APP MTH 7045 - Applied Mathematics Topic B

North Terrace Campus - Semester 1 - 2017

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at

  • General Course Information
    Course Details
    Course Code APP MTH 7045
    Course Applied Mathematics Topic B
    Coordinating Unit Mathematical Sciences
    Term Semester 1
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Assessment Ongoing assessment 30%, exam 70%
    Course Staff

    Course Coordinator: Dr Luke Bennetts

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes

    Course learning outcomes

    The course title is Nonlinear PDEs and Waves.

    Waves impact on every facet of our experience. The simple acts of seeing and hearing rely on electromagnetic and sound waves. Traffic flows in waves. Waves carry the information required for our technological society to function. Earthquake and tsunami waves cause enormous devastation to our world.

    PDEs are used to model all these manifestations of waves. This course builds on Modelling with ODEs and PDEs & Waves, with a focus on nonlinear PDEs and the associated phenomena caused by the nonlinearity. This will include: dissipative shocks in gas dynamics and traffic flow, produced by Burgers equation; solitons in shallow-water waves and acoustics, produced by the Korteweg de Vries equation; and breathers in deep-water waves and optical fibres, produced by the Schrödinger and sine-Gordon equations. Analytical and numerical mathematical methods will be used to find the solutions. Where practicable, the PDEs will be derived to emphasise connections to the applications.

    Assumed knowledge: Modelling with ODEs; PDEs & Waves.

    Learning outcomes

    On successful completion of this course students will be able to:

    1. interpret several canonical nonlinear PDEs as models in different application areas;
    2. describe fundamental nonlinear wave phenomena predicted by PDEs;
    3. use analytical methods to obtain solutions to certain PDEs;
    4. use asymptotic methods in appropriate regimes to derive approximate solutions;
    5. employ appropriate numerical methods to solve nonlinear PDEs.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    Teamwork and communication skills
    • developed from, with, and via the SGDE
    • honed through assessment and practice throughout the program of studies
    • encouraged and valued in all aspects of learning
    Self-awareness and emotional intelligence
    • a capacity for self-reflection and a willingness to engage in self-appraisal
    • open to objective and constructive feedback from supervisors and peers
    • able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
  • Learning Resources
    Required Resources
    Recommended Resources
    Billingham, J. and King, A.C. Wave Motion, Cambridge Uni Press, 2000.
    Online Learning
    MyUni will be used to provide electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that the students make appropriate use of these resources.

  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures and exercises as the primary learning mechanism for the material. A sequence of written and/or online assignments provides assessment opportunities for students to gauge their progress and understanding.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Quantity Workload Hours
    Lectures 30 90
    Tutorials 6 18
    Assignments 4 24
    Project 1 24
    Total 156
    Learning Activities Summary
    1. Burgers equation and the split-step method
    2. Korteweg de Vries equation and the inverse scattering transform
    3. Schrödinger and sine-Gordon equations
    4. Stoke's waves and perturbation methods
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Component Weighting Objective Assessed
    Assignments+project 30% all
    Exam 70% all
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Assessment Item Distributed Due Date Weighting
    Assignment 1 Week 2 Week 4 4%
    Assignment 2 Week 4 Week 6 4%
    Assignment 3 Week 7 Week 9 4%
    Assignment 4 Week 9 Week 11 4%
    Project Week 6 Week 7 14%
    Assignments and projects must be left in the course hand-in box or given to the lecturer in person by the specified deadline. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy ( course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

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