MULTIVARIABLE CALCULUS

PARTIAL DERIVATIVES

  1. Functions of Several Variables

  2. Limits and Continuity

  3. Partial Derivatives

  4. Tangent Planes and Linear Approximations

  5. The Chain Rule

  6. Directional Derivatives and the Gradient Vector

  7. Maximum and Minimum Values

  8. Lagrange Multipliers

MULTIPLE INTEGRALS

  1. Double Integrals over Rectangles

  2. Iterated Integrals

  3. Double Integrals over General Regions

  4. Double Integrals in Polar Coordinates

  5. Applications of Double Integrals

  6. Surface Area

  7. Triple Integrals

  8. Triple Integrals in Cylindrical Coordinates

  9. Triple Integrals in Spherical Coordinates

  10. Change of Variables in Multiple Integrals

VECTOR CALCULUS

  1. Vector Fields Line

  2. Integrals

  3. The Fundamental Theorem for Line Integrals

  4. Green’s Theorem

  5. Curl and Divergence

  6. Parametric Surfaces and Their Areas

  7. Surface Integrals

  8. Stokes’ Theorem

  9. The Divergence Theorem

SECOND-ORDER DIFFERENTIAL EQUATIONS

  1. Second-Order Linear Equations

  2. Nonhomogeneous Linear Equations

  3. Applications of Second-Order Differential Equations

  4. Series Solutions

PARAMETRIC EQUATIONS AND POLAR COORDINATES

  1. Curves Defined by Parametric Equations

  2. Calculus with Parametric Curves

  3. Polar Coordinates

  4. Areas and Lengths in Polar Coordinates

  5. Conic Sections

  6. Conic Sections in Polar Coordinates

INFINITE SEQUENCES AND SERIES

  1. Sequences

  2. Series

  3. The Integral Test and Estimates of Sums

  4. The Comparison Tests

  5. Alternating Series

  6. Absolute Convergence and the Ratio and Root Tests

  7. Strategy for Testing Series

  8. Power Series

  9. Representations of Functions as Power Series

  10. Taylor and Maclaurin Series

  11. Applications of Taylor Polynomials

VECTORS AND THE GEOMETRY OF SPACE

  1. Three-Dimensional Coordinate Systems

  2. Vectors

  3. The Dot Product

  4. The Cross Product

  5. Equations of Lines and Planes

  6. Cylinders and Quadric Surfaces

VECTOR FUNCTIONS

  1. Vector Functions and Space Curves

  2. Derivatives and Integrals of Vector Functions

  3. Arc Length and Curvature

  4. Motion in Space: Velocity and Acceleration