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Dear Martin, Please compile the followings with latex, \documentclass[a4paper,10pt]{article} \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{fontenc} \usepackage{graphicx} \usepackage[dvips]{hyperref} \author{JCsontos} \title{1.14 Szabo-Ostlund} \date{11/04/11} \begin{document} Â\begin{align*} Â \int_{-\infty}^{\ \infty}{a(x) \cdot \delta(x)}\ dx & = Â \int_{-\infty}^{-\epsilon}{a(x) \cdot 0}\ dx + Â \int_{-\epsilon}^{\ \epsilon}{a(x) \cdot \delta_{\epsilon}(x)}\ dx + Â \int_{\ \epsilon}^{\ \infty}{a(x)\cdot 0}\ dx \\ Â & = \int_{-\epsilon}^{\ \epsilon}{a(x) \cdot \delta_{\epsilon}(x)}\ dx \\ Â & = \int_{-\epsilon}^{\ \epsilon}{a(x) \cdot \frac{1}{2\epsilon}}\ dx \\ Â & = \lim_{\epsilon \to 0} \frac{1}{2\epsilon} \int_{-\epsilon}^{\ \epsilon}{a(x)}\ dx\\ Â & = \lim_{\epsilon \to 0} \frac{1}{2\epsilon} Â {[\epsilon-(-\epsilon)]}{a(\xi)}, \ \xi \in (-\epsilon, \epsilon) Â ;\ \textbf{mean value theorem for integration} Â\end{align*} \begin{align*} \text{if $\epsilon \to 0$ then $\xi \to 0$ and } Â \lim_{\epsilon \to 0} \frac{1}{2\epsilon} Â {[\epsilon-(-\epsilon)]}{a(\xi)} & = Â \frac{2\epsilon}{2\epsilon}{a(0)} \end{align*} \end{document} Best, Jozsef On 11/03/2011 04:56 PM, Martin Hediger ma.hed-x-bluewin.ch wrote:
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