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University Calculus, Part Two (Multivariable, Chap 8-14)
ISBN: 9780321454218 | 0321454219
Edition: 1stFormat: Paperback
Publisher: Addison Wesley
Pub. Date: 1/1/2007
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This streamlined version of 'Thomas' Calculus' provides a faster-paced, precise and accurate presentation of multivariable calculus for a college-level calculus course. '"University Calculus, Part Two' "is the ideal choice for professors who want a faster-paced multivariable text with a more conceptually balanced exposition. It is a blend of intuition and rigor. Transcendental functions, introduced in '"University Calculus, Part One'", are covered in more depth in this text.
University Calculus: Alternate Edition P... MORE
University Calculus: Alternate Edition P... MORE
| Preface | p. vii |
| Infinite Sequences and Series | p. 502 |
| Sequences | p. 502 |
| Infinite Series | p. 515 |
| The Integral Test | p. 523 |
| Comparison Tests | p. 529 |
| The Ratio and Root Tests | p. 533 |
| Alternating Series, Absolute and Conditional Convergence | p. 537 |
| Power Series | p. 543 |
| Taylor and Maclaurin Series | p. 553 |
| Convergence of Taylor Series | p. 559 |
| The Binomial Series | p. 569 |
| Questions to Guide Your Review | p. 572 |
| Practice Exercises | p. 573 |
| Additional and Advanced Exercises | p. 575 |
| Polar Coordinates and Conics | p. 577 |
| Polar Coordinates | p. 577 |
| Graphing in Polar Coordinates | p. 582 |
| Areas and Lengths in Polar Coordinates | p. 586 |
| Conic Sections | p. 590 |
| Conics in Polar Coordinates | p. 599 |
| Conics and Parametric Equations; The Cycloid | p. 606 |
| Questions to Guide Your Review | p. 610 |
| Practice Exercises | p. 610 |
| Additional and Advanced Exercises | p. 612 |
| Vectors and the Geometry of Space | p. 614 |
| Three-Dimensional Coordinate Systems | p. 614 |
| Vectors | p. 619 |
| The Dot Product | p. 628 |
| The Cross Product | p. 636 |
| Lines and Planes in Space | p. 642 |
| Cylinders and Quadric Surfaces | p. 652 |
| Questions to Guide Your Review | p. 657 |
| Practice Exercises | p. 658 |
| Additional and Advanced Exercises | p. 660 |
| Vector-Valued Functions and Motion in Space | p. 663 |
| Vector Functions and Their Derivatives | p. 663 |
| Integrals of Vector Functions | p. 672 |
| Arc Length in Space | p. 678 |
| Curvature of a Curve | p. 683 |
| Tangential and Normal Components of Acceleration | p. 689 |
| Velocity and Acceleration in Polar Coordinates | p. 694 |
| Questions to Guide Your Review | p. 698 |
| Practice Exercises | p. 698 |
| Additional and Advanced Exercises | p. 700 |
| Partial Derivatives | p. 702 |
| Functions of Several Variables | p. 702 |
| Limits and Continuity in Higher Dimensions | p. 711 |
| Partial Derivatives | p. 719 |
| The Chain Rule | p. 731 |
| Directional Derivatives and Gradient Vectors | p. 739 |
| Tangent Planes and Differentials | p. 747 |
| Extreme Values and Saddle Points | p. 756 |
| Lagrange Multipliers | p. 765 |
| Taylor's Formula for Two Variables | p. 775 |
| Questions to Guide Your Review | p. 779 |
| Practice Exercises | p. 780 |
| Additional and Advanced Exercises | p. 783 |
| Multiple Integrals | p. 785 |
| Double and Iterated Integrals over Rectangles | p. 785 |
| Double Integrals over General Regions | p. 790 |
| Area by Double Integration | p. 799 |
| Double Integrals in Polar Form | p. 802 |
| Triple Integrals in Rectangular Coordinates | p. 807 |
| Moments and Centers of Mass | p. 816 |
| Triple Integrals in Cylindrical and Spherical Coordinates | p. 825 |
| Substitutions in Multiple Integrals | p. 837 |
| Questions to Guide Your Review | p. 846 |
| Practice Exercises | p. 846 |
| Additional and Advanced Exercises | p. 848 |
| Integration in Vector Fields | p. 851 |
| Line Integrals | p. 851 |
| Vector Fields, Work, Circulation, and Flux | p. 856 |
| Path Independence, Potential Functions, and Conservative Fields | p. 867 |
| Green's Theorem in the Plane | p. 877 |
| Surfaces and Area | p. 887 |
| Surface Integrals and Flux | p. 896 |
| Stokes' Theorem | p. 905 |
| The Divergence Theorem and a Unified Theory | p. 914 |
| Questions to Guide Your Review | p. 925 |
| Practice Exercises | p. 925 |
| Additional and Advanced Exercises | p. 928 |
| First-Order Differential Equations (online) | |
| Solutions, Slope Fields, and Picard's Theorem | |
| First-Order Linear Equations | |
| Applications | |
| Euler's Method | |
| Graphical Solutions of Autonomous Equations | |
| Systems of Equations and Phase Planes | |
| Second-Order Differential Equations (online) | |
| Second-Order Linear Equations | |
| Nonhomogeneous Linear Equations | |
| Applications | |
| Euler Equations | |
| Power Series Solutions | |
| Appendices | p. AP-1 |
| Real Numbers and the Real Line | p. AP-1 |
| Mathematical Induction | p. AP-7 |
| Lines, Circles, and Parabolas | p. AP-10 |
| Trigonometry Formulas | p. AP-19 |
| Proofs of Limit Theorems | p. AP-21 |
| Commonly Occurring Limits | p. AP-25 |
| Theory of the Real Numbers | p. AP-26 |
| The Distributive Law for Vector Cross Products | p. AP-29 |
| The Mixed Derivative Theorem and the Increment Theorem | p. AP-30 |
| Answers | p. A-1 |
| Index | p. I-1 |
| A Brief Table of Integrals | p. T-1 |
| Credits | p. C-1 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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