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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kcline@carroll.edu