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

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  2. 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

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

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

      Delete
  4. 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)

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  5. Tasks for October 13, 2020:

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

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  6. 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

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  7. 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.

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  8. 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.

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  9. Tasks for November 10, 2020:

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

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  10. 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.

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  12. Tasks for December 1, 2020:

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

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  13. 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. 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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