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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2010 • Question 4

Question

Math 6420 • PDE Fall 2010 • Question 4

  1. Find the weak formulation for the boundary value problem \[ u''-\delta (x)u=1 \] subject to boundary conditions \(u(-1)=u(1)=0\).
  2. Find the solution to this boundary value problem.

Raw LaTeX

\begin{enumerate}
\item[(a)] Find the weak formulation for the boundary value problem
\[
  u''-\delta(x)u=1
\]
subject to boundary conditions \(u(-1)=u(1)=0\).

\item[(b)] Find the solution to this boundary value problem.
\end{enumerate}

Topic Tags

Boundary Value Problems Distributions and Weak Solutions Fundamental Solutions Linear Programming and Optimization