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Multivariable Calculus, International Metric Edition
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The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
To the Student.
A Preview of Calculus.
10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations.
Laboratory Project: Families of Hypocycloids.
Calculus with Parametric Curves.
Laboratory Project: Bzier Curves.
Laboratory Project: Families of Polar Curves.
Areas and Lengths in Polar Coordinates.
Conic Sections in Polar Coordinates.
11. INFINITE SEQUENCES AND SERIES.
Laboratory Project: Logistic Sequences.
The Integral Test and Estimates of Sums.
The Comparison Tests.
Absolute Convergence and the Ratio and Root Tests.
Strategy for Testing 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.
12. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems.
The Dot Product.
The Cross Product.
Discovery Project: The Geometry of a Tetrahedron.
Equations of Lines and Planes.
Cylinders and Quadric Surfaces.
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: Keplers Laws.
14. PARTIAL DERIVATIVES.
Functions of Several Variables.
Limits and Continuity.
Tangent Planes and Linear Approximation.
Applied Project: The Speedo LZR Race Suit.
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.
Applied Project: Rocket Science.
Applied Project: Hydro-Turbine Optimization.
15. Multiple Integrals.
Double Integrals over Rectangles.
Double Integrals over General Regions.
Double Integrals in Polar Coordinates.
Applications of Double 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.
16. Vector Calculus.
The Fundamental Theorem for Line Integrals.
Curl and Divergence.
Parametric Surfaces and Their Areas.
Writing Project: Three Men and Two Theorems.
The Divergence Theorem.
17. Second-Order Differential Equations.
Second-Order Linear Equations.
Nonhomogeneous Linear Equations.
Applications of Second-Order Differential Equations.