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OpenStax Calculus 3

Study guide for Calculus Volume 3 (Gilbert Strang, 2016 edition)

A study guide for OpenStax Calculus Volume 3 by Gilbert Strang and Edwin Herman, covering every section with practice problems and quizzes.

Independent study guide. Not affiliated with OpenStax or Rice University.

Chapter 1: Parametric Equations and Polar Coordinates

  1. 1.1Parametric Equations
  2. 1.2Calculus of Parametric Curves
  3. 1.3Polar Coordinates
  4. 1.4Area and Arc Length in Polar Coordinates
  5. 1.5Conic Sections

Chapter 2: Vectors in Space

  1. 2.1Vectors in the Plane
  2. 2.2Vectors in Three Dimensions
  3. 2.3The Dot Product
  4. 2.4The Cross Product
  5. 2.5Equations of Lines and Planes in Space
  6. 2.6Quadric Surfaces
  7. 2.7Cylindrical and Spherical Coordinates

Chapter 3: Vector-Valued Functions

  1. 3.1Vector-Valued Functions and Space Curves
  2. 3.2Calculus of Vector-Valued Functions
  3. 3.3Arc Length and Curvature
  4. 3.4Motion in Space

Chapter 4: Differentiation of Functions of Several Variables

  1. 4.1Functions of Several Variables
  2. 4.2Limits and Continuity
  3. 4.3Partial Derivatives
  4. 4.4Tangent Planes and Linear Approximations
  5. 4.5The Chain Rule
  6. 4.6Directional Derivatives and the Gradient
  7. 4.7Maxima and Minima Problems
  8. 4.8Lagrange Multipliers

Chapter 5: Multiple Integration

  1. 5.1Double Integrals over Rectangular Regions
  2. 5.2Double Integrals over General Regions
  3. 5.3Double Integrals in Polar Coordinates
  4. 5.4Triple Integrals
  5. 5.5Triple Integrals in Cylindrical and Spherical Coordinates
  6. 5.6Calculating Centers of Mass and Moments of Inertia
  7. 5.7Change of Variables in Multiple Integrals

Chapter 6: Vector Calculus

  1. 6.1Vector Fields
  2. 6.2Line Integrals
  3. 6.3Conservative Vector Fields
  4. 6.4Green's Theorem
  5. 6.5Divergence and Curl
  6. 6.6Surface Integrals
  7. 6.7Stokes' Theorem
  8. 6.8The Divergence Theorem

Chapter 7: Second-Order Differential Equations

  1. 7.1Second-Order Linear Equations
  2. 7.2Nonhomogeneous Linear Equations
  3. 7.3Applications
  4. 7.4Series Solutions of Differential Equations