Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level.  However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. University Calculus, Part Two responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.    University Calculus, Part Two is suitable for the multivariable calculus course. The Alternate Edition is the perfect alternative for instructors who want the same quality and quantity of exercises as Thomas’ Calculus, Media Upgrade, Eleventh Edition but prefer a faster-paced presentation.   University Calculus is now available with an enhanced MyMathLab™ course—the ultimate homework, tutorial and study solution for today’s students.  The enhanced MyMathLab™ course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL® exercises.  This text is also available with WebAssign® and WeBWorK®.

Table of Contents:
8 Infinite Sequences and Series 8.1 Sequences 502 8.2 Infinite Series 515 8.3 The Integral Test 523 8.4 Comparison Tests 529 8.5 The Ratio and Root Tests 533 8.6 Alternating Series, Absolute and Conditional Convergence 537 8.7 Power Series 543 8.8 Taylor and Maclaurin Series 553 8.9 Convergence of Taylor Series 559 8.10 The Binomial Series 569 QUESTIONS TO GUIDE YOUR REVIEW 572 PRACTICE EXERCISES 573 ADDITIONAL AND ADVANCED EXERCISES 575   9 Polar Coordinates and Conics 9.1 Polar Coordinates 577 9.2 Graphing in Polar Coordinates 582 9.3 Areas and Lengths in Polar Coordinates 586 9.4 Conic Sections 590 9.5 Conics in Polar Coordinates 599 9.6 Conics and Parametric Equations; The Cycloid 606 QUESTIONS TO GUIDE YOUR REVIEW 610 PRACTICE EXERCISES 610 ADDITIONAL AND ADVANCED EXERCISES 612       10 Vectors and the Geometry of Space 10.1 Three-Dimensional Coordinate Systems 614 10.2 Vectors 619 10.3 The Dot Product 628 10.4 The Cross Product 636 10.5 Lines and Planes in Space 642 10.6 Cylinders and Quadric Surfaces 652 QUESTIONS TO GUIDE YOUR REVIEW 657 PRACTICE EXERCISES 658 ADDITIONAL AND ADVANCED EXERCISES 660   11 Vector-Valued Functions and Motion in Space 11.1 Vector Functions and Their Derivatives 663 11.2 Integrals of Vector Functions 672 11.3 Arc Length in Space 678 11.4 Curvature of a Curve 683 11.5 Tangential and Normal Components of Acceleration 689 11.6 Velocity and Acceleration in Polar Coordinates 694 QUESTIONS TO GUIDE YOUR REVIEW 698 PRACTICE EXERCISES 698 ADDITIONAL AND ADVANCED EXERCISES 700   12 Partial Derivatives 12.1 Functions of Several Variables 702 12.2 Limits and Continuity in Higher Dimensions 711 12.3 Partial Derivatives 719 12.4 The Chain Rule 731 12.5 Directional Derivatives and Gradient Vectors 739 12.6 Tangent Planes and Differentials 747 12.7 Extreme Values and Saddle Points 756 12.8 Lagrange Multipliers 765 12.9 Taylor’s Formula for Two Variables 775 QUESTIONS TO GUIDE YOUR REVIEW 779 PRACTICE EXERCISES 780 ADDITIONAL AND ADVANCED EXERCISES 783   13 Multiple Integrals 13.1 Double and Iterated Integrals over Rectangles 785 13.2 Double Integrals over General Regions 790 13.3 Area by Double Integration 799 13.4 Double Integrals in Polar Form 802 13.5 Triple Integrals in Rectangular Coordinates 807 13.6 Moments and Centers of Mass 816 13.7 Triple Integrals in Cylindrical and Spherical Coordinates 825 13.8 Substitutions in Multiple Integrals 837 QUESTIONS TO GUIDE YOUR REVIEW 846 PRACTICE EXERCISES 846 ADDITIONAL AND ADVANCED EXERCISES 848   14 Integration in Vector Fields 14.1 Line Integrals 851 14.2 Vector Fields, Work, Circulation, and Flux 856 14.3 Path Independence, Potential Functions, and Conservative Fields 867 14.4 Green’s Theorem in the Plane 877 14.5 Surfaces and Area 887 14.6 Surface Integrals and Flux 896 14.7 Stokes’Theorem 905 14.8 The Divergence Theorem and a Unified Theory 914 QUESTIONS TO GUIDE YOUR REVIEW 925 PRACTICE EXERCISES 925 ADDITIONAL AND ADVANCED EXERCISES 928   Appendices AP-1 A.1 Real Numbers and the Real Line AP-1 A.2 Mathematical Induction AP-7 A.3 Lines, Circles, and Parabolas AP-10 A.4 Trigonometry Formulas AP-19 A.5 Proofs of Limit Theorems AP-21 A.6 Commonly Occurring Limits AP-25 A.7 Theory of the Real Numbers AP-26 A.8 The Distributive Law for Vector Cross Products AP-29 A.9 The Mixed Derivative Theorem and the Increment Theorem AP-30