Calculus on the unit circles | Arithmetic and Geometry Math Foundations 78 | N J Wildberger скачать в хорошем качестве

Calculus on the unit circles | Arithmetic and Geometry Math Foundations 78 | N J Wildberger

We illustrate algebraic calculus on the simplest algebraic curves: the unit circle and its imaginary counterpart. Starting with a polynumber/polynomial of two variables, the derivation of the Taylor polynumber, subderivatives, Taylor expansion around a point [r,s] and various tangents are analogous to the case of a polynumber/polynomial of one variable. We get tangent planes and tangent lines both corresponding to the first tangent. The algebraic derivation is illustrated with three-dimensional diagrams involving the associated elliptic paraboloid to the unit circle. The background noise in parts of the video is due to crickets, common in the Australian summer---sorry about that. I will tell them to keep it down next time. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. Video Content: 00:00 Intro to subderivatives 6:12 Taylor expansions for bipolynumbers 8:50 Arranging subderivatives 10:58 Reversing the roles of alpha, beta, gamma and delta 13:43 Tangents 17:18 Using the tangent plane to approximate a polynumber 21:29 Formula for the tangent plane 23:42 3D picture of equation of the tangent line 27:46 Slopes of the tangent line 29:30 Usual calculus approach 32:32 The imaginary unit circle ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. *********************** My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Patreon,   / njwildberger   . Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист