Ordinary differential equations — различия между версиями

Материалы по математике, 2013-14 учебный год, НИУ ВШЭ и РЭШ
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(refactoring + lesson 2)
(References)
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* Main textbook is [http://books.google.ru/books?id=JtZFAQAAIAAJ&dq=editions:tlezMQI65w0C&redir_esc=y ''Ordinary differential equations''] by V. I. Arnold.  
 
* Main textbook is [http://books.google.ru/books?id=JtZFAQAAIAAJ&dq=editions:tlezMQI65w0C&redir_esc=y ''Ordinary differential equations''] by V. I. Arnold.  
 
* Problems were taken mostly from ''Problems in differential equations'' by A. F. Filippov.  
 
* Problems were taken mostly from ''Problems in differential equations'' by A. F. Filippov.  
* The program and assignments are based on the course ''Ordinary differential equations'' (Math in Moscow, 2010-11) by Yury Kudryashov and Ilya Schurov and [http://math-hse.info/2012-13/ODE?uselang=en the same course] of 2013/14 academic year (by Dmitry Filimonov, Ilya Schurov and Alexandra Pushkar).
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* The program and assignments are based in part on the following courses:
 
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** [http://www.dyn-sys.org/wiki/MIM/2010-spring ODE] (Math in Moscow, 2009-10) by Yury Kudryashov and Ilya Schurov
* [http://www.mccme.ru/mathinmoscow/courses/view.php?name=Ordinary%20Differential%20Equations.htm Curriculum] (it seems that only the first 14 items will be covered in the course due to lack of time).
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** [http://math-hse.info/2012-13/ODE?uselang=en ODE] (Math in Moscow, 2013-14) by Dmitry Filimonov, Ilya Schurov and Alexandra Pushkar.
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** [[Дифференциальные уравнения|ODE]] (HSE-NES joint program, 2013-14) by Irina Khovanskaya, Ilya Schurov, Pavel Solomatin, Andrey Petrin and Nikita Solodovnikov.
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* [http://www.mccme.ru/mathinmoscow/courses/view.php?name=Ordinary%20Differential%20Equations.htm Curriculum] (it seems that only the first 14 items will be covered in the course due to lack of time). See also the curriculum of our [http://www.dyn-sys.org/wiki/MIM/2010-spring 2009-10] course
  
 
== Lessons ==
 
== Lessons ==

Версия 23:42, 17 февраля 2014

Dear Math in Moscow students!

This page will contain information related to course Ordinary differential equations.

Instructor: Ilya Schurov (ilyaСоб@каschurov.com).

References

  • Main textbook is Ordinary differential equations by V. I. Arnold.
  • Problems were taken mostly from Problems in differential equations by A. F. Filippov.
  • The program and assignments are based in part on the following courses:
    • ODE (Math in Moscow, 2009-10) by Yury Kudryashov and Ilya Schurov
    • ODE (Math in Moscow, 2013-14) by Dmitry Filimonov, Ilya Schurov and Alexandra Pushkar.
    • ODE (HSE-NES joint program, 2013-14) by Irina Khovanskaya, Ilya Schurov, Pavel Solomatin, Andrey Petrin and Nikita Solodovnikov.
  • Curriculum (it seems that only the first 14 items will be covered in the course due to lack of time). See also the curriculum of our 2009-10 course

Lessons

02/10: Introduction to ODEs

  • Examples of mathematical models that lead to differential equations: Malthusian population grows, free fall, harmonic oscillator.
  • Examples of ODEs and their solutions:
  • Phase space, extendended phase space, direction field, integral curves.
  • Barrow's formula: the solution of an equation (autonomous equation in dimension 1).

Excercises

02/17: ODEs in dimension 1

  • Example of nonuniqueness for the solution of differential equation: .
  • Theorem of existence and uniqueness for
    • autonomous differential equations in dimension 1 (with the proof);
    • non-autonomous differential equations in dimension 1 (without the proof, it will be discussed later).
  • Separation of the variables (with the proof).

Excercises