<story><title>PDEs you should know</title><url>https://www.lucaspauker.com/pdes</url></story><parent_chain><item><author>marginalia_nu</author><text>The point is that equations without closed form solutions are pretty useless if you aren&amp;#x27;t into pretty hairy maths, Green&amp;#x27;s functions and the like.&lt;p&gt;An equation everyone should know is Hooke&amp;#x27;s law. That&amp;#x27;s useful at a high school level.</text></item><item><author>medo-bear</author><text>Most useful equations don&amp;#x27;t have a closed form solution. This is why things like machine learning exist. More specifically PDEs are a hot topic in DNNs at the moment. See physics informed neural networks: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Physics-informed_neural_networks&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Physics-informed_neural_netw...&lt;/a&gt;</text></item><item><author>marginalia_nu</author><text>PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don&amp;#x27;t have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don&amp;#x27;t need to know these.&lt;p&gt;Hard to say what&amp;#x27;s the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you should know these.</text></item></parent_chain><comment><author>nautilius</author><text>You really should read up on numerical math, we really don&amp;#x27;t need closed form solutions, and this makes PDE far from useless.</text></comment>
<story><title>PDEs you should know</title><url>https://www.lucaspauker.com/pdes</url></story><parent_chain><item><author>marginalia_nu</author><text>The point is that equations without closed form solutions are pretty useless if you aren&amp;#x27;t into pretty hairy maths, Green&amp;#x27;s functions and the like.&lt;p&gt;An equation everyone should know is Hooke&amp;#x27;s law. That&amp;#x27;s useful at a high school level.</text></item><item><author>medo-bear</author><text>Most useful equations don&amp;#x27;t have a closed form solution. This is why things like machine learning exist. More specifically PDEs are a hot topic in DNNs at the moment. See physics informed neural networks: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Physics-informed_neural_networks&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Physics-informed_neural_netw...&lt;/a&gt;</text></item><item><author>marginalia_nu</author><text>PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don&amp;#x27;t have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don&amp;#x27;t need to know these.&lt;p&gt;Hard to say what&amp;#x27;s the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you should know these.</text></item></parent_chain><comment><author>aqme28</author><text>The math isn&amp;#x27;t &lt;i&gt;that&lt;/i&gt; hairy. I took numerical methods and computational physics classes in undergrad.</text></comment>