<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>http://direct.ecency.com</link><image><url>http://direct.ecency.com/logo512.png</url><title>RSS Feed</title><link>http://direct.ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Tue, 14 Apr 2026 09:30:50 GMT</lastBuildDate><atom:link href="http://direct.ecency.com/created/calculus/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[Graphing Real Spherical Harmonics in Desmos Calculator]]></title><description><![CDATA[In this video, I graph out the real spherical harmonics using the amazing Desmos graphing calculator via a project someone made. I do a quick breakdown of the formulas they used, noting the added normalization]]></description><link>http://direct.ecency.com/hive-111030/@mes/graphing-real-spherical-harmonics-in-desmos-calculator</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/graphing-real-spherical-harmonics-in-desmos-calculator</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 02 Apr 2026 04:04:15 GMT</pubDate><enclosure url="https://images.ecency.com/p/DogN7fF3oJDRFfTX2FWi5pAnsujYqzMqcFsYpSovLq9mFvGSKqHGDBwwWTTiTPfdg3sfw8G1fyTC7bHDz4tf2hg2Cv5g6gBUHw9ZXGZVJVW6qf56nXqChFMK6tx12Ljkbt2VpawBNNBnodwGxv37CRSZovPwHzthT23dX1ioGFqBnBcfDUFNA3uhWwvQ9nKPUdXgvuaLq2QgP?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Graphing Real Spherical Harmonics in Desmos Calculator]]></title><description><![CDATA[In this video, I graph out the real spherical harmonics using the amazing Desmos graphing calculator via a project someone made. I do a quick breakdown of the formulas they used, noting the added normalization]]></description><link>http://direct.ecency.com/hive-128780/@mes/a058e2ca</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/a058e2ca</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 01 Apr 2026 22:15:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhiji3DbidoVRDp4b5xpLSsdy4HQjHP11qqeYufKZkw2f?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Real Spherical Harmonics – Removing the Imaginary Terms]]></title><description><![CDATA[In this video, I derive the real spherical harmonics by excluding the imaginary complex i terms from the complex spherical harmonics. The real spherical harmonics are what are typically plotted when graphing]]></description><link>http://direct.ecency.com/hive-111030/@mes/real-spherical-harmonics-removing-the-imaginary-terms</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/real-spherical-harmonics-removing-the-imaginary-terms</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 30 Mar 2026 22:21:39 GMT</pubDate><enclosure url="https://images.ecency.com/p/2CwnDyeL7SRXDBVj6Mv9E1ywiCUQYqtApawXC2GYmQVWd3WHkD4BbLxA2hh8NnzV1xhmEBLLo4oj1nSdDJs11eJxw76AccPZ3p1FbfJY4QJmAkWU9xAvCyHaFFmNyN8ZNZiMkb5RMD6gDUyJmXcebiiPWry4ikCx5csFDzEqpvgcLYPDsbnPq?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Real Spherical Harmonics – Removing the Imaginary Terms]]></title><description><![CDATA[In this video, I derive the real spherical harmonics by excluding the imaginary complex i terms from the complex spherical harmonics. The real spherical harmonics are what are typically plotted when graphing]]></description><link>http://direct.ecency.com/hive-128780/@mes/2d1e95ad</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/2d1e95ad</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 30 Mar 2026 22:05:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDheyETGcx4zev8uiUDAToxynLPxTGu3c3meu538vUnSQX?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Spherical Harmonics – Solutions to the Angular Laplacian]]></title><description><![CDATA[In this video, I go over the actual spherical harmonics equations, which exclude the radial terms from the solid spherical harmonics I had derived earlier. The spherical harmonics can be combined into]]></description><link>http://direct.ecency.com/hive-111030/@mes/spherical-harmonics-solutions-to-the-angular-laplacian</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/spherical-harmonics-solutions-to-the-angular-laplacian</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 27 Mar 2026 17:52:57 GMT</pubDate><enclosure url="https://images.ecency.com/p/5s4dzRwnVbzGM3JdyYKz6jx9fFPTMbZhYMErUJH1tgUBpmQC5hkUcvUZmkpzP4ec6xnMiwTv54M56TGKYxPKU517ZsV9Q8KRkJam1sMsT22Uugxv9332aeJrcbdK72ViCF7p9txTqid3tBzCcs3LZSs1dCmFxJhPGgJPM11?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Spherical Harmonics – Solutions to the Angular Laplacian]]></title><description><![CDATA[In this video, I go over the actual spherical harmonics equations, which exclude the radial terms from the solid spherical harmonics I had derived earlier. The spherical harmonics can be combined into]]></description><link>http://direct.ecency.com/hive-128780/@mes/65445edf</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/65445edf</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 27 Mar 2026 17:25:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhevbAVSeyaoE8wWYmh88Wq6HTcDQwfHk8q1LFzQa8Cco?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Solid Spherical Harmonics – Solutions to Laplace's Equation in Spherical Coordinates]]></title><description><![CDATA[In this video, I go over the derivation of the solid spherical harmonics, which are solutions to the Laplace equation in spherical harmonics. They are referred to as "solid" because they include]]></description><link>http://direct.ecency.com/hive-111030/@mes/solid-spherical-harmonics-solutions-to-laplaces-equation-in-spherical-coordinates</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/solid-spherical-harmonics-solutions-to-laplaces-equation-in-spherical-coordinates</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 24 Mar 2026 04:51:45 GMT</pubDate><enclosure url="https://images.ecency.com/p/QVdSJhgNm7rytEdw6Y8ua3ELysg9umAYoQxsRewpowcr9BKTDetB9PLRRb7LsDXUXuz2tCPwvfHhAGhLKE5zDELHgKhr6iuGbtS5Ah47HLCZeuwm2g5wFx2fSiMKmayeHEMKDujws7n1mJF5cKWAaEWwVAn8UYc7BiWieaYsnoJ24s4ZqWeFRsV?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Solid Spherical Harmonics – Solutions to Laplace's Equation in Spherical Coordinates]]></title><description><![CDATA[In this video, I go over the derivation of the solid spherical harmonics, which are solutions to the Laplace equation in spherical harmonics. They are referred to as "solid" because they include]]></description><link>http://direct.ecency.com/hive-128780/@mes/9d41089b</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/9d41089b</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 23 Mar 2026 22:25:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhesvgJSSvsqucxnK3Vr8D9vnADmXmnFZbbW8RxvsB4ij?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Laplace Operator (Laplacian) in Spherical Coordinates – PROOF]]></title><description><![CDATA[In this video I derive the Laplace Operator or Laplacian in spherical coordinates by applying the Laplacian in polar coordinates twice: once for the azimuthal (ф) angle and once for the polar angle (θ).]]></description><link>http://direct.ecency.com/hive-111030/@mes/laplace-operator-laplacian-in-spherical-coordinates-proof</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/laplace-operator-laplacian-in-spherical-coordinates-proof</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sat, 21 Mar 2026 16:27:15 GMT</pubDate><enclosure url="https://images.ecency.com/p/5s4dzRwnVbzGM3JdyYKz6jx9fFPTMbZhYMErUJH1tgUBpmQC5hkUcvUeqPUtGkHdpfPihxu3UQ3i3HeC4BcYZuvYaTsh3zwPACU6me2qDnzyY3sPxowqrtxc3bTny13QFhdi98SW7gtVuTrxiqegHtwovNpURbyRbKuNBfd?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Laplace Operator (Laplacian) in Spherical Coordinates – PROOF]]></title><description><![CDATA[In this video I derive the Laplace Operator or Laplacian in spherical coordinates by applying the Laplacian in polar coordinates twice: once for the azimuthal (ф) angle and once for the polar angle (θ).]]></description><link>http://direct.ecency.com/hive-128780/@mes/034f3436</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/034f3436</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 20 Mar 2026 22:15:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDheqHbNYUWzqLBs2WqdXXa3QwtFp9mYxbj5Xt7kB9AeQX?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Laplace Operator (Laplacian) in Polar Coordinates – PROOF]]></title><description><![CDATA[In this video I derive the Laplace Operator or Laplacian in polar coordinates, which will come in handy when I derive the Laplacian in spherical coordinates in the next video. Since polar coordinates are]]></description><link>http://direct.ecency.com/hive-111030/@mes/laplace-operator-laplacian-in-polar-coordinates-proof</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/laplace-operator-laplacian-in-polar-coordinates-proof</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 19 Mar 2026 18:01:51 GMT</pubDate><enclosure url="https://images.ecency.com/p/7b4bio5hobgskW8qdJJeDjrJHTiT5uLGk5BQErotAHijnZQZsvzoyRZ9HMhkkthsxqYGWKuFoxH5wRSb3NZEdgFipG3We3jZ365exJxQEY8ng3THf1dNitfDze3iV5kQcZgB2F3TkEAWgVAy8H6r6EYkmTzo?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Laplace Operator (Laplacian) in Polar Coordinates – PROOF]]></title><description><![CDATA[In this video I derive the Laplace Operator or Laplacian in polar coordinates, which will come in handy when I derive the Laplacian in spherical coordinates in the next video. Since polar coordinates are]]></description><link>http://direct.ecency.com/hive-128780/@mes/294e58ab</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/294e58ab</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 18 Mar 2026 22:45:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhb3xuohF8YY4nyXF78R9uoi1Lxjqpuw1E7Hq6PY3jerK?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Mathematical Review: Partial Differential Equations (PDE), Laplace's Equation, Gradient, Divergence]]></title><description><![CDATA[In this video I go over a quick math review of the terms involved in the Laplace equation in 3D rectangular coordinates. Laplace's equation is defined as the divergence of the gradient of a function set]]></description><link>http://direct.ecency.com/hive-111030/@mes/mathematical-review-partial-differential-equations-pde-laplaces-equation-gradient-divergence</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/mathematical-review-partial-differential-equations-pde-laplaces-equation-gradient-divergence</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 15 Mar 2026 22:06:24 GMT</pubDate><enclosure url="https://images.ecency.com/p/cyxkEVqiiLy2ofdgqoFZZvKu4kbPFPDk9wCrchy9kYHYoLFggvBkv6T8qsv66Y4kkgwtttZ6SdTgBnGDLfCXgPUCxGcmkHRfbqx3scgCh7r5zbFW5cpnm3Za6G7rtzEp9dZ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Mathematical Review: Partial Differential Equations (PDE), Laplace's Equation, Gradient, Divergence]]></title><description><![CDATA[- Telegram - YouTube - Summary In this video I go over a quick math review of the terms involved in the Laplace equation in 3D rectangular coordinates. Laplace's equation is defined as the divergence of]]></description><link>http://direct.ecency.com/hive-128780/@mes/a305d74f</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/a305d74f</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 15 Mar 2026 21:50:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/32FTXiZsHoAWFxzgF7aevFQV6E69FQteY5wxrfE7ufstmYzpAG7zswxuQYGGpbhuWf2mJT4AoZ6Na1WqtUZPohuWZsVEb2RBLxnKha7HWrGxPxSeashh7VSnwkGLDkQW7Goxbedgp8CycxiP?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Spherical Harmonics in Atomic Orbitals and Magnetic Fields]]></title><description><![CDATA[In this video, I go over an overview of how spherical harmonics show up in the equations for atomic orbitals and magnetic fields. The Schrödinger equation is a partial differential equation that governs]]></description><link>http://direct.ecency.com/hive-111030/@mes/spherical-harmonics-in-atomic-orbitals-and-magnetic-fields</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/spherical-harmonics-in-atomic-orbitals-and-magnetic-fields</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 13 Mar 2026 17:05:54 GMT</pubDate><enclosure url="https://images.ecency.com/p/54TLbcUcnRm3sWQK3E3A5LrCpeXCj7zpE6HRNLjpmk1F3fE1D2xNMzuguoc6tSFKUd5Gr7ixYg2iu4shxozF82LMhzZP2SdfGG7m2AUN2x6wNxXjKzTSsQeunNdvdzdb2CLucYa5V?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Spherical Harmonics in Atomic Orbitals and Magnetic Fields]]></title><description><![CDATA[In this video, I go over an overview of how spherical harmonics show up in the equations for atomic orbitals and magnetic fields. The Schrödinger equation is a partial differential equation that governs]]></description><link>http://direct.ecency.com/hive-128780/@mes/27ef8fad</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/27ef8fad</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 13 Mar 2026 16:15:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/32FTXiZsHoAWFxzgF7aevFQV6E69FQteY5wxrfEDs9WG8LTGZATAgKzVN3c1pbU9bt6pAKpkqdSv2ktrjF2ev6hFY86dp2pN5yJxKDjhJmScoMxjRqQ8gLwr9zjPmsxDdyjTEoCBKjry72C2?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Introduction to Spherical Harmonics]]></title><description><![CDATA[In this video, I go over an introduction to spherical harmonics by giving an overview of how they are obtained from the solution to Laplace's equation in spherical coordinates. #math #sphericalharmonics]]></description><link>http://direct.ecency.com/hive-111030/@mes/introduction-to-spherical-harmonics</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/introduction-to-spherical-harmonics</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 11 Mar 2026 20:52:00 GMT</pubDate><enclosure url="https://images.ecency.com/p/3zpz8WQe4SNGWd7Tzma21bfbp1De9N1PiS848Vc7tBRicyTYGerDZstTmsppzwPvFtxNge1JsT9VCnDZBjywUdwc2sE24tyN9H7rmXUcsTGkigU7aKf84im8wa8wZrJmUFwrL9EmBnnYRBrszpS3?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Introduction to Spherical Harmonics]]></title><description><![CDATA[In this video, I go over an introduction to spherical harmonics by giving an overview of how they are obtained from the solution to Laplace's equation in spherical coordinates. The general solution to]]></description><link>http://direct.ecency.com/hive-128780/@mes/cac50999</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/cac50999</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 10 Mar 2026 22:50:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/32FTXiZsHoAWFxzgF7aevFQV6E69FQteY5wxrfE6X2GUoN2zqvqk65Q3CjYiYuqFCW6LnA8AWqxYV7YRG77Ly3XC3MxyTE4K465DknApetXc7UzGEgPwm51jv4Jrx3Ly3JBGCS99xbiYmKVM?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Spherical Harmonics: Atomic Orbitals, Laplacian in Polar and Spherical Coordinates, Laplace Equation]]></title><description><![CDATA[In this video, I go over a deep dive into the famous spherical harmonics, which are the solutions to Laplace’s equation in spherical coordinates and are very prevalent in physics, especially in the quantized]]></description><link>http://direct.ecency.com/hive-111030/@mes/spherical-harmonics-atomic-orbitals-laplacian-in-polar-and-spherical-coordinates-laplace-equation</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/spherical-harmonics-atomic-orbitals-laplacian-in-polar-and-spherical-coordinates-laplace-equation</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 06 Mar 2026 21:48:51 GMT</pubDate><enclosure url="https://images.ecency.com/p/k75bsZMwYNtze9xHurD95Vbqvj1H34B627iFyeTf6ec4QF6swMasdLNQKJMdofuuBCKW2cGtTBd9FELbjcGujVEuqBwvixPYifYQDpUcBwmA1s1rLTem9Ks7ZwZy9zgRuvFuowkcfKpt3zGiUBv5FD2V8UHCEG8JK?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Spherical Harmonics: Atomic Orbitals, Laplacian in Polar and Spherical Coordinates, Laplace Equation]]></title><description><![CDATA[In this video, I go over a deep dive into the famous spherical harmonics, which are the solutions to Laplace’s equation in spherical coordinates and are very prevalent in physics, especially in the quantized]]></description><link>http://direct.ecency.com/hive-128780/@mes/220d6572</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/220d6572</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 06 Mar 2026 18:40:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/32FTXiZsHoAWFxzgF7aevFQV6E69FQteY5wxrfE8mQGQ3zet8PCNSzeuHoX6oWdQCJC2y6GDuDDgSUrJ36ZM7pca1e6gvCWCDuBkd8XKc5YmzF62zwGv1rYUmRiuvJC1bY6Yh5S9yrAUxSst?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>