Dr. Z's Multivariable Calculus Handouts

These are the handouts I gave out when I taught Multivariable Calculus (Math 251), during the Fall Semester of 2006-2007. The section numbers refer to the textbook, which was `Calculus, fifth edition', by James Stewart, Thompson, Brooks/Cole.

• Chapter 12 (Vectors and the Geomery of Space)
  • HandOut 12.1 (Three-Dimensional Coordinate Systems)
  • HandOut 12.2 (Vectors)
  • HandOut 12.3 (The Dot Product)
  • HandOut 12.4 (The Cross Product)
  • HandOut 12.5 (Equations of Lines and Planes)
• Chapter 13 (Vectors Functions)
  • HandOut 13.1 (Vector Functions and Space Curves)
  • HandOut 13.2 (Derivatives and Integrals of Vector Functions)
  • HandOut 13.3 (Arclength and Curvature)
  • HandOut 13.4 (Motin in Space: Velocity and Acceleration)
  • HandOut 13.4 (Motin in Space: Velocity and Acceleration)
• Chapter 14 (Partial Derivatives)
  • HandOut 14.2 (Limits and Continuity)
  • HandOut 14.3 (Partial Derivatives)
  • HandOut 14.4 (Tangent Planes and Linear Approximation)
  • HandOut 14.5 (The Chain Rule)
  • HandOut 14.6 (Directional Derivative and the Gradient Vector)
  • HandOut 14.7 (Maximum and Minimum Values)
  • HandOut 14.8 (Lagrange Multipliers)
• Chapter 15 (Multiple Integrals)
  • HandOut 15.2 (Iterated Integrals)
  • HandOut 15.3 (Double Integrals over General Regions)
  • HandOut 15.4 (Double Integrals in Polar Coordinates)
  • HandOut 15.6 (Surface Area)
  • HandOut 15.7 (Triple Integrals)
  • HandOut 15.8 (Triple Integrals in Cylindrical and Spherical Coordinates)
  • HandOut 15.9 (Change of Variables in Multiple Integrals)
• Chapter 16 (Vector Calculus)
  • HandOut 16.2 (Line Integrals Integrals)
  • HandOut 16.3 (The Fundamental Theorem for Line Integrals)
  • HandOut 16.4 (Green's Theorem)
  • HandOut 16.5 (Curl and Divergence)
  • HandOut 16.6 (Parametric Surfaces and their Areas)
  • HandOut 16.7 (Surface Integrals)
  • HandOut 16.8 (Stokes' Theorem)
  • HandOut 16.9 (The Divergence Theorem)
• The Last Handout (The Meaning of It All)

Doron Zeilberger's Homepage

Rutgers (NB) Math 251 Fall 2006, Secs. 01-06