MATH 3220-002 FALL 2025 - Week 14 - Differential Forms 3 скачать в хорошем качестве

MATH 3220-002 FALL 2025 - Week 14 - Differential Forms 3

--- This is MATH 3220-002, the advanced multivariable calculus class at the University of Utah. View the complete course: https://github.com/AlpUzman/MATH_3220... --- Table of Contents: 00:00:00 1 of 3 00:00:54 recap and review: three approaches to differential forms 00:16:21 example: visualizing exact 1-forms 00:18:48 more on the "speedometer" or "radar gun" heuristic for differential 1-forms 00:21:00 example continued 00:29:11 recap: exactness as a pde, exact implies closed 00:31:34 example continued 00:38:12 exercise: visualize f = x^2 + y^2 and df 00:41:16 preview: integration of differential 1-forms 00:43:02 pullback 00:45:35 heuristics for pullbacks of differential 1-forms 00:47:59 2 of 3 00:48:37 current (aka generalized differential form) 00:49:41 C^k uniform convergence on compacta 00:54:14 p-current 00:55:37 C^{l+1} p-chain 00:57:02 bra-ket notation for current-form pairs 00:57:56 C^{l+1} 1-cell 01:02:23 discussion of 1-cells 01:07:50 cells and chains as currents 01:08:59 line integral notation 01:10:48 examples of cells 01:27:08 exercise 01:27:31 exercise: 1-cells and change of coordinates 01:31:52 examples of chains 01:33:39 discussion of formal linear combos 01:34:38 preview: fundamental theorem of line integrals 01:36:48 3 of 3 01:37:18 regarding problem set grades 01:41:51 plan for the remaining classes 01:43:52 preview: the two fundamental theorems of calculus: FTC-1: Stokes (integral of the derivative), FTC-2: Poincare (derivative of the integral) 01:49:38 plan continued 01:53:18 0-cell (aka Dirac delta function) 01:55:42 discussion of 0-cells 01:58:24 0-chain 01:59:33 1D FTC-1 in terms of differential forms 02:01:26 boundary operator from 1-chains to 0-chains 02:04:06 heuristics on 1-chains and 0-chains 02:06:39 FTC-1 for 1-cells (aka the Fundamental Theorem of Line Integrals aka Stokes theorem for 1-cells) 02:08:42 more on heuristics on 1-chains and 0-chains 02:11:27 exercise 02:13:33 FTC-1 for 1-cells in classical notation 02:14:31 proof of FTC-1 for 1-cells 02:20:51 discussion of proof --- License: CC BY-NC-SA 4.0 Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Public License https://creativecommons.org/licenses/... Alp Uzman https://alpuzman.github.io/