MAGIC058: Theory of Partial Differential Equations

Course details

A core MAGIC course


Autumn 2023
Monday, October 2nd to Friday, December 8th


Live lecture hours
Recorded lecture hours
Total advised study hours


10:05 - 10:55 (UK)
11:05 - 11:55 (UK)

Course forum

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This course unit surveys analytical methods for linear and first and second order PDEs.

We will discuss exact solutions, series solutions, Fourier series and existence and uniqueness questions, including analytical methods that serve as the basis for many of the modern numerical methods.


Standard undergraduate courses in calculus (single variable, multi variable), as well as vector calculus, will be required.


1. Introduction to Partial Differential Equations (PDEs): notation, examples

2. The diffusion equation on the real line

3. Fourier series

4. Solutions via separation of variables on an interval:
      a. The wave equation
      b. The diffusion equation

5. Laplace's equation in a bounded domain

Time permitting, we will cover additional topics of interest, such as
  • More equations coming from physics
  • Wave phenomena and variants of the wave equation
  • Nonlinear PDEs


  • JB

    Dr Jonathan Ben-Artzi

    Cardiff University


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The assessment for this course will be released on Monday 8th January 2024 at 00:00 and is due in before Friday 19th January 2024 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


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