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NUS Math Module Review: MA4221 Partial Differential Equations

Assessment Structure:

25% Homework (2 sets, 12%-13%)

75% Online Quiz (3 quizzes)

This is a module under both lists MA4 and AM4-General, hence both Pure Math and Applied Math majors can take this module to satisfy their core requirements. The module’s topics include first order linear equations, initial boundary conditions, wave and diffusion equations in various boundary conditions, reflections and sources, separation of variables under various boundary conditions, Fourier series, completeness and the Gibbs phenomenon, inhomogeneous boundary conditions, harmonic functions, Poisson’s formula and Green’s identities. The textbook of reference is Partial Differential Equations: An Introduction (Second Edition), Walter Strauss. The chapters taught are all of chapter 1-7.

Lecture attendance is not compulsory. Tutorial attendance was initially graded, but this was dropped due to the COVID-19 situation (as some students may not be willing the attend class on campus). Lectures were not webcast until the department made it compulsory to do so, also due to the COVID-19 situation. Tutorial sessions just involve Prof. Yu going through selected solutions. Almost all tutorial and homework problems were taken from the textbook, and tutorial and homework problems share similar formats and difficulty.

I have mixed feelings on the difficulties of this module. On one hand, most concepts in this module are hand-waved (i.e. proofs are often omitted), so generally one does not need very in-depth understanding of this module to do well. This module reminds me largely of MA2104 – I call modules like this a “methods” module, where you mostly learn the techniques to solve problems (in this module, relatively simple PDEs and BVPs), but proofs are almost never tested. On the other hand, it’s not easy to appreciate the techniques taught in this module. For instance, one may take time to understand the steps needed to find the eigenvalues of a wave equation over R, under Dirichlet conditions. As such, one should still expect to spend a good amount on time on this module to do well.

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