Calculus Volume 3

• Preface
• 1. Parametric Equations and Polar Coordinates
  • 1.1 Parametric Equations
  • 1.2 Calculus of Parametric Curves
  • 1.3 Polar Coordinates
  • 1.4 Area and Arc Length in Polar Coordinates
  • 1.5 Conic Sections
• 2. Vectors in Space
  • 2.1 Vectors in the Plane
  • 2.2 Vectors in Three Dimensions
  • 2.3 The Dot Product
  • 2.4 The Cross Product
  • 2.5 Equations of Lines and Planes in Space
  • 2.6 Quadric Surfaces
  • 2.7 Cylindrical and Spherical Coordinates
• 3. Vector-Valued Functions
  • 3.1 Vector-Valued Functions and Space Curves
  • 3.2 Calculus of Vector-Valued Functions
  • 3.3 Arc Length and Curvature
  • 3.4 Motion in Space
• 4. Differentiation of Functions of Several Variables
  • 4.1 Functions of Several Variables
  • 4.2 Limits and Continuity
  • 4.3 Partial Derivatives
  • 4.4 Tangent Planes and Linear Approximations
  • 4.5 The Chain Rule
  • 4.6 Directional Derivatives and the Gradient
  • 4.7 Maxima/Minima Problems
  • 4.8 Lagrange Multipliers
• 5. Multiple Integration
  • 5.1 Double Integrals over Rectangular Regions
  • 5.2 Double Integrals over General Regions
  • 5.3 Double Integrals in Polar Coordinates
  • 5.4 Triple Integrals
  • 5.5 Triple Integrals in Cylindrical and Spherical Coordinates
  • 5.6 Calculating Centers of Mass and Moments of Inertia
  • 5.7 Change of Variables in Multiple Integrals
• 6. Vector Calculus
  • 6.1 Vector Fields
  • 6.2 Line Integrals
  • 6.3 Conservative Vector Fields
  • 6.4 Green’s Theorem
  • 6.5 Divergence and Curl
  • 6.6 Surface Integrals
  • 6.7 Stokes’ Theorem
  • 6.8 The Divergence Theorem
• 7. Second-Order Differential Equations
  • 7.1 Second-Order Linear Equations
  • 7.2 Nonhomogeneous Linear Equations
  • 7.3 Applications
  • 7.4 Series Solutions of Differential Equations
• Appendix A: Table of Integrals
• Appendix B: Table of Derivatives
• Appendix C: Review of Pre-Calculus