第十章 Parametric Equations and Polar Coordinates

• 10.3 Polar Coordinates
  10.4 Areas and Lengths in Polar Coordinates

• 11.1 Sequences
  11.2 Series
  11.3 The Integral Test and Estimates of Sums
  11.4 The Comparison Tests
  11.5 Alternating Series
  11.6 Absolute Convergence and the Ratio and Root Tests
  11.8 Power Series
  11.9 Representations of Functions as Power Series
  11.10 Taylor and Maclaurin Series
  11.11 Applications of Taylor Polynomials

• 12.1 Three-Dimensional Coordinate Systems
  12.2 Vectors
  12.3 The Dot Product (12.1 12.2 與 12.3 為複習課程)
  12.4 The Cross Product
  12.5 Equations of Lines and Planes
  12.6 Cylinders and Quadric Surface

• 13.1 Vector Functions and Space Curves
  13.2 Derivatives and Integrals of Vector Functions
  13.3 Arc Length And Curvature (Curvatre 選教)
  13.4 Motion in Space: Velocity and Acceleration(本節選教)

• 14.1 Functions of Several Variables
  14.2 Limits and Continuity
  14.3 Partial Derivatives
  14.4 Tangent Plans and Differentials
  14.5 The Chain Rule
  14.6 Directional Derivatives and the Gradient Vector
  14.7 Maximum and Minimum Values
  14.8 Lagrange Multipliers

• 15.1 Double Integrals over Rectangles
  15.2 Iterated Integrals
  15.3 Double Integrals over General Regions
  15.4 Double Integrals in Polar Coordinates
  15.5 Application of Double Integrals
  15.6 Surface Area (選教)
  15.7 Triple Integrals
  15.8 Triple Integrals in Cylindrical Coordinates
  15.9 Triple Integrals in Spherical Coordinates
  15.10 Change of Variables in Multiple Integrals

• 16.1 Vector fields
  16.2 Line integrals
  16.3 The fundamental Theorem for line integrals
  16.4 Green's Theorem