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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2004 • Question 5

Question

Math 6510 • Differentiable Manifolds Winter 2004 • Question 5

Let \(f:\mathbb {R}^2\to \mathbb {R}^2\) be given by \[ f(x,y)=(x^2+y,x-y^2). \] Explicitly compute \(f^*dx\), \(f^*dy\), \(f^*(dx\wedge dy)\).

Raw LaTeX

Let \(f:\mathbb{R}^2\to\mathbb{R}^2\) be given by
\[
  f(x,y)=(x^2+y,x-y^2).
\]
Explicitly compute \(f^*dx\), \(f^*dy\), \(f^*(dx\wedge dy)\).

Topic Tags

Differential Forms and Exterior Calculus