Multivariable Calculus Trivia
Gradients, tangent planes, and triple integrals—because one variable just wasn’t complicated enough.
EXAMPLE QUESTIONS
Unlike distance, which describes magnitude alone, what does a vector describe in addition to its magnitude?
Direction
In ordinary diffusion, particles move from higher to lower concentration. Does the net diffusive flux point with or against the concentration gradient?
Against it
On a mathematical landscape, which way relative to the gradient does a hiker travel to descend as steeply as possible?
Against the gradient
For the elevation map f(x,y)=x²+y², what elevation does it show at the point (3,4)?
25
For the surface z = x² + y², what is z when x = 1 and y = 1?
2