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Solving the heat equation inside of a sphere.

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Tags: differential-equationsheat-equationlaplacianlegendre-polynomialsspherical-coordinates

(Note: this video is narrated in Catalan, my mother language, though subtitled in English. In my channel, there is a version dubbed in English, however my pronunciation there is not as firm) The aim of my video is to present a real-life problem where the heat equation can be applied, and go through the steps to solve it, in a space with spherical symmetry. Through this process, I present the steps needed (Laplacians, spherical coordinates, Legendre polynomials, and more), go through the logic that guides them, and reach an end result, but without extensive technicality to make it more of an overview. The reason I chose this topic is that I am an undergraduate currently studying Physics, and I was amazed at learning of these methods to solve problems that, before, seemed too much to tackle. My fellows did not feel this way, however, as they did not comprehend the real reasons behind some steps, and only memorized them. That is why I tried to input what helped me to follow the topic into the video, so that it may help whoever views it. Also note that this is my first time trying to do a video like this, and have no previous experience dubbing, so please excuse my inexperience. Thank you so much!!!

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Motivation - It was clear to me that the use of the topic that you wanted to teach was in calculating the temprature of sphere half dipped in cold/hot water Clarity - I was particularly sad with the skipping of most math jargons which were clear to me as I have done basic math at undergraduate level but those could be intimidating to people who have not been exposed to that level of math. For example azimuth and polar angles were not properly seprated in visualisation. Laplacian was taken as granted that yes people know about it etc… Novelty - It was novel as a topic but could have been presented better for consumption of audience. Memorability - Towards the end it became so dense that I lost the chain of thoughts and missed the central point that video was trying to convey.