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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1994 • Question 7

Question

Math 6420 • PDE Fall 1994 • Question 7

Find the adjoint operator, its domain and the least squares solution of the problem \(Lu\equiv 4u''+u=e^x\) for \(0\le x\le \pi /2\) if \(u(0)=\alpha \) and \(u(\pi /2)=\beta \).

Raw LaTeX

Find the adjoint operator, its domain and the least squares
solution of the problem \(Lu\equiv4u''+u=e^x\) for \(0\le x\le\pi/2\) if \(u(0)=\alpha\) and
\(u(\pi/2)=\beta\).

Topic Tags

Adjoint Operators and Riesz Representation Distributions and Weak Solutions Least Squares and Normal Equations Linear Programming and Optimization