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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2012 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 2012 • Question 4

Let \(h:\mathbb {R}^3\to \mathbb {R}\) be the function \(h(x,y,z)=xyz\). Let \(s\) be the vector field on \(\mathbb {R}^3\) given by \[ s(x,y,z)=xy\frac {\partial }{\partial x} +(y-z^3)\frac {\partial }{\partial y} +3\frac {\partial }{\partial z}. \] Find \(L_s(f)(1,1,2)\), the Lie derivative of \(f\) in the direction of \(s\) at the point \((1,1,2)\).

Raw LaTeX

Let \(h:\R^3\to\R\) be the function \(h(x,y,z)=xyz\). Let \(s\) be the vector
field on \(\R^3\) given by
\[
  s(x,y,z)=xy\frac{\partial}{\partial x}
  +(y-z^3)\frac{\partial}{\partial y}
  +3\frac{\partial}{\partial z}.
\]
Find \(L_s(f)(1,1,2)\), the Lie derivative of \(f\) in the direction of \(s\) at the
point \((1,1,2)\).

Topic Tags

Left-Invariant Vector Fields Tangent Spaces and Differential Maps Vector Fields and Flows