Linear Algebra and Differential Equations - Who cares about Wronskians anyway? скачать в хорошем качестве

Linear Algebra and Differential Equations - Who cares about Wronskians anyway?

If you're interested in personal help, I've posted my tutoring services on Fiverr: https://www.fiverr.com/s/dDYkBlz I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to do some online tutoring. Many of us have, or presently are, taking, or have taken a course in either linear algebra or ordinary differential equations. The primary focus is typically on how to solve them, and this is not the difficult part for many students. But sooner or later, there is one topic that, although on the face of it is not so difficult, and in some sense, can just be treated as another computation, it remains a little more mysterious. This is the so-called Wronskian. In the course of today's discussion of (the lead up to) Wronskians, we'll see how linear algebra is really underpinning much of the discussion of differential equations up to this point, as well as how powerful of a tool linear algebra is when it comes to understanding certain classes of differential equations. We'll review the definitions of linear independence, span, basis, vector space, and give insight into how these are important concepts for applications to ordinary differential equations and the meaning behind these mathematical concepts. Whenever we are learning something in mathematics, we want to ask what the meaning is behind them, and aim to get an intuition and feeling for these concepts, as opposed to simply memorising mathematical terms. Timestamps: 0:00 Disclaimer. 0:08 Intro chit chat 3:53 Part 1 -- What is a linear ODE? 5:39 Some reminders from Linear Algebra. 6:02 Definition of a Vector Space. 7:19 Definition and intuition for Linear independence. 8:35 Definition of a basis. 9:19 What does this have to do with ODEs? 9:50 Refined definition of linear ODEs 10:15 Example of showing that an ODE is linear. 11:58 The power of linear algebra 14:52 Motivation for the Wronskian. Video on Linear Maps referenced in the video:    • Linear Maps | Linear Algebra   👍 To support the channel, hit the like button and subscribe. 🐸 To learn how I make these animations using Grant Sanderson's (3Blue1Brown) program Manim, check out my quick intro to Manim on Skillshare: https://www.skillshare.com/r/profile/... 🎸 Music in this video is from Epidemic Sound: https://www.epidemicsound.com/referra... Ways to support the channel: 🏆 Support the channel over on Patreon   / kylebroder   🐸 Support the channel by signing up to a free trial of Skillshare using the link https://www.skillshare.com/r/profile/... FYI, these are affiliate links 💪🙏 These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University. Hi, my name is Kyle and I'm currently doing my doctoral mathematics degree in complex differential geometry under the supervision of Professor Gang Tian and Professor Ben Andrews.