APP MTH 7049 - Applied Mathematics Topic D

North Terrace Campus - Semester 2 - 2016

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 7049
    Course Applied Mathematics Topic D
    Coordinating Unit Mathematical Sciences
    Term Semester 2
    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 Edward Green

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 2016, the topic of this course is PRACTICAL APPLIED MATHEMATICS.


    Mathematical modelling has been described as an `unreasonably effective' tool for helping us to understand our world. It has given us new insights into problems from physics, engineering, economics, biology, and many other areas. But the real world is a complicated, and little is gained if a mathematician simply converts an intractable practical problem into an equally intractable mathematical one. Approximations are therefore necessary to enable us to analyse simplified versions of the problem, and gain real understanding. They can be introduced both in the formulation phase, where the model is developed (usually as a set of differential equations derived on some physical principle such as conservation of mass) and the solution phase, where the behaviour of the solution of the model is investigated. The aim of this course is to provide students with a `toolbox' of useful techniques, which will equip them to tackle real world problems in their future careers, whether in industry or academic research. Topics discussed will include: similarity solutions, travelling wave solutions, asymptotic and perturbation methods, and stability of solutions. The techniques will be illustrated by several case studies.

    Assumed knowledge for the course is some form of multivariable calculus, Modelling with ODEs III and PDEs and Waves III.

    Learning Outcomes

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

    1. develop ODE and PDE models of real world problems using principles such as conservation of mass or momentum;
    2. understand the concept of a similarity solution, and be able to find such solutions for the diffusion equation and similar problems;
    3. understand the concept of a travelling wave solution, and be able to find such solutions for Fisher's equation and similar problems;
    4. understand the concept and properties of an asymptotic expansion;
    5. apply asymptotic and perturbation methods to calculate solutions to ODE and PDE problems involving small parameters;
    6. determine the stability of a solution of a PDE problem.
    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
  • Learning Resources
    Required Resources
    Recommended Resources
    There are many excellent books on mathematical modelling and analytical methods for ODEs and PDEs in the Barr Smith library. The following is a short selection of some that are very compatible with the objectives and the level of this course:

    1. T. Witelski and M. Bowen: Methods of Mathematical Modelling (online book)

    2. S. Howison: Practical Applied Mathematics

    3. E. J. Hinch: Perturbation Methods

    4. J. D. Murray: Asymptotic Analysis
    Online Learning
    The course will have an active MyUni website.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The lecturer guides the students through the course material in 30 lectures. Students are expected to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.

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

    Activity Quantity Workload hours
    Lectures 30 100
    Assignments 5 56
    Total 156


    Learning Activities Summary
    1. Philosophy of mathematical modelling, review of simple conservation laws (lectures 1-3);
    2. Similarity solutions  (lectures 4-9);
    3. Travelling wave solutions (lectures 10-13);
    4. Introduction to perturbatrion methods: Asymptotic expansions and their properties (lectures 14-16);
    5. Regular and singular perturbation problems, boundary layers (lectures 17-22);
    6. Slender approximations (lectures 23-25);
    7. Stability analysis for reaction-diffusion problems (lectures 26-30);

  • 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
    Assessment task Task type Due  Weighting Learning outcomes
    Assignments Formative and summative Weeks 3, 5, 7, 9, 11 30% All
    Exam Summative Exam period 70% All
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    There will be a total of 5 homework assignments, distributed during each even week of the semester and due at the end of the following week. Each will cover material from the lectures, and in addition, will sometimes go beyond that so that students may have to undertake some additional research.
    Homework assignments must be given to the lecturer in person or emailed as a pdf. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty for that assignment.
    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
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