Math 005C Review 5

draw pic, cyl, sph

cyl, sph, vert plane, cone

along theta vs along phi

dS for cyl, sph

boundaries of S and R, graph R equals…

dA, F = (x,y), r(u,v)

jacobian det, dA, S

point r = (x,y), position vector, vector field (F), streamline, 3d (r, F)

deriv of vec wrt vec, F(r), d(P,Q)

F, dF/dr, geometrically

del * f, del orthog * f

r, del, F(r), F, divergence, 2d curl

expansion, circulation

expansion, circulation, (pure) deflection

for sure on test

laplacian, uphill direction…

dr, ds, antideriv of f(r) ds along c

r(t), dr/dt, mag dr/dt, antideriv of f ds along c

ds, mag ds, dr, definitions (integral, words, draw)

for sure on test (int, words, draw)

dr, ds, F, antideriv of F dot dr along c

F, dr, F dot dr, F wedge dr, r(t), dr/dt, F dot dr/dt (along antideriv c)

eg. express in cyl/sph coords, name type of surface

solve z, shows up 2 times

r = (2,9); F(r)