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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 9

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 9

  1. What theorem from multivariable calculus is the proof of the regular value theorem dependent on?
  2. What theorem from single variable calculus is the proof of Stokes’ theorem dependent on?
  3. What theorem from differential topology is used to prove that transverse intersection of manifolds is a manifold?

Raw LaTeX

\begin{enumerate}
\item[(a)] What theorem from multivariable calculus is the proof of the regular value
theorem dependent on?
\item[(b)] What theorem from single variable calculus is the proof of Stokes' theorem
dependent on?
\item[(c)] What theorem from differential topology is used to prove that transverse
intersection of manifolds is a manifold?
\end{enumerate}

Topic Tags

Compactly Supported Forms and Integration Regular Values and Level Sets Stokes' Theorem and Integration on Manifolds Transversality and Intersection Theory