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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1994 • Question 6

Question

Math 6420 • PDE Fall 1994 • Question 6

Construct the Green’s function for the equation \(u''(x)=f(x)\) 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's function for the equation
\(u''(x)=f(x)\) 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