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Summary
Summary
Stewart's CALCULUS, FOURTH EDITION reflects the same old-world dedication to excellence that characterized the first three editions. It has been revised with dedication, precision, and patient care to further emphasize conceptual understanding. A phenomenon of the Stewart success is the texts' use in such a wide variety of colleges and universities throughout the world. Just as he teaches to every student in his classes from the most unprepared to the most mathematically gifted, Stewart writes to a range of students - adding the explanations that make ideas come alive as well as the problems that challenge. Stewart's heuristic examples reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject.
Table of Contents
| 11 Parametric Equations and Polar Coordinates |
| Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycloids |
| Calculus with Parametric Curves, Laboratory Project: Bezier Curves |
| Polar Coordinates |
| Areas and Lengths in Polar Coordinates |
| Conic Sections |
| Conic Sections in Polar Coordinates |
| Review |
| Problems Plus |
| 12 Infinite Sequences and Series |
| Sequences, Laboratory Project: Logistic Sequences |
| Series |
| The Integral Test and Estimates of Sums |
| The Comparison Tests |
| Alternating Series |
| Absolute Convergence and the Ratio and Root Tests |
| Strategy for Testing Series |
| Power Series |
| Representation of Functions as Power Series |
| Taylor and Maclaurin Series |
| Laboratory Project: An Ellusive Limit |
| The Binomial Series, Writing Project: How Newton Discovered the Binomial Series |
| Applications of Taylor Polynomials, Applied Project: Radiation from the Stars |
| Review |
| Problems Plus |
| 13 Vectors and the Geometry of Space |
| Three-Dimensional Coordinate Systems |
| Vectors |
| The Dot Product |
| The Cross Product, Discovery Project: The Geometry of a Tetrahedron |
| Equations of Lines and Planes |
| Cylinders and Quadric Surfaces |
| Cylindrical and Spherical Coordinates, Laboratory Project: Families of Surfaces |
| Review |
| Problems Plus |
| 14 Vector Functions |
| Vector Functions and Space Curves |
| Derivatives and Integrals of Vector Functions |
| Arc Length and Curvature |
| Motion in Space: Velocity and Acceleration, Applied Project: Kepler's Laws |
| Review |
| Problems Plus |
| 15 Partial Derivatives |
| Functions of Several Variables |
| Limits and Continuity |
| Partial Derivatives |
| Tangent Planes and Linear Approximations |
| The Chain Rule |
| Directional Derivatives and the Gradient Vector |
| Maximum and Minimum Values, Applied Project: Designing a Dumpster, Discovery Project: Quadratic Approximations and Critical Points |
| Lagrange Multipliers, Applied Project: Rocket Science, Applied Project: Hydro-Turbine Optimization |
| Review |
| Problems Plus |
| 16 Multiple Integrals |
| Double Integrals over Rectangles |
| Iterated Integrals |
| Double Integrals over General Regions |
| Double Integrals in Polar Coordinates |
| Applications of Double Integrals |
| Surface Area |
| Triple Integrals, Discovery Project: Volumes of Hyperspheres |
| Triple Integrals in Cylindrical and Spherical Coordinates, Applied Project: Roller Derby, Discovery Project: The Intersection of Three Cylinders |
| Change of Variables in Multiple Integrals |
| Review |
| Problems Plus |
| 17 Vector Calculus |
| Vector Fields |
| Line Integrals |
| The Fundamental Theorem for Line Integrals |
| Green's Theorem |
| Curl and Divergence |
| Parametric Surfaces and Their Areas |
| Surface Integrals |
| Stokes' Theorem, Writing Project: Three Men and Two Theorems |
| The Divergence Theorem |
| Summary |
| Review |
| Problems Plus |
| 18 Second-Order Differential Equations |
| Second-Order Linear Equations |
| Nonhomogeneous Linear Equations |
| Applications of Second-Order Differential Equations |
| Series Solutions. Review. Problems Plus |
| Appendixes |
| Answers to Odd-Numbered Exercises |
| Index |
