Course Description
Course Name
Applied Mathematics 3041
Session: VCPS3124
Hours & Credits
36 Host University Units
Prerequisites & Language Level
Course entry requirements: MAM2000W and either MAM2046W or both MAM2047H and MAM2048H
Taught In English
- There is no language prerequisite for courses at this language level.
Overview
Course outline:
The aim of this course is to introduce the student to a selection of advanced topics in Applied Mathematics. This half course consists of two modules of MAM3040W, at least one of which should be 3MP: METHODS OF MATHEMATICAL PHYSICS (coded as MAM3043S for Engineering students) which covers: The Fourier-transform and Laplace-transform solution of linear PDEs on the line; the influence function; the Parseval identity. The long-term asymptotic behaviour of solutions: the methods of Laplace, stationary phase and steepest descents. Nonlinear waves: the method of characteristics; Riemann invariants. The effect of dissipation; the Cole-Hopf transform for the Burgers equation; travelling fronts for the KPP equation. The effect of dispersion: KdV, nonlinear Schroedinger and sine-Gordon equation. Elliptic integrals and elliptic functions; cnoidal waves and solitons; kinks and breathers for the sine-Gordon equation. Multisoliton solutions: the Hirota method and Baecklund transformations.
The aim of this course is to introduce the student to a selection of advanced topics in Applied Mathematics. This half course consists of two modules of MAM3040W, at least one of which should be 3MP: METHODS OF MATHEMATICAL PHYSICS (coded as MAM3043S for Engineering students) which covers: The Fourier-transform and Laplace-transform solution of linear PDEs on the line; the influence function; the Parseval identity. The long-term asymptotic behaviour of solutions: the methods of Laplace, stationary phase and steepest descents. Nonlinear waves: the method of characteristics; Riemann invariants. The effect of dissipation; the Cole-Hopf transform for the Burgers equation; travelling fronts for the KPP equation. The effect of dispersion: KdV, nonlinear Schroedinger and sine-Gordon equation. Elliptic integrals and elliptic functions; cnoidal waves and solitons; kinks and breathers for the sine-Gordon equation. Multisoliton solutions: the Hirota method and Baecklund transformations.
*Course content subject to change