View source for Joseph Krasil'shchik's introductory lectures on the Geometry of Differential Equations

Autumn 2010 - Spring 2011

__TOC__
==Short syllabus==

* Jets of bundles<br>The Cartan distribution<br>Symmetries of the Cartan distribution<br>The Lie-Bäcklund theorem

* Nonlinear differential equations and operators<br>Classical symmetries of differential equations, their computation and application<br>The Bianchi-Lie theorem

* Infinite jets and geometric structures on them<br>The Cartan distribution on infinite jets and its symmetries<br>Linearizations and evolutionary vector fields

* Prolongations of differential equations<br>Infinitely prolonged equations<br>Higher symmetries of differential equations, their computation and application

* Recursion operators for symmetries<br>Nijenhuis brackets

* Differential coverings and nonlocal symmetries

==Video records of the lectures==

''Via [http://erb-files.narod.ru http://erb-files.narod.ru] and [http://ium.mccme.ru/IUM-video.html http://ium.mccme.ru/IUM-video.html]''

* [https://video.gdeq.org/GDEq-lec-20100915.mp4 Lecture 1 (15 September 2010)]

* [https://video.gdeq.org/GDEq-lec-20100922.mp4 Lecture 2 (22 September 2010)]

* [https://video.gdeq.org/GDEq-lec-20101006.mp4 Lecture 3 (6 October 2010)]

* [https://video.gdeq.org/GDEq-lec-20101020.mp4 Lecture 4 (20 October 2010)]

* [https://video.gdeq.org/GDEq-lec-20101027.mp4 Lecture 5 (27 October 2010)]

* [https://video.gdeq.org/GDEq-lec-20101103.mp4 Lecture 6 (3 November 2010)]

* [https://video.gdeq.org/GDEq-lec-20101110.mp4 Lecture 7 (10 November 2010)]

* [https://video.gdeq.org/GDEq-lec-20101117.mp4 Lecture 8 (17 November 2010)]

* Lecture 9 (24 November 2010) is missing

* [https://video.gdeq.org/GDEq-lec-20101201.mp4 Lecture 10 (1 December 2010)], audio is missing

* [https://video.gdeq.org/GDEq-lec-20101208.mp4 Lecture 11 (8 December 2010)]

* [https://video.gdeq.org/GDEq-lec-20101215.mp4 Lecture 12 (15 December 2010)]

* [https://video.gdeq.org/GDEq-lec-20110209.mp4 Lecture 13 (9 February 2011)]

* [https://video.gdeq.org/GDEq-lec-20110216.mp4 Lecture 14 (16 February 2011)]

* [https://video.gdeq.org/GDEq-lec-20110302.mp4 Lecture 15 (2 March 2011)]

* [https://video.gdeq.org/GDEq-lec-20110309.mp4 Lecture 16 (9 March 2011)]

* [https://video.gdeq.org/GDEq-lec-20110316.mp4 Lecture 17 (16 March 2011)]

* [https://video.gdeq.org/GDEq-lec-20110323.mp4 Lecture 18 (23 March 2011)]

* [https://video.gdeq.org/GDEq-lec-20110330.mp4 Lecture 19 (30 March 2011)]

* [https://video.gdeq.org/GDEq-lec-20110406.mp4 Lecture 20 (6 April 2011)]

* [https://video.gdeq.org/GDEq-lec-20110413.mp4 Lecture 21 (13 April 2011)]

* [https://video.gdeq.org/GDEq-lec-20110420.mp4 Lecture 22 (20 April 2011)]

* [https://video.gdeq.org/GDEq-lec-20110427.mp4 Lecture 23 (27 April 2011)]

* [https://video.gdeq.org/GDEq-lec-20110504.mp4 Lecture 24 (4 May 2011)]

* [https://video.gdeq.org/GDEq-lec-20110511.mp4 Lecture 25 (11 May 2011)]

* [https://video.gdeq.org/GDEq-lec-20110518.mp4 Lecture 26 (18 May 2011)]

==Recommended literature==

[[Media:Bocharov_A.V.,_i_dr._Simmetrii_i_zakony_sohranenija_uravnenij_matematicheskoj_fiziki_(2_izd.,_Faktorial,_2005)(ru)(600dpi)(K)(T)(373s)_MPs_.djvu|''A. V. Bocharov, A. M. Verbovetsky, A. M. Vinogradov (editor), S. V. Duzhin, I. S. Krasil'shchik (editor), A. V. Samokhin, Yu. N. Torkhov, N. G. Khor'kova, and V. N. Chetverikov'' Simmetrii i zakony sokhraneniya uravnenij matematicheskoj fiziki, Factorial, Moscow, 2nd edition, 2005.]]

(English translation: Symmetries and conservation laws for differential equations of mathematical physics, AMS, 1999.)

[[Category:Lectures|Krasil'shchik 7989s]]