Applied Mathematics 3041

University of Cape Town

Course Description

  • Course Name

    Applied Mathematics 3041

  • Host University

    University of Cape Town

  • Location

    Cape Town, South Africa

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    Course entry requirements: MAM2000W and either MAM2046W or both MAM2047H and MAM2048H

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • Host University Units

    36
  • Recommended U.S. Semester Credits
    6
  • Recommended U.S. Quarter Units
    9
  • 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.

Course Disclaimer

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.