Classroom Voting Questions: Multivariable Calculus

Click Here, for the complete set of multivariable calculus questions, ordered following the topic headings below (as in the Hughes-Hallett et al text).

Click Here, for these questions in a larger font, which may be more useful if you plan to cut and paste these questions from the pdf file into PowerPoint.

• Functions of Two Variables
• Graphs of Functions of Two Variables
• Contour Diagrams
• Linear Functions
• Functions of Three Variables
• Displacement Vectors
• Vectors in General
• The Dot Product
• The Cross Product
• The Partial Derivative
• Computing Partial Derivatives Algebraically
• Local Linearity and the Differential
• Gradients and Directional Derivatives in the Plane
• Gradients and Directional Derivatives in Space
• The Chain Rule
• Second Order Partial Derivatives
• Local Extrema
• Optimization
• Constrained Optimization: Lagrange Multipliers
• The Definite Integral of a Funtion of Two Variables
• Iterated Integrals
• Triple Integrals
• Double Integrals in Polar Coordinates
• Integrals in Cylindrical and Spherical Coordinates
• Parameterized Curves
• Motion, Velocity, and Acceleration
• Vector Fields
• The Flow of a Vector Field
• The Idea of a Line Integral
• Computing Line Integrals Over Parameterized Curves
• Gradient Fields and Path-Independent Fields
• Path Dependent Vector Fields and Green's Theorem
• The Idea of a Flux Integral
• Flux Integrals for Graphs, Cylinders, and Spheres
• The Divergence of a Vector Field
• The Divergence Theorem
• The Curl of a Vector Field
• Stokes' Theorem

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