<?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>https://ecency.com</link><image><url>https://ecency.com/logo512.png</url><title>RSS Feed</title><link>https://ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Sun, 09 Aug 2026 13:00:32 GMT</lastBuildDate><atom:link href="https://ecency.com/created/vectorfunctions/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[Tangential and Normal Components of Acceleration]]></title><description><![CDATA[In this video, I write the vector equation of acceleration in terms of its unit tangent and unit normal vector components, which is useful when analyzing the motion of a particle along a curve. The unit]]></description><link>https://ecency.com/@mes/5ce9a8c6</link><guid isPermaLink="true">https://ecency.com/@mes/5ce9a8c6</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 05 May 2026 21:55:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhvSuadBQN5e9H12mVZc9KcrXyGgYVt9D9RiuHguj684X?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 3: Integrating Acceleration and Velocity Vectors to get the Position Vector]]></title><description><![CDATA[In this video, I show that we can obtain the velocity of a moving object by first integrating its acceleration vector to obtain its velocity and then integrating the velocity vector. This follows from]]></description><link>https://ecency.com/@mes/example-3-integrating-acceleration-and-velocity-vectors-to-get-the-position-vector</link><guid isPermaLink="true">https://ecency.com/@mes/example-3-integrating-acceleration-and-velocity-vectors-to-get-the-position-vector</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 26 Apr 2026 17:47:54 GMT</pubDate><enclosure url="https://i.ecency.com/p/ATHztMY7eTanRk3GJThkibYnoPqfpCahxXDEzQqunddesTewXm5qdPXvoQarQBjLTdSjhQMMhKYAQJLk9E6eHHHkBL112Z9hVjVpca4Yi4Ymo1AYzHMNkz3PQuiQGCEdaf4p8syRuvmTvTb4hhKSDXy7tENxGYyczxst1jFdvBFkfH3bRpkDCJyJdb7ajrTV28VPhRaudu68toA47ZcbRtsq?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Motion in Space: Velocity and Acceleration]]></title><description><![CDATA[In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that]]></description><link>https://ecency.com/@mes/motion-in-space-velocity-and-acceleration</link><guid isPermaLink="true">https://ecency.com/@mes/motion-in-space-velocity-and-acceleration</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 17 Apr 2026 22:04:33 GMT</pubDate><enclosure url="https://i.ecency.com/p/21PRtjKRXPQybj4WUWdMCQaLeYN1FoMhBWfahUmoEfebrAzUAPoKGSg9dFS3ywonC8E4WWRttBSJBNndoGX5wSymvVNfHyVydsre48VEVncjP86Sj3z2P6PXtYXnbyy4zGYnrcsYt2bguZ2j1Ef1aQP?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Motion in Space: Velocity and Acceleration]]></title><description><![CDATA[In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that]]></description><link>https://ecency.com/@mes/e443f9d3</link><guid isPermaLink="true">https://ecency.com/@mes/e443f9d3</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 17 Apr 2026 21:50:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhnheTyoSqDtLBY42YQwocWZ6zNYGyTzaiyxGgJr3effu?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas]]></title><description><![CDATA[In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a given point on a space curve. I illustrate this by determining the]]></description><link>https://ecency.com/@mes/osculating-circle-of-a-parabola-summary-of-tnb-vectors-and-curvature-formulas</link><guid isPermaLink="true">https://ecency.com/@mes/osculating-circle-of-a-parabola-summary-of-tnb-vectors-and-curvature-formulas</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 15 Jan 2026 21:36:42 GMT</pubDate><enclosure url="https://i.ecency.com/p/8th8uW8KLF3eHoH9cP9Etf4AqMgNKtKoyu4fqZraWgFsdvwTnXiBR7fHJEcqanALKN3Y87hrGfQ7utK8XQCXyS1fdu99PTT2nkcAzkwvPbzYDSXGrNqyzmPc6CXYiAr2p4SM3tQsFidR27m46v6qGK2q4AZnKvNoeEfQZqUwud2CM1bjpbWeXrqqH1?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Normal and Binormal Vectors + Example on a Circular Helix]]></title><description><![CDATA[In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. Since the unit tangent vector is a constant-length one, its]]></description><link>https://ecency.com/@mes/klkebgpa</link><guid isPermaLink="true">https://ecency.com/@mes/klkebgpa</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 11 Jan 2026 06:45:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVgY8ex6gcB6PigrZDwCwAQFy8ciubZx4hdqBq78QVJjwW9e4ZvkEBEna6fUd9wPsrqhLdmjnN?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature of a Plane Curve y = f(x) + Example on a Parabola]]></title><description><![CDATA[In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and using our earlier cross product curvature formula. YouTube - Summary]]></description><link>https://ecency.com/@mes/curvature-of-a-plane-curve-y-f-x-example-on-a-parabola</link><guid isPermaLink="true">https://ecency.com/@mes/curvature-of-a-plane-curve-y-f-x-example-on-a-parabola</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 07 Jan 2026 22:51:39 GMT</pubDate><enclosure url="https://i.ecency.com/p/YpihifdXP4WMLzfwe2d1rg9TCZREQLPRYL4YgsSppLMNpvS2ixKzPv81WQjvRBmt26bsiU1YXx6cxDxCSZTQyePdKGnSd47YRGLFaWgWGrWzXdaFQdmQR1crVQPzaXBoAiDp23pwv66DEgbpN6VMFvyWU4VP4vFREFCtDpK7FBeP?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature of a Plane Curve y = f(x) + Example on a Parabola]]></title><description><![CDATA[In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and using our earlier cross product curvature formula. The magnitude]]></description><link>https://ecency.com/@mes/dblwgcxw</link><guid isPermaLink="true">https://ecency.com/@mes/dblwgcxw</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 07 Jan 2026 22:35:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVbKFz9sZfgDd6HuLgJGk99K3iAZPeqqh3HNfrBdihk9Ty5w7iXs6FaBcKdRiCcxG8ADe56Ft2?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Curvature Cross Product Formula: Proof and Example on Twisted Cubic]]></title><description><![CDATA[In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross product of the first two derivatives of the vector function. I derive this using the fact]]></description><link>https://ecency.com/@mes/curvature-cross-product-formula-proof-and-example-on-twisted-cubic</link><guid isPermaLink="true">https://ecency.com/@mes/curvature-cross-product-formula-proof-and-example-on-twisted-cubic</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 06 Jan 2026 05:44:45 GMT</pubDate><enclosure url="https://i.ecency.com/p/4bEjbgCbFMvA8T33kGvF6kHce4BTcm88Pv5WXm8EBoMz3u29V4LrZvMDXSFP2Y8y2jqDzRWJe7k1YYiaPLg3uS6HGWgP29B1QUVmx9T2TGCi9LyUTaxYVnibcc8UNc9W87pPuwLz4GgBQKCwHx6pxcKBKAuGG2Yfp6XVfHCHwvs1eEkvQX?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Arc Length of a Space Curve + Example on Circular Helix]]></title><description><![CDATA[In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative]]></description><link>https://ecency.com/@mes/nizhfvfl</link><guid isPermaLink="true">https://ecency.com/@mes/nizhfvfl</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Dec 2025 22:05:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVeDx4VBSZLpZVzA9Vk3cg3Vr3zjfr2EQd3VBBPFZZYsDDcGTyjYEDRtsH7GwGPybn78D82dZ8?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Vector Functions: Arc Length and Curvature]]></title><description><![CDATA[In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. I also go over normal, binormal vectors, as well as the TNB frame,]]></description><link>https://ecency.com/@mes/vector-functions-arc-length-and-curvature</link><guid isPermaLink="true">https://ecency.com/@mes/vector-functions-arc-length-and-curvature</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 24 Dec 2025 05:43:42 GMT</pubDate><enclosure url="https://i.ecency.com/p/FUkUE5bzkAZSUQtscfU67XyuspKfVPvhJ6PgMwaumQRFSqc8YzUHX1Q1a8BCmr2exgDZdpMWAyRxkbi8Rne4dqVdD1ae6nnyeazeHA4CgJpww9Kwizt2CBMCS9xZ1wHc2iNdVQ62eRK8h8TUph8zbeEsFxyDXPuS359q?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 4: Tangent Vector is Orthogonal to Vector of Constant Length]]></title><description><![CDATA[In this video I show that the tangent vector (derivative of a vector function) is orthogonal or perpendicular to a vector of constant length. Geometrically this means that the curve is on the surface of]]></description><link>https://ecency.com/@mes/example-4-tangent-vector-is-orthogonal-to-vector-of-constant-length</link><guid isPermaLink="true">https://ecency.com/@mes/example-4-tangent-vector-is-orthogonal-to-vector-of-constant-length</guid><category><![CDATA[hive-147010]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 08 Oct 2025 04:21:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/2xVmzkbNCvpwrGAp45WKwgAaUaJnmHfvZ7RZqiyQWofSGyTTtrRkun2oTNhMujgHTbeh57HN8TbntLp7sN6jbBq5yEP9j3DMJq4YyhAsCF4683mW8cBzyZcY8Z38SPoCzUjR4ciaW7BLL6KxYnbivoNwLgnGDkpYgStkNkj9zM397mEu8cK5CEvyqnwJ3W7zBqCCf1No?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Differentiation Rules for Vector Functions]]></title><description><![CDATA[In this video I go over the six main differentiation rules for vector functions, as well as the 2nd (or higher) derivatives. The rules have their similar counterparts for real valued functions, and I leave]]></description><link>https://ecency.com/@mes/pzzlgjdt</link><guid isPermaLink="true">https://ecency.com/@mes/pzzlgjdt</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Thu, 02 Oct 2025 04:10:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVzgVQaW1YiQjBudnkBZVEp9H3VLNKBHhzE3DJMTdmffMG2K9gLFEq4TFtRrfzE8U2BSNTFch4?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 2: Sketching the Tangent Vector]]></title><description><![CDATA[In this video I go over another example on derivatives of vector functions, and this time sketch the tangent vector to a plane curve manually as well as with GeoGebra's 3D graphing calculator. The tangent]]></description><link>https://ecency.com/@mes/vrcvsdfe</link><guid isPermaLink="true">https://ecency.com/@mes/vrcvsdfe</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Sep 2025 21:05:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxX1mENP6R8LAQ2PYAZkzfxgcSg4ufpzBKHGgZc3abfSoprPGnHS3zyAwRbFenihUzjEqUvnr?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivative for Vector Functions by Components + Proof]]></title><description><![CDATA[In this video I show that the derivative of a vector function is equal to the derivative of the real-valued functions in its components. I prove this by applying the definition of derivatives for vector]]></description><link>https://ecency.com/@mes/derivative-for-vector-functions-by-components-proof</link><guid isPermaLink="true">https://ecency.com/@mes/derivative-for-vector-functions-by-components-proof</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 22 Sep 2025 17:05:12 GMT</pubDate><enclosure url="https://i.ecency.com/p/2CwnDyeL7SRXDBVj6Mv9E1ywiCUQYqtApawXC2GYmQVWd3WHkD4BbLxAfokZx47zKPYYiTGMr9hhzpqH74qhx5buXPT4iP6uYF8MZbXZVTzTcQcYk5W4rcVuFVUr1s7LkzaMLdNQkBNXEn7qYPWgz4hhgqU4EKFP9UJyEUwPUgzFpUqsD8Wk7?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivative for Vector Functions by Components + Proof]]></title><description><![CDATA[In this video I show that the derivative of a vector function is equal to the derivative of the real-valued functions in its components. I prove this by applying the definition of derivatives for vector]]></description><link>https://ecency.com/@mes/hgohyesk</link><guid isPermaLink="true">https://ecency.com/@mes/hgohyesk</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sat, 20 Sep 2025 03:40:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVuMcJ1mokDwMfV92Xwaz1j2dv4ANKnBUPU1emUFekomZxfVkucqYHQBERigasy4ciTwBhtKVQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition of Derivative for Vector Functions]]></title><description><![CDATA[In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit]]></description><link>https://ecency.com/@mes/definition-of-derivative-for-vector-functions</link><guid isPermaLink="true">https://ecency.com/@mes/definition-of-derivative-for-vector-functions</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 17 Sep 2025 04:14:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/2xVmzkbNCvpwrGAp45WKwgAaUaJnmHfvZ7RZqiyQWofSGyTTtrRkun2rS8GKML2yawzCu5frXpqKJMSHZ9qUhD4AZqFJqSXDMeXuEi4wbFfigi1pcVzLbxo9SvsVzRtMckrH6BndJQURmumgSKuieK2HaV157kV3JiJehHGSVUNxb8XugbiwbEj2zXQjrfu7HBG9VbT5?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition of Derivative for Vector Functions]]></title><description><![CDATA[In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit]]></description><link>https://ecency.com/@mes/jfezftxf</link><guid isPermaLink="true">https://ecency.com/@mes/jfezftxf</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 16 Sep 2025 04:44:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVziURmfLRjrbk2Xzdc8q81Tn4vSpGABf5rvcRtJ4YzEMZmCu5JT8wdSBj45ftWnxmkUgAVp14?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives and Integrals of Vector Functions]]></title><description><![CDATA[In this video I go further into vector functions and this time show how to obtain their derivatives and integrals. The definition of derivative for a vector function is much the same as with a real valued]]></description><link>https://ecency.com/@mes/hfsetrue</link><guid isPermaLink="true">https://ecency.com/@mes/hfsetrue</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sat, 13 Sep 2025 07:42:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/k75bsZMwYNu2L3iBMXq5y7xeiy1isFJsZxnMZSXuXEsxe4ee1cUkGyPeqsdq1z8ihq2Wu3QJEehiZWJArnD949sEJc2d6iM2XLyVYLLMuNX1wusoBBzVqfTQD1z4fuNUyZF3bniLBkm6fssmyNXKSLWY3h43F3hW6?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Derivatives and Integrals of Vector Functions]]></title><description><![CDATA[In this video I go further into vector functions and this time show how to obtain their derivatives and integrals. The definition of derivative for a vector function is much the same as with a real valued]]></description><link>https://ecency.com/@mes/derivatives-and-integrals-of-vector-functions</link><guid isPermaLink="true">https://ecency.com/@mes/derivatives-and-integrals-of-vector-functions</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sat, 13 Sep 2025 03:52:54 GMT</pubDate><enclosure url="https://i.ecency.com/p/V9N4wevejZUbdQxawfdFtcb6UnCVe92CzSNEhVDTcYUCvfNio3G2cYzDpuqXhRZThoxFh8ZiTMy92ifQpSp3bSwYKcNMzJsn5WfL1Yykm4NRD836d1cnYd6gzFTpaBFdhiB1ox35yjq9GPUZ9DS6R8caZXq32E4tK43mtLWkSrihPmJT7nR4u8oKziVBMrCYCSC1byUQx6YeBQPMGPcaj?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>