View source for Alexander Verbovetsky's Introductory lectures on the Geometry of Differential Equations

Spring 2012 (continuation of [[Joseph Krasil'shchik's introductory lectures on the Geometry of Differential Equations|Joseph Krasil'shchik's lectures]])

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==Short syllabus==

* The Vinogradov spectral sequence

* Conservation laws

* Lagrangian formalism. Noether's theorem

* Tangent and cotangent coverings over equations

* Schouten bracket and Hamiltonian structures. Bi-Hamiltonian equations

==Video records of the lectures==

''Via [http://ium.mccme.ru/IUM-video.html http://ium.mccme.ru/IUM-video.html]''

* [https://video.gdeq.org/GDEq-lec-20120208.mp4 Lecture 1 (8 February 2012)]

* [https://video.gdeq.org/GDEq-lec-20120215.mp4 Lecture 2 (15 February 2012)]

* [https://video.gdeq.org/GDEq-lec-20120222.mp4 Lecture 3 (22 February 2012)]

* [https://video.gdeq.org/GDEq-lec-20120229.mp4 Lecture 4 (29 February 2012)]

* [https://video.gdeq.org/GDEq-lec-20120314.mp4 Lecture 5 (14 March 2012)]

* [https://video.gdeq.org/GDEq-lec-20120321.mp4 Lecture 6 (21 March 2012)]

* [https://video.gdeq.org/GDEq-lec-20120425.mp4 Lecture 7 (25 April 2012)]

* Lecture 8 (2 May 2012) is missing 

* [https://video.gdeq.org/GDEq-lec-20120516.mp4 Lecture 9 (16 May 2012)]

==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.)
* Joseph Krasil'shchik and Alexander Verbovetsky, ''Geometry of jet spaces and integrable systems'', J. Geom. Phys. '''61''' (2011), 1633-1674, {{arXiv|1002.0077}}

[[Category:Lectures|Krasil'shchik 7987a]]