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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1997 • Question 5

Question

Math 6420 • PDE Fall 1997 • Question 5

Use a Green’s function to find the representation of a possible solution to \[ y''+\omega ^2y=f(x),\qquad y(0)=y'(1)=0 \] for arbitrary values of the parameter \(\omega \). For what values of \(\omega \) does the solution exist? If the solution does not exist find the least square solution. Explain the meaning of the least square solution.

Raw LaTeX

Use a Green's function to find the representation of a possible
solution to
\[
  y''+\omega^2y=f(x),\qquad y(0)=y'(1)=0
\]
for arbitrary values of the parameter \(\omega\). For what values of \(\omega\) does the
solution exist? If the solution does not exist find the least square solution. Explain the
meaning of the least square solution.

Topic Tags

Distributions and Weak Solutions Fundamental Solutions Least Squares and Normal Equations Linear Programming and Optimization