APP MTH 7088 - Applied Mathematics Topic F

North Terrace Campus - Semester 2 - 2015

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au

  • General Course Information
    Course Details
    Course Code APP MTH 7088
    Course Applied Mathematics Topic F
    Coordinating Unit Applied Mathematics
    Term Semester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Course Description Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au
    Course Staff

    Course Coordinator: Dr Sarthok Sircar

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 2015, the topic of this course is Applied Methods in Biology and Engineering.

    Syllabus

    The goal for this class is for students to develop a fundamental understanding of how mathematics is applied as a tool to aid in studying complex systems in biological and engineering sciences. We will thoroughly investigate case studies in several fields including: Neuron Action Potential Propagation, Cardiac dynamics, Tumor/cancer growth and Pattern formation. Graded work will include a mix of theoretical and computational homework, culminating in a final exam.

    Practically speaking, this class is designed for advanced undergraduate, honours, MPhil and beginning PhD students in the mathematical, physical, and biological sciences with a solid mathematical background, i.e., Linear Algebra and Differential Equations. The course prerequisite (which can be waived with instructor approval) is Modelling with Ordinary Differential Equations (APP MTH 3021) and may be taken simultaneously with this course. Also note that familiarity with MATLAB or other programming language is assumed (prerequisites include classes which use MATLAB). The list of mathematical tools and methods that we will learn in this course include:

    1) Matched asymptotics, multi-scale modeling: This method will be taught via Michaelis-Menton kinetics, Fitzhugh-Nagumo and Hodgkin-Huxley models.

    2) Solving moving boundary problems, traveling wave solutions: This method will be introduced while solving advection-diffusion-reaction equations for tumor growth, pattern formation and the Fisher’s equation.


    Learning Outcomes

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

    1) understand modelling of chemical reactions involving multiple time-scales
    2) develop regular as well as singular perturbation formulation for these models
    3) understand the concept of non-dimensionalization which distinguishes various time-scales
    4) analyse theory of motion, directed motion or taxis, diffusion, steady-state solutions
    5) develop and solve traveling wave solutions to reaction-diffusion systems, Fisher’s equation
    6) understand pattern formation, Turing instabilities and bifurcations
    7) analyse pattern activation and inhibition coupled with biological motion
    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)
    Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all
    The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. all
    An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. all
    Skills of a high order in interpersonal understanding, teamwork and communication. all
    A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
    A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. all
    An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. all
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    Books

    [1] James Keener and James Sneyd, Mathematical Physiology I: Cellular Physiology, 2nd edition, Springer, 2009.

    [2] N. Britton, Essential Mathematical Biology, Springer, 2005.

    [3] L. Edelstein-Keshet, Mathematical models in biology, SIAM, 2005.

    [4] J. D. Murray, Mathematical Biology, Springer-Verlag, New York, 2nd edition, 1993.
    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.

    See https://myuni.adelaide.edu.au/webapps/login/
  • 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.
    Workload

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

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

    Lectures (x30) = 90 workload hours
    Assignments (x6) = 60 workload hours
    Test = 6 workload hours

    Total = 156 workload hours
    Learning Activities Summary
    1) Introduction to biochemical kinetics
    2) Non-dimentionalization, time-scale analysis, regular and singular perturbation, matched asymptotics
    3) Theory of motion, directed motion, diffusion
    4) Traveling wave solution, Fisher's equation
    5) Pattern formation, Turing instability
    6) Solutions at steady-state for non-linear PDEs
    Specific Course Requirements
    Course prerequisite: Modelling with Ordinary Differential Equations (APP MTH 3021).
  • 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: Assignments
    Due: Even weeks
    Weighting: 30%
    Learning outcomes: All

    Assessment: Examination
    Due: Examination period
    Weighting: 70%
    Learning outcomes: All
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    There will be a total of 6 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. The 6 assignments will constitute 30% of the final grade. 
    Submission
    Homework assignments must either be given to the lecturer in person or left in the box outside the lecturer's office by the given due time. 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 (http://www.adelaide.edu.au/policies/101/) 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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