Solution: Find the eigenvalues and the eigenfunctions of the following problem.
Question: Find the eigenvalues and the eigenfunctions of the following problem.
\[\begin{array}{r} \frac{\partial^{4} u}{\partial x^{4}}=-\frac{1}{a^{2}} \frac{\partial^{2} u}{\partial t^{2}}, \quad x \in(0, \pi), \quad t>0 \\ \text { B.C.: } u(0, t)=u(\pi, t)=u_{x x}(0, t)=u_{x x}(\pi, t)=0 \end{array}\]
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[Step-by-Step] Cohort study by Madsen et al (NEJM 2002) Of the 537,303
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Solution: Describe the characteristics in Table 1 in terms of
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