Unit · year 2
MU-203 · Multivariable & Vector Calculus
Threads space · change5 theorems
Calculus in many dimensions, culminating in the great integral theorems.
Theorems in this unit
T-052
Change of variables and the Jacobian
How volumes transform under a smooth change of coordinates.
T-053
The method of Lagrange multipliers
Constrained extrema occur where gradients align.
T-054
Green's theorem
A planar circulation integral equals a double integral of curl.
T-055
Stokes' theorem
Circulation around a boundary equals the flux of curl through the surface.
T-056
The divergence theorem
Flux through a closed surface equals the integral of divergence inside.