A1: Differential Equations 1 (2021-22)

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  • Select activity Announcements

    

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• Select topic Course Materials

  Course Materials
  • Select activity Lecture notes

    

    Lecture notes File

    The lecture notes consist of 4 main chapters on 

    1 ODEs and Picard’s Theorem
    

    2 Plane autonomous systems of ODEs
    

    3 First order semi-linear PDEs: the method of characteristics
    

    4 Second order semi-linear PDEs

    There are 26 videos of varying length each of which covers a particular topic and the titles of the videos correspond to the section(s) from the lecture notes.  Please have a look at the Suggested Schedule for Lecture Videos to plan your schedule.

    
    

  • Select activity Suggested Schedule for Lecture Videos

    

    Suggested Schedule for Lecture Videos File
  • Select activity Sheet 1

    

    Sheet 1 Assignment

    This problem sheet is on ODEs and Picard's Theorem. 

    The relevant sections of the lecture notes and the videos are 1.1-1.5.

  • Select activity Sheet 2

    

    Sheet 2 Assignment

    The first half of the problem sheet is on Picard's theorem for systems and higher order ODEs covered in sections 1.6 and 1.7 of the lecture notes and the corresponding videos. 

    The second half of the problem sheet is on plane autonomous systems, in particular the classification of critical points, covered in sections 2.1-2.3 of the lecture notes and the corresponding videos. 

  • Select activity Sheet 3

    

    Sheet 3 Assignment

    Questions 1 and 2 are further examples of plane autonomous systems covered in chapter 2 of the lecture notes and the corresponding videos. 
    
    Questions 3-6 are on the method of characteristics for first order PDEs and correspond to chapter 3 from the lecture notes and the corresponding videos. 
    

  • Select activity Sheet 4

    

    Sheet 4 Assignment

    Sheet 4 is on second order PDEs.

    Questions 1-4 correspond to material covered in the videos on sections 4.1-4.3 while questions 5 and 6 are on the maximum principle which is covered in section 4.4 of the lecture notes and the corresponding videos.