial Derivatives13.1 Functions of Several Variables13.2 Limits and Continuity in Higher Dimensions13.3 Partial Derivatives13.4 The Chain Rule13.5 Directional Derivatives and Gradient Vectors13.6 Tangent Planes and Differentials13.7 Extreme Values and Saddle Points13.8 Lagrange Multipliers  14. Multiple Integrals14.1 Double and Iterated Integrals over Rectangles14.2 Double Integrals over General Regions14.3 Area by Double Integration14.4 Double Integrals in Polar Form14.5 Triple Integrals in Rectangular Coordinates14.6 Moments and Centers of Mass14.7 Triple Integrals in Cylindrical and Spherical Coordinates14.8 Substitutions in Multiple Integrals  15. Integration in Vector Fields15.1 Line Integrals15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux15.3 Path Independence, Conservative Fields, and Potential Functions15.4 Green's Theorem in the Plane15.5 Surfaces and Area15.6 Surface Integrals15.7 Stokes' Theorem15.8 The Divergence Theorem and a Unified Theory  16. First-Order Differential Equations (Online)16.1 Solutions, Slope Fields, and Euler's Method16.2 First-Order Linear Equations16.3 Applications16.4 Graphical Solutions of Autonomous Equations16.5 Systems of Equations and Phase Planes  17. Second-Order Differential Equations (Online)17.1 Second-Order Linear Equations17.2 Nonhomogeneous Linear Equations17.3 Applications17.4 Euler Equations17.5 Power Series Solutions