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	<title>Comments on: Heaviside&#8217;s Operator Calculus</title>
	<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/</link>
	<description>Lost Art in the Mathematical Sciences</description>
	<pubDate>Fri, 12 Mar 2010 01:42:22 +0000</pubDate>
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		<title>By: Calendars, Cats, and Connections &#8212; The Endeavour</title>
		<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-1421</link>
		<author>Calendars, Cats, and Connections &#8212; The Endeavour</author>
		<pubDate>Wed, 06 Jan 2010 14:32:54 +0000</pubDate>
		<guid>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-1421</guid>
		<description>[...] on the calendar here. When I discovered Ron Doerfler&#8217;s blog, I bookmarked his article on Oliver Heaviside to read later. (Heaviside was a pioneer in what was later called distribution theory, a way of [...]</description>
		<content:encoded><![CDATA[<p>[&#8230;] on the calendar here. When I discovered Ron Doerfler&#8217;s blog, I bookmarked his article on Oliver Heaviside to read later. (Heaviside was a pioneer in what was later called distribution theory, a way of [&#8230;]</p>
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		<title>By: A.B.Leal</title>
		<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-858</link>
		<author>A.B.Leal</author>
		<pubDate>Mon, 20 Apr 2009 11:42:38 +0000</pubDate>
		<guid>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-858</guid>
		<description>&lt;p&gt;"The best result of mathematics is to be able to do without it."&lt;br /&gt;
-- Oliver Heaviside&lt;/p&gt;
&lt;p&gt;Many moons ago, I had this quotation neatly penned and displayed in my study area. I must have found it in a book or magazine (yeah, those days ;-). Right now, Google only finds it in 3 pages from a couple of sources, apparently in audio electronics circles.&lt;/p&gt;
&lt;p&gt;It may be spurious, but it's at least "bene trovato" ... Any confirmation/source gratefully received.&lt;/p&gt;
&lt;p&gt;&lt;em&gt;I haven't heard this quote, but Heaviside was prolific in writing letters as well as articles, so I'm not surprised that he might have written it and not surprised that I haven't come across it. Sounds just like him, though. If I come across the source of the quote I'll drop you an email. Thanks for sharing it.  ---  Ron&lt;/em&gt;&lt;p&gt;
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		<content:encoded><![CDATA[<p>&#8220;The best result of mathematics is to be able to do without it.&#8221;<br />
&#8211; Oliver Heaviside</p>
<p>Many moons ago, I had this quotation neatly penned and displayed in my study area. I must have found it in a book or magazine (yeah, those days ;-). Right now, Google only finds it in 3 pages from a couple of sources, apparently in audio electronics circles.</p>
<p>It may be spurious, but it&#8217;s at least &#8220;bene trovato&#8221; &#8230; Any confirmation/source gratefully received.</p>
<p><em>I haven&#8217;t heard this quote, but Heaviside was prolific in writing letters as well as articles, so I&#8217;m not surprised that he might have written it and not surprised that I haven&#8217;t come across it. Sounds just like him, though. If I come across the source of the quote I&#8217;ll drop you an email. Thanks for sharing it.  &#8212;  Ron</em></p></p>
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		<title>By: Anonymous</title>
		<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-855</link>
		<author>Anonymous</author>
		<pubDate>Mon, 20 Apr 2009 02:20:18 +0000</pubDate>
		<guid>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-855</guid>
		<description>&lt;p&gt;Can I please ask you to convert the equations to a more readable format? Plain text formulas don't look very good. :(&lt;/p&gt;
&lt;p&gt;&lt;em&gt;This was one of my early essays. In later essays I started creating the equations in LaTeX or Word Equation Editor and inserting them as images, which is infinitely better, particularly considering what the Georgia font does to numbers, etc. When I get a chance I'll redo these. Thanks for the suggestion--I had totally forgotten that this essay had equations rendered in text. Meanwhile, if you click on the link at the bottom of the essay for the printer-friendly PDF version, you will see that the equations are rendered much better in the Times New Roman font of that file.&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;ps. also what the heck is with that anti-spam thing - do you really expect people to read that they have to add 80?...&lt;/p&gt;
&lt;p&gt;&lt;em&gt; :) The Wordpress Askimet plug-in has caught over 7,000 spam comments submitted to this blog over the last year or so. It was only a matter of time before spam got through their filter. So I started using a Wordpress anti-spam plug-in that required just the simple sum to be calculated, but it only slowed the spam mostly because, I guess, spambots worked around it. By modifying the plug-in code to require adding another value (chosen as 80) written in the text above the box, I've really reduced the spam that gets through to the Askimet filter. It's also true that if an incorrect sum is submitted, a message appears reminding the commenter to add the 80.  --- Ron&lt;/em&gt;&lt;/p&gt;</description>
		<content:encoded><![CDATA[<p>Can I please ask you to convert the equations to a more readable format? Plain text formulas don&#8217;t look very good. <img src='http://myreckonings.com/wordpress/wp-includes/images/smilies/icon_sad.gif' alt=':(' class='wp-smiley' /> </p>
<p><em>This was one of my early essays. In later essays I started creating the equations in LaTeX or Word Equation Editor and inserting them as images, which is infinitely better, particularly considering what the Georgia font does to numbers, etc. When I get a chance I&#8217;ll redo these. Thanks for the suggestion&#8211;I had totally forgotten that this essay had equations rendered in text. Meanwhile, if you click on the link at the bottom of the essay for the printer-friendly PDF version, you will see that the equations are rendered much better in the Times New Roman font of that file.</em></p>
<p>ps. also what the heck is with that anti-spam thing - do you really expect people to read that they have to add 80?&#8230;</p>
<p><em> <img src='http://myreckonings.com/wordpress/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> The Wordpress Askimet plug-in has caught over 7,000 spam comments submitted to this blog over the last year or so. It was only a matter of time before spam got through their filter. So I started using a Wordpress anti-spam plug-in that required just the simple sum to be calculated, but it only slowed the spam mostly because, I guess, spambots worked around it. By modifying the plug-in code to require adding another value (chosen as 80) written in the text above the box, I&#8217;ve really reduced the spam that gets through to the Askimet filter. It&#8217;s also true that if an incorrect sum is submitted, a message appears reminding the commenter to add the 80.  &#8212; Ron</em></p>
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		<title>By: slon</title>
		<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-850</link>
		<author>slon</author>
		<pubDate>Fri, 10 Apr 2009 19:42:07 +0000</pubDate>
		<guid>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-850</guid>
		<description>Heaviside was the real man.</description>
		<content:encoded><![CDATA[<p>Heaviside was the real man.</p>
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		<title>By: Ed Borasky</title>
		<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-14</link>
		<author>Ed Borasky</author>
		<pubDate>Mon, 14 Jan 2008 03:06:51 +0000</pubDate>
		<guid>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-14</guid>
		<description>&lt;p&gt;There's one other piece of the story. As you note, Laplace transforms replaced the Heaviside operational calculus. But there is yet another form, discovered/invented by Mikusinski, which is purely algebraic in nature. http://en.wikipedia.org/wiki/Jan_Mikusinski. He started with a ring of functions under two operations -- pointwise addition and (Laplace) convolution. Then using a well-known theorem, he showed that this ring was in fact an integral domain -- there are no zero divisors. Given an integral domain, he constructed a field in the same manner one constructs the rationals from the integers or rational functions as ratios of polynomials. I think the book is out of print now, but there are a few available on line.&lt;/p&gt;
&lt;em&gt;&lt;p&gt;Thank you for your comment, Ed---it makes a nice addendum to the essay! I had seen Mikusinski's name when I was looking for references on Heaviside, but I didn't pursue it. It's also a fact that abstract algebra is not a strong suit of mine. I see that Mikusinski's "Operational Calculus" is held by a local university library, and now I'm intrigued enough to retrieve the book and have a go at it. We'll see.&lt;/p&gt;
&lt;p&gt;Again, thanks for describing Mikusinski's achievement in "algebrising" differential equations. I'm continually amazed at how rich the mathematical experience really is, and how knowledgeable people are on sophisticated topics such as this. --- Ron&lt;/p&gt;&lt;/em&gt;
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		<content:encoded><![CDATA[<p>There&#8217;s one other piece of the story. As you note, Laplace transforms replaced the Heaviside operational calculus. But there is yet another form, discovered/invented by Mikusinski, which is purely algebraic in nature. <a href="http://en.wikipedia.org/wiki/Jan_Mikusinski." rel="nofollow">http://en.wikipedia.org/wiki/Jan_Mikusinski.</a> He started with a ring of functions under two operations &#8212; pointwise addition and (Laplace) convolution. Then using a well-known theorem, he showed that this ring was in fact an integral domain &#8212; there are no zero divisors. Given an integral domain, he constructed a field in the same manner one constructs the rationals from the integers or rational functions as ratios of polynomials. I think the book is out of print now, but there are a few available on line.</p>
<p><em>
<p>Thank you for your comment, Ed&#8212;it makes a nice addendum to the essay! I had seen Mikusinski&#8217;s name when I was looking for references on Heaviside, but I didn&#8217;t pursue it. It&#8217;s also a fact that abstract algebra is not a strong suit of mine. I see that Mikusinski&#8217;s &#8220;Operational Calculus&#8221; is held by a local university library, and now I&#8217;m intrigued enough to retrieve the book and have a go at it. We&#8217;ll see.</p>
<p>Again, thanks for describing Mikusinski&#8217;s achievement in &#8220;algebrising&#8221; differential equations. I&#8217;m continually amazed at how rich the mathematical experience really is, and how knowledgeable people are on sophisticated topics such as this. &#8212; Ron</p>
<p></em></p>
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		<title>By: Jagger</title>
		<link>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-8</link>
		<author>Jagger</author>
		<pubDate>Sat, 05 Jan 2008 06:37:49 +0000</pubDate>
		<guid>http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/#comment-8</guid>
		<description>"computational observation" - hmmm I am quite intrigued.  Nice discussion</description>
		<content:encoded><![CDATA[<p>&#8220;computational observation&#8221; - hmmm I am quite intrigued.  Nice discussion</p>
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