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Parametric Equations and Polar Coordinates | |
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Curves Defined by Parametric Equations | |
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Laboratory Project: Families of Hypocycloids | |
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Tangents and Areas | |
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Laboratory Project: Bezier Curves | |
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Arc Length and Surface Area | |
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Polar Coordinates | |
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Areas and Lengths in Polar Coordinates | |
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Conic Sections | |
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Conic Sections in Polar Coordinates | |
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Applied Project: Transfer Orbits | |
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Review | |
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Problems Plus | |
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Infinite Sequences and Series | |
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Sequences | |
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Laboratory Project: Logistic Sequences | |
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Series | |
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The Integral Test and Estimates of Sums | |
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The Comparison Tests | |
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Alternating Series | |
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Absolute Convergence and the Ratio and Root Tests | |
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Strategy for Testing Series | |
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Power Series | |
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Representation of Functions as Power Series | |
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Taylor and Maclaurin Series The Binomial Series | |
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Writing Project: How Newton Discovered the Binomial Series | |
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Applications of Taylor Polynomials | |
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Applied Project: Radiation from the Stars | |
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Review | |
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Problems Plus | |
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Vectors and the Geometry of Space | |
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Three-Dimensional Coordinate Systems | |
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Vectors | |
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The Dot Product | |
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The Cross Product | |
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Discovery Project: The Geometry of a Tetrahedron | |
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Equations of Lines and Planes | |
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Quadric Surfaces | |
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Cylindrical and Spherical Coordinates | |
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Laboratory Project: Families of Surfaces | |
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Review | |
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Problems Plus | |
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Vector Functions | |
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Vector Functions and Space Curves | |
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Derivatives and Integrals of Vector Functions | |
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Arc Length and Curvature | |
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Motion in Space: Velocity and Acceleration | |
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Applied Project: Kepler?s Laws | |
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Review | |
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Problems Plus | |
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Partial Derivatives Functions of Several Variables | |
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Limits and Continuity | |
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Partial Derivatives | |
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Tangent Planes and Differentials | |
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The Chain Rule | |
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Directional Derivatives and the Gradient Vector | |
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Maximum and Minimum Values | |
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Applied Project: Designing a Dumpster | |
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Discovery Project: Quadratic Approximations and Critical Points | |
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Lagrange Multipliers | |
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Applied Project: Rocket Science | |
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Applied Project: Hydro-Turbine Optimization | |
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Review | |
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Problems Plus | |
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Multiple Integrals | |
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Double Integrals Over Rectangles | |
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Iterated Integrals | |
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Double Integrals over General Regions | |
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Double Integrals in Polar Coordinates | |
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Applications of Double Integrals | |
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Surface Area | |
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Triple Integrals | |
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Discovery Project: Volumes of Hyperspheres | |
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Triple Integrals in Cylindrical and Spherical Coordinates | |
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Applied Project: Roller Derby | |
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Discovery Project: The Intersection of Three Cylinders | |
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Change of Variables in Multiple Integrals | |
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Review | |
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Problems Plus | |
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Vector Calculus | |
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Vector Fields | |
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Line Integrals | |
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The Fundamental Theorem for Line Integrals | |
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Green?s Theorem | |
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Curl and Divergence | |
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Parametric Surfaces and Their Areas | |
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Surface Integrals | |
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Stokes? Theorem | |
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Writing Project: Three Men and Two Theorems | |
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The Divergence Theorem | |
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Summary | |
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Review | |
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Problems Plus | |
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Second-Order Differential Equations | |
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Second-Order Linear Equations | |
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Nonhomogeneous Linear Equations | |
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Applications of Second-Order Differential Equations | |
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Series Solutions | |
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Review | |
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Problems Plus | |
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Appendixes | |
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Numbers, Inequalities, and Absolute Values | |
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Coordinate Geometry and Lines | |
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Graphs of Second-Degree Equations | |
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Trigonometry | |
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Sigma Notation | |
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Proofs of Theorems | |
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The Logarithm Defined as an Integral | |
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Complex Numbers | |
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Answers to Odd-Numbered Exercises | |