5

Kinetics of Materials

Page 125 — 5 corrections

Eq. 5.129

Eq. 5.133

$$c(x,t) = A_{0} + \sum_{m=1}^{\infty} A_{m} \sin\left(\frac{2\pi m}{\lambda} x \right) e^{-4 \pi^2 m^2 Dt/\lambda^2}$$

Eq. 5.134

$$A_0 = \frac{1}{\lambda} \int_0^\lambda c(x,0) dx \hspace{0.25in... ...bda} \int_0^\lambda c(x,0) \sin \left( \frac{2 m \pi x}{\lambda} \right) dx$$

Text after Eq. 5.134

The coefficients can be determined by using the initial condition given by Eq. 5.128. When t = 0, Eq. 5.133 is a standard Fourier series with coefficients given by

Eq. 5.135

$$c(x,t) = \frac{c_{0}}{2} + \frac{2c_{0}}{\pi}\sum_{m=\text{odd}}... ...c{1}{m}\sin\left(\frac{2\pi m}{\lambda}x \right) e^{-4 \pi^2 m^2 Dt/\lambda^2}$$

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