From: bangerth Date: Tue, 27 Mar 2007 20:37:17 +0000 (+0000) Subject: Fix a few small issues. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=0ca5ab8bed7c1bb76355a9b6789e83d386ea840a;p=dealii-svn.git Fix a few small issues. git-svn-id: https://svn.dealii.org/trunk@14602 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-24/doc/intro.dox b/deal.II/examples/step-24/doc/intro.dox index 8d95a41cb5..f40c132616 100644 --- a/deal.II/examples/step-24/doc/intro.dox +++ b/deal.II/examples/step-24/doc/intro.dox @@ -240,7 +240,6 @@ the indefinite integral with respect to time of both sides: This immediately leads to the statement @f[ P(t,\mathbf r) - \frac{1}{c_0^2} \frac{\partial p}{\partial t} -\; dt = \lambda a(\mathbf r) \delta(t), @f] @@ -254,10 +253,10 @@ $t=+\epsilon$ to find \int_{-\epsilon}^{\epsilon} \lambda a(\mathbf r) \delta(t) \; dt. @f] If we use the property of the delta function that $\int_{-\epsilon}^{\epsilon} -\delta(t)\; dt = 1$, and assume that $P$ is a smooth function in time, we find +\delta(t)\; dt = 1$, and assume that $P$ is a continuous function in time, we find as we let $\epsilon$ go to zero that @f[ -- \frac{1}{c_0^2} \left[ p(\epsilon,\mathbf r) - p(-\epsilon,\mathbf r) \right] +- \lim_{\epsilon\rightarrow 0}\frac{1}{c_0^2} \left[ p(\epsilon,\mathbf r) - p(-\epsilon,\mathbf r) \right] = \lambda a(\mathbf r). @f] @@ -303,7 +302,7 @@ see that in fact 0. @f] -Now, let $\epsilon\rightarrow 0$. Assuming that $P$ is a smooth function in +Now, let $\epsilon\rightarrow 0$. Assuming that $P$ is a continuous function in time, we see that @f[ P(\epsilon)-P(-\epsilon) \rightarrow 0,