Timeline for Demystifying complex numbers
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2011 at 3:09 | comment | added | timur | There are many different spellings of Joukovsky, like Tschebyscheff :) | |
| Jul 2, 2010 at 5:18 | comment | added | Wadim Zudilin | @Victor, I'll check whether the students are happy with the Zhukovsky function (does it have the same name in English?!). I am pretty sure that my Russian textbooks (I have not only LS and Markushevich!) will be too advanced but it's a must to go through them. | |
| Jul 2, 2010 at 3:02 | comment | added | jeremy | Yes, those examples are great! I was thinking about those examples, too, when I said "conformal methods," but they are a little less basic than the E&M example. There are many more examples, too, though, such as classical gravity, or just about anything that can be described with a potential. They would make excellent topics to visit after developing some of the formalism more carefully, since they can lead to a lot of intuition about why things are constructed like they are, and why they're useful! | |
| Jul 2, 2010 at 2:04 | comment | added | Victor Protsak | I think most older Russian textbooks on complex analysis (e.g. Lavrentiev and Shabat or Markushevich) had examples from 2D hydrodynamics (Euler-D'Alambert equations $\iff$ Cauchy-Riemann equations). Also, of course, the Zhukovsky function and airwing profile. They serve more as applications of theory than motivations, since nontrivial mathematical work is required to get there. | |
| Jul 1, 2010 at 11:45 | comment | added | Wadim Zudilin | Thanks, Jeremy! I'll definitely do the search, the magic word "the method of conformal mapping" is really important here. | |
| Jul 1, 2010 at 11:20 | comment | added | jeremy | This is in a number of advanced math methods for physics, and graduate electromagnetism texts, but one offhand I know it's in is "Electrodynamics of Continuous Media" by Landau and Lifshitz, chapter 1 section 3, on methods of solving electrostatic problems. But there are other books out there with more involved and more sophisticated treatments, but offhand I don't know any titles. If you search amazon's "search inside this book" for "the method of conformal mapping" you can find part of the discussion. But the basics of it are elementary enough that that book should be sufficient. | |
| Jul 1, 2010 at 10:30 | comment | added | Wadim Zudilin | Jeremy, can you expand your answer or provide a reference where your example is worked in details? | |
| Jul 1, 2010 at 10:21 | history | answered | jeremy | CC BY-SA 2.5 |