Finding a Jacobian In Exercises 3540, find the Jacobian for the indicated change of

Chapter 14, Problem 36

(choose chapter or problem)

In Exercises 35 - 40, find the Jacobian

\(\frac{\partial(x, y, z)}{\partial(u, v, w)}\)

for the indicated change of variables. If

x = 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

\(\frac{\partial(x, y, z)}{\partial(u, v, w)}=\left|\begin{array}{lll}\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} & \frac{\partial x}{\partial w} \\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v} & \frac{\partial y}{\partial w} \\ \frac{\partial z}{\partial u} & \frac{\partial z}{\partial v} & \frac{\partial z}{\partial w}\end{array}\right|\)

x = 4u - v, y = 4v - w, z = u + w

Text Transcription:

partial(x, y, z) / partial(u, v, w)

partial(x, y, z) / partial(u, v, w)} = |partial x / partial u  partial x / partial v  partial x partial w partial y / partial u  partial y / partial v partial y / partial w partial z / partial u partial z / partial v partial z / partial w|