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Calculus 3
Vectors, partial derivatives, multiple integrals and vector calculus. 440 problems, in the order most textbooks teach them.
Vectors and space
Partial derivatives
Partial derivatives
Differentiate in one variable while holding the others fixed.
23 problemsGradient and directional derivatives
∇f, and the rate of change in any direction: D_u f = ∇f · u.
30 problemsTangent planes
The plane that touches a surface z = f(x, y) at a point.
24 problemsLocal extrema and saddle points
Critical points of f(x, y), classified with the second derivative test.
30 problemsLagrange multipliers
Maximize or minimize subject to a constraint: ∇f = λ∇g.
30 problemsMultiple integrals
Double integrals over rectangles
Iterated integrals and Fubini's theorem.
30 problemsDouble integrals over general regions
Type I and Type II regions: set the bounds, then integrate.
30 problemsDouble integrals in polar coordinates
Disks and circles: dA = r dr dθ.
12 problemsTriple integrals
Integrate over a box, one variable at a time.
30 problems