PMCOL305 Study Guide - World Socialist Web Site

Finding a Jacobian In Exercises 35-40, find the Jacobian x.y.a alu, v, w) for the indicated change of variables. If r=f(u, v, w), y=g(u, v, w), and z=h(u, v, w) then the Jacobian of x, y, and z with respect to u, v, and w is ax ax a du av aw az az a du v w

Let W(s, t) = F(u(s, t), v(s, t)) where u(1, 0) = -9, us(1, 0) = 7, ut(1,0) = 2 v(1, 0) = -1, vs(1, 0) = -6, vt(1, 0) = 3 Fu(-9, -1) = -2, Fv(-9, -1) = 7 Ws(1, 0) = Wt(1, 0) = Let w = -xy - 3yz + 5 xz, x = st, y = est, z = t2 Compute (5, 2) = -2y + 10z + 2xe^(10) - 6ze^(10) (5, 2) = 300 + 43e^(10)

Let W(s, t) = F(u(s, t), v(s, t)) where u(1, 0) = -9, us(1, 0) = 7, ut(1,0) = 2 v(1, 0) = -1, vs(1, 0) = -6, vt(1, 0) = 3 Fu(-9, -1) = -2, Fv(-9, -1) = 7 Ws(1, 0) = Wt(1, 0) = Let w = -xy - 3yz + 5 xz, x = st, y = est, z = t2 Compute (5, 2) = -2 + 10z + 2xe^(10) - 6ze^(10) (5, 2) = 300 + 43e^(10)