How to contact me?

Personally, after the lectures
Email:Robertus [at] sheffield.ac.uk
Tel.: 2223832
Office: H16, Hicks Building

Syllabus for MAS315

This course is designed for Level 3/4 SoMaS student. All Notes, Exercises and Solutions are in pdf format

Detailed Syllabus
Introduction including the HW plan
Chapter 1: Waves on Strings, Exercises 1, Solutions 1
Chapter 2: Use of Fourier Series, Exercises 2, Solutions 2
Chapter 3: Sound Waves and the Equation of Continutity, Exercises 3, Solutions 3
Chapter 4: Surface Waves on Liquids, Exercises 4, Solutions 4
Chapter 5: Modelling Traffic Flow, Exercises 5, Solutions 5
Exam paper from last year: Exam paper with Solutions
Exam paper from two years ago: Exam paper with Solutions

Auxilary Java applets

Here you find a list of Java applests that may help you to visualize the course material.
With time I will add more applets, so watch this space.

Oscillations on finite strings
Simulation of wave motion of a string.
Oscillations of a rectangular membrane
Vibrational modes in a 2-dimensional rectengular membrane.
Oscillations of a circular membrane
Vibrational modes in a 2-dimensional circular membrane.
Fourier series
Frequency analysis of periodic functions.

Reference Literature

R. Knobel: An Introduction to the Mathematical Theory of Waves
American Mathematical Society, 2000
ISBN: ISBN: 0-8218-2039-7 (pbk)
[Covers almost all course material. Excellent book.]

J. Billingham & A.C. King: Wave Motion
Cambridge Texts in Applied Mathematics, CUP, 2001
0-521-634504 (pbk)
[Covers all the course. Many parts of the book may be hard for UK maths UGs.]

G.B. Whitham: Linear and Nonlinear Waves
Pure and Applied Mathematics, Wiley, 1999
0-471-35942 (pbk)
[Covers all the course. Really a text for graduate and research students. Authoritative reference.]

Sir J. Lighthill: Waves in Fluids
Cambridge Mathematical Library, CUP, 2003
ISBN: 0-521-01045 (pbk)
[Covers part of the course on fluid waves. Excellent insight.]


Thanks: I would like to sincerely thank all those colleagues and friends (Professor Chatwin, Drs Fedun, Carter, Hargreaves, Malins, and Verth) who helped me putting these notes together.