Ordinary differential equations — различия между версиями

Материалы по математике, 2013-14 учебный год, НИУ ВШЭ и РЭШ
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== References ==
 
== References ==
 
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. The program and assignments are based on the course ''Ordinary differential equations'' (Math in Moscow, 2010-11) by Yury Kudryashov and Ilya Schurov and the same course of 2013/14 academic year (by Dmitry Filimonov, Ilya Schurov and Alexandra Pushkar).
 
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. The program and assignments are based on the course ''Ordinary differential equations'' (Math in Moscow, 2010-11) by Yury Kudryashov and Ilya Schurov and the same course of 2013/14 academic year (by Dmitry Filimonov, Ilya Schurov and Alexandra Pushkar).
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== Lectures ==
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=== 02/10: Introduction to ODE ===
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* Examples of mathematical models that lead to differential equations: Malthusian population grows, free fall, harmonic oscillator.
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* Examples of ODEs and their solutions:
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** <math>\dot x=0</math>
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** <math>\dot x=k</math>
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** <math>\dot x=f(t)</math>
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* Phase space, extendended phase space, direction field, integral curves.
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* Barrow's formula: the solution of an equation <math>\dot x=f(x)</math> (autonomous equation in dimension 1).
  
 
== Seminars ==
 
== Seminars ==

Версия 10:50, 11 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 on the course Ordinary differential equations (Math in Moscow, 2010-11) by Yury Kudryashov and Ilya Schurov and the same course of 2013/14 academic year (by Dmitry Filimonov, Ilya Schurov and Alexandra Pushkar).

Lectures

02/10: Introduction to ODE

  • 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).

Seminars

Assignments

assignment due date
Assignment 1 01/17/2014