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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1998 • Question 3

Question

Math 6420 • PDE Fall 1998 • Question 3

Construct the Green function for the equation \[ u''(x)=f(x)\quad \text {on the interval }0\le x\le 1 \] if \(u\) satisfies the auxiliary conditions \[ \int _0^1 xu(x)\,dx=0\qquad \text {and}\qquad u(0)+u'(1)=0. \]

Raw LaTeX

Construct the Green function for the equation
\[
  u''(x)=f(x)\quad\text{on the interval }0\le x\le 1
\]
if \(u\) satisfies the auxiliary conditions
\[
  \int_0^1 xu(x)\,dx=0\qquad\text{and}\qquad u(0)+u'(1)=0.
\]

Topic Tags

Fundamental Solutions Linear Programming and Optimization Zero-Stability and Root Conditions