# Ordinary differential equations — различия между версиями

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Dear Math in Moscow students!

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).
• Curriculum (it seems that only the first 14 items will be covered in the course due to lack of time).

## 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).

### 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).