The formal unit description for the course can be found by clicking here. Also see the first page of the notes to see a summary of the course on a page.

Notes from the course in PDF format are uploaded at the end of each week. They may vary slightly from the notes on the board and may be different to last years notes. They will also include extra information (i.e. non-examinable) under "Online Extra" sections.

• Lecture notes from week 1
  
• Lecture notes from week 2
  
• Lecture notes from week 3
  
• Lecture notes from week 4
  
• Lecture notes from week 5
  
• Lecture notes from week 6
  
• Lecture notes from week 7
  

Worksheets and solution sheets from the course are available in PDF format, starting Monday.

• Problems 1 and Solutions 1 and Feedback
  
• Problems 2 and Solutions 2 and Feedback
  
• Problems 3 and Solutions 3 and Feedback
  
• Problems 4 and Solutions 4 and Feedback
  
• Problems 5 and Solutions 5
  
• Problems 6 and Solutions 6
  
  
• Problems 7
  

Problems class handouts. Questions only.

• Week 3
  
• Week 4
  
• Week 5
  
• Week 6
  
• Week 7
  

Electronic versions of exam papers from the last three years are available from Blackboard but I've dug them up and the solutions and they are here:

• 2010 Exam and Solutions
• 2011 Exam and Solutions
• 2012 Exam and Solutions

Maple worksheets (.mw files) to go with the lectures and problem sheets. Download the files to your PC and open them in Maple.

• E.g.'s 1 and 2 from section 3.3 of notes: Fourier sine series approximation to x(1-x) and 1 on (0,1)
• Example 1 from Section 3.5, p29 of the notes. The 1D diffusion of heat on an interval with zero BCs at the endpoints and initially heat 1
• Example 2 from Section 3.5, p30 of the notes. The 1D diffusion of heat on an interval with zero BCs at the endpoints and initially a step in heat from 1 to 0 at x=1/2.
• Example 2 from Section 3.7, p32 of the notes. The 1D diffusion of heat on an interval with derivative BCs at the endpoints (0,1) and initially a step in heat from 1 to 0 at x=1/2.
• Example from Section 3.8, p34 of the notes. The 1D wave equation on interval (-L,L) with periodic BCs and initially a constant slope displacement.
• Definition of the delta function from p40 of the notes. Animation of the limiting form. Also Fourier Transform of delta function.
• The fundamental solution of the heat equation: a source at the origin. Section 4.5.1 of notes
• The diffusion of heat on an infinite line when the initial heat is a discontinuous Heaviside function.
• The diffusion of heat on a semi-infinite line for a source next to a zero BC. Section 4.6.1 of the notes
• The diffusion of heat on a semi-infinite line for a source next to a derivative BC. Section 4.6.1 of the notes
• D'Alembert's solution for the wave equation for general initial conditions. Section 5.1, of the notes, example 1
• D'Alembert's solution for a wave next to a wall with a zero/derivative BS. Section 5.2, of the notes, example 1
• Reflection and transmission of waves at an interface
• Nonlinear PDE, breaking waves example from section 6.2, p.60 of the notes
• Traffic flow example
• Steady-state diffusion on a rectangle
• Steady-state diffusion on a semi-infinite rectangular strip
• Steady-state diffusion on a circular disk
• Normal modes on a rectangular drumskin
• Normal modes on a circular drumskin