This unit of study introduces Sturm-Liouville eigenvalue problems and their role in finding solutions to boundary value problems. Analytical solutions of linear PDEs are found using separation of variables and integral transform methods. Three of the most important equations of mathematical physics - the wave equation, the diffusion (heat) equation and Laplace's equation - are treated, together with a range of applications. There is particular emphasis on wave phenomena, with an introduction to the theory of sound waves and water waves. To pass MATH3078, students must achieve satisfactory performance in the in-semester assessment component in order to pass the unit of study.
Three 1 hour lectures and one 1 hour tutorial per week.
One 2 hour exam, assignments, quizzes (100%). To pass MATH3078/3978, students must achieve satisfactory performance in the in-semester assessment component.
[MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22]
12 credit points of Intermediate MathematicsProhibitions
MATH3018 or MATH3921 or MATH3978