Melanie #541
Melanie #541
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… checked the limit as r goes to zero with LHopital's rule, then rewrote the code
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| "\\begin{align*}\n", | ||
| " -\\frac{1}{r^2}\\bigl(-D_1\\, r^2 u_1'\\bigr)'(r) - \\Sigma_{a,1}\\,u_1(r) + s_{0,1} &= 0 \\quad\\quad \\forall \\quad\\quad r\\in\\ ]0,R[, \\\\\n", |
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Eliminating the small space makes the equation look odd since the diffusion coefficient shows up too close to the unknown variable. Proper typesetting calls for a small space to make the distinction. Note the difference
| @@ -179,13 +180,13 @@ | |||
| "\n", | |||
| "\\begin{align*}\n", | |||
| "y = c_1 e^{m_1x} + c_2 e^{m_2 x} \n", | |||
| " + \\frac{e^{m_1x}}{m_1-m_2} \\int R\\left(x\\right) e^{-m_1x} \\, dx\n", | |||
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The integrand and the differential should be separated by a space:
| "\\end{align*}\n", | ||
| "\n", | ||
| "where $a$ and $b$ are constants, and $m_1$ and $m_2$ are the real and distinct roots of $m^2+am+b=0$.\n", | ||
| "\n", | ||
| "Thus, for $w_i=r\\,u_i$, $a=0$, $b=-\\frac{\\Sigma_{a,i}}{D_i}$, $R=- r\\frac{s_{0,i}}{D_i}$, and the roots are\n", | ||
| "Thus, for $w_i=r u_i$, $a=0$, $b=-\\frac{\\Sigma_{a,i}}{D_i}$, $R=- r\\frac{s_{0,i}}{D_i}$, and the roots are\n", |
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