Homework, 14.5, 14.6
MAT329
Andy Long   Fall, 2015

#36, p. 955

dwdr=8
drdt=-.1
dwdT=-2
dTdt=.15
b=dwdr*drdt+dwdT*dTdt

#44, p. 955

c=332
fs=460
fo[vo_,vs_]:=((c+vo)/(c-vs))*fs
fovo[vo_,vs_]=D[fo[vo,vs],vo]
fovs[vo_,vs_]=D[fo[vo,vs],vs]
dfodt=fovo[34,40]*1.4+fovs[34,40]*1.2
N[fo[34,40]]

#10, p. 967

f[x_,y_,z_]:=y^2E^(x y z)
gradf[x_,y_,z_]={D[f[x,y,z],x],D[f[x,y,z],y],D[f[x,y,z],z]}
gradf[0,1,-1]
Dot[gradf[0,1,-1],{3,4,12}/13]

#36, p. 968: you need to move perpendicular to the level lines, from point A to Mud Lake, and from point B to the Creek -- just be reasonable, physically realizable!