Topic outline

  • General

  • Course Materials

    • 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

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

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

    • 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. 

      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 note. 

    • Questions 1 and 2 are further examples of plane autonomous systems covered in chapter 2 of the lecture notes. 

      Questions 3-6 are on the method of characteristics for first order PDEs and correspond to chapter 3 from the lecture notes. 

    • Sheet 4 is on second order PDEs.

      Questions 1-4 correspond to material covered in 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.