MATH 3403 - Partial Differential Equations III

This subject is intended to introduce students to the principal categories of second order linear partial differential equations - Elliptic, Parabolic and Hyperbolic. The initial and boundary conditions appropriate to each class of equations are considered, together with questions of existence and uniqueness of solutions.

For details about the lecture times, assessment and other relevant material, see the

  • Course Profile

    Lecture notes for most of this year's course are available below. Students are advised to download them and read them prior to the lectures. However, the lecturer retains the right to add new material or delete existing material without notice. The course content is defined by the material covered in the lectures.

  • First order linear equations
  • Classification of second order operators
  • The Wave equation
  • The Wave equation continued
  • Separation of variables
  • Laplace's equation
  • Green's functions
  • Dirichlet's Principle
  • A Rayleigh-Ritz Example
  • The Heat equation
  • Fourier Transforms

    Ordinary differential equations notes:

  • Solution in series
  • Eigenfunction expansions

    Some Algebraic Asides:

  • Quadratic Forms
  • Orthogonality and Approximations

    Tutorial sheets with assignments indicated are shown here.

  • Sheet 1
  • Sheet 2
  • Sheet 3
  • Sheet 4
  • Sheet 5
  • Sheet 6
  • Sheet 7
  • Sheet 8
  • Sheet 9
  • Sheet 10

    Solutions to the tutorial sheets will be published after the assignments have been marked.

  • Sheet 1
  • Sheet 2
  • Sheet 3
  • Sheet 4
  • Sheet 5
  • Sheet 6
  • Sheet 7
  • Sheet 8
  • Sheet 9
  • Sheet 10

    Solutions to the midsemester exams (2001) and the final exam (2002) are in these files.

  • Exam 1
  • Exam 1, 2004
  • Exam 2
  • Exam 2, 2004
  • Final