Multivariable calculus /

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Bibliographic Details
Author / Creator: Stewart, James, 1941-
Format: Book
Language:English
Edition:Seventh edition.
Imprint: Australia ; Belmont, CA : Brooks/Cole, Cengage Learning, [2012]
Subjects:
Table of Contents:
  • Parametric Equations And Polar Coordinates
  • Curves Defined by Parametric Equations
  • Laboratory Project: Families of Hypocycloids
  • Calculus with Parametric Curves
  • Laboratory Project: B?zier Curves
  • Polar Coordinates
  • Laboratory Project: Families of Polar Curves
  • Areas and Lengths in Polar Coordinates
  • Conic Sections
  • Conic Sections in Polar Coordinates
  • Review
  • Problems Plus
  • 11. 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
  • Representations of Functions as Power Series
  • Taylor and Maclaurin Series
  • Laboratory Project: An Elusive Limit
  • Writing Project: How Newton Discovered the Binomial Series
  • Applications of Taylor Polynomials
  • Applied Project: Radiation from the Stars
  • Review
  • Problems Plus
  • 12. 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
  • Review
  • Problems Plus
  • 13. 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
  • 14. Partial Derivatives
  • Functions of Several Variables
  • Limits and Continuity
  • Partial Derivatives
  • Tangent Planes and Linear Approximation
  • 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
  • 15. Multiple Integrals
  • Double Integrals over Rectangles
  • Iterated Integrals
  • Double Integrals over General Regions
  • Double Integrals in Polar Coordinates
  • Applications of Double Integrals
  • Triple Integrals
  • Discovery Project: Volumes of Hyperspheres
  • Triple Integrals in Cylindrical Coordinates
  • Discovery Project: The Intersection of Three Cylinders
  • Triple Integrals in Spherical Coordinates
  • Applied Project: Roller Derby
  • Change of Variables in Multiple Integrals
  • Review
  • Problems Plus
  • 16. Ector Calculu
  • 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
  • 17. Second-Order Differential Equations
  • Second-Order Linear Equations
  • Nonhomogeneous Linear Equations
  • Applications of Second-Order Differential Equations
  • Series Solutions
  • Review
  • Problems Plus
  • Appendixes
  • F. Proofs of Theorems
  • G. Graphing Calculators and Computers
  • H. Complex Numbers
  • I. Answers to Odd-Numbered Exercises