Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Partial Differential Equations
Fourier Transform
Initial Value Problem

Formulas

Fourier Transform: \( \hat{u}(k, t) = \int_{-\infty}^{\infty} u(x, t) e^{-ikx} \, dx \)
PDE: \( u_{tt} + 2u_t + u = u_{xx} \)
sinc Function: \( \text{sinc}(x) = \frac{\sin(x)}{x} \)

Theorems

Fourier Transform Method for Solving PDEs

Suitable Grade Level

Undergraduate Level (Advanced Calculus/Partial Differential Equations)