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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2010 • Question 5

Question

Math 6420 • PDE Spring 2010 • Question 5

Using Green’s functions, solve the problem \[ \frac {d^2u}{dx^2}=\frac {1}{1+x^2},\qquad u(-1)=u(1)=0 \] for \(u(x)\), \(x\in [-1,1]\) (obtain an integral representation for the solution, but do not evaluate the integral).

Raw LaTeX

Using Green's functions, solve the problem
\[
  \frac{d^2u}{dx^2}=\frac{1}{1+x^2},\qquad u(-1)=u(1)=0
\]
for \(u(x)\), \(x\in[-1,1]\) (obtain an integral representation for the solution, but do not
evaluate the integral).

Topic Tags

Cauchy Integral Formula and Integral Theorems Fundamental Solutions Linear Programming and Optimization Real Integral Evaluation by Complex Methods