Howard College

Welcome to Math 354 – Mathematics 3A (Eng). This module aim to provide students with essential tools of advanced applied mathematics.  Students are expected to attend lectures regularly and punctually. I hope you will all enjoy this module and work hard to make a success of it.

 Syllabus: Fourier series, application to boundary value problems for ordinary differential equations (Sturm-Liouville problem). Series solution of ordinary differential equations, basic special functions. Separation of variables for one and two dimensional PDE’s. Fourier transform applications to PDE’s. Further complex variable theory, Laurent’s and Taylor’s theorem, isolated singularities and residues, evaluation of integrals by residues. Applications.

 The Learning website: http://learn2025.ukzn.ac.za is your gateway to up-to-date information regarding the course in terms of weekly announcements, tutorials, notes, quizzes, additional problems and discussions.  It is your responsibility to visit the Learn website and access daily updates.

 As a prerequisite to this module, students must be familiar with the contents of Math238 and Math248.

 There will be series of exercises and tutorial problems for students to work on in this module.

Aim: To develop concepts of differential and integral calculus and introduce elements of differential equations and
complex numbers. Content: Further techniques of integration, improper integrals, further applications of integration, sequences and series,
Taylor expansion, conic sections, polar coordinates, basic differential equations, complex numbers and basic complex
functions.