Reading course in differential equations

The aim of this course is to gain a solid knowledge in differential equations. If you wish to attend this course, you need to have the Russian or English edition of the book Ordinary Differential Equations by Vladimir Arnold. The course is scheduled to start in the first week of September of 2020. In the beginning of each week, you will get the tasks to carry out, which will be discussed during a one-hour online meeting in the end of the week. All the questions outside the online meeting should be asked on this blog. 

Comments

  1. Armen Shirikyan20 September 2020 at 11:31

    MathJax is on for this blog, so you can write mathematical formulas: ˙x=v(t,x).

    ReplyDelete
  2. Armen Shirikyan22 September 2020 at 07:53

    I'll post every week the homework to do. All the numbers and pages refer to the English edition of the book: V. Arnold, Ordinary Differential Equations.

    For September 29, 2020:

    1. Justify the dimensions of the phase spaces on page 15
    2. Resolve problems 1.2.1, 1.6.1, 1.8.2
    3. Prove Propositions 1.5.1, 1.5.2 and 1.5.3
    4. Work out the details in Sections 1.9 and 1.10

    ReplyDelete
  3. Tsovinar22 September 2020 at 07:57

    նամակում ժամն ինձ մոտ նշված է 9.30։ Մենք 7.30 էինք պայմանավորվել։ Այսինքն այժմ փոխվում է 9.30՞

    ReplyDelete
    Replies
    1. Armen Shirikyan22 September 2020 at 08:53

      That's a misprint, I'll modify it. We meet on Tuesday, at 7:30pm (Yerevan time).

      Delete
  4. Armen Shirikyan29 September 2020 at 13:14

    Tasks for October 6, 2020:

    1. Work out the details about the Lotka-Volterra system, including Lamerey diagrams
    2. Solve problems 1.14.1, 1.15.1-5, 1.16.1, 1.18.1, 1.18.2
    3. Derive the equation for pendulum and draw its phase velocity field (Section 1.16)

    ReplyDelete
  5. Armen Shirikyan7 October 2020 at 11:00

    Tasks for October 13, 2020:

    1. Read Subsections 1-4 of Section 2 (Chapter 1)
    2. Resolve Exercises 1.2.1-1.2.7.

    ReplyDelete
  6. Armen Shirikyan14 October 2020 at 01:00

    Tasks for October 20:

    1. Solve Problems 2.3.5-2.3.7
    2. Read Sections 2.5 and 2.6
    3. Solve Problems 2.5.1-2.5.5 and 2.6.1-2.6.3

    ReplyDelete
  7. Armen Shirikyan26 October 2020 at 05:48

    Tasks for October 27:

    1. Read Section 2.7 of Chapter 1, in particular, the theorem about the existence of an equilibrium position.
    2. Solve problems 2.7.1 and 2.7.2 without missing details.

    ReplyDelete
  8. Armen Shirikyan3 November 2020 at 01:31

    Tasks for November 3, 2020:

    1. Read Sections 3.1 and 3.2 of Chapter 1.
    2. Solve Problems 3.2.1 and 3.2.2 of Chapter 1.
    3. Finalise solutions of Problems 2.7.1 and 2.7.2.

    ReplyDelete
  9. Armen Shirikyan6 November 2020 at 02:43

    Tasks for November 10, 2020:

    1. Read Section 3.3 of Chapter 1.
    2. Write down solutions of the exercises discussed on November 3.

    ReplyDelete
  10. Armen Shirikyan23 November 2020 at 09:22

    Tasks for November 24, 2020:

    1. Read Sections 3.4 and 3.5 of Chapter 1.
    2. Solve Problems 3.4.1, 3.5.1, and 3.5.2 of Chapter 1.

    ReplyDelete
  11. Armen Shirikyan29 November 2020 at 06:45

    This comment has been removed by the author.

    ReplyDelete
  12. Armen Shirikyan29 November 2020 at 06:47

    Tasks for December 1, 2020:

    1. Solve Problem 3.5.2 of Chapter 1.
    2. Read Section 4.1 and solve all the problems.

    ReplyDelete
  13. Armen Shirikyan2 December 2020 at 01:08

    Tasks for December 8, 2020:

    1. Solve Problems 4.1.10 and 4.1.11.
    2. Read Sections 4.2 and 4.3 of Chapter 1 and solve Problems 4.3.1 and 4.3.2.

    ReplyDelete
  14. Armen Shirikyan8 December 2020 at 13:40

    Tasks for December 15, 2020:

    1. Read Section 4.4 of Chapter 1
    2. Solve Problems 4.4.1 – 4.4.8

    ReplyDelete

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