APP MTH 7049 - Applied Mathematics Topic D

North Terrace Campus - Semester 2 - 2019

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

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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, exam

Course Staff

Course Coordinator: Dr Edward Green

Course Timetable

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

Course Learning Outcomes

In 2019, the topic of this course is Mathematical Biology and Physiology.

Synopsis

For centuries, mathematical models have been used in the physical sciences to help us understand problems such as the propagation of light, the motion of the planets, or the flow of fluids. More recently, mathematical models have been applied to problems in the life sciences, yielding important new insights into biological problems, and stimulating the development of new mathematics. This cross-fertilisation between the disciplines makes mathematical biology and physiology one of the most exciting (and challenging) areas of applied mathematics. In this course, we will study some important biological problems where mathematical models in the form of systems of ODEs and PDEs have produced new understanding. Unfortunately, most biologically interesting models cannot be solved analytically, and so we we need to develop expertise in alternative techniques for understanding their behaviour, including phase plane analysis, bifurcation theory and perturbation methods.

Topics covered will include:
-enzyme-catalysed reactions
-ion transport and propagation of signals in nerve cells (Hodgkin-Huxley equations)
-model development using conservation laws
-models for cell movement
-travelling waves
-development of patterns in tissues (Keller-Segel model, Turing patterns)
-tissue growth

Assumed knowledge for the course is a basic understanding of ODEs and PDEs, as covered in Modelling with ODEs III and Waves and PDES III.

Learning Outcomes

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

1. develop ODE models for enzyme-catalysed reactions using the Law of Mass Action;

2. understand how Michaelis-Menten kinetics can be derived using perturbation theory;

3. understand and explain models for ion transport;

4. use phase-plane techniques to study the dynamics of ODE models such as the Hodgkin-Huxley equations;

5. understand conservation laws, and be able to use them to develop new models;

6. understand what is meant by a travelling wave solution, and be able to demonstrate their existence for Fisher's equation and other; systems;

7. understand the principles underpinning the Keller-Segel and Turing models for pattern formation, and use stability analysis to predict when it will occur in these and similar models;

8. recognise free boundary problems arising in tumour growth, and use some basic analytical techniques to study them.

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)	all
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	all
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	1,5
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	all

Learning Resources

Required Resources

None.

Recommended Resources

L. Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics, 2005.

J. D. Murray, Mathematical Biology (two volumes), Springer, 2002.

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.

Workload

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

Assignments 4 66

Total 156

Learning Activities Summary

Lecture outline

Enzyme catalysed reactions, the Law of Mass Action, Michaelis-Menten kinetics (4 Lectures).

Ion transport, excitable systems the Hodgkin-Huxley equations (5 Lectures).

Conservation laws, cell movement, reaction-advection diffusion equations, age-structured models (6 Lectures).

Fisher's equation, travelling waves (4 Lectures)

Pattern formation, Keller-Segel model, linear stability analysis, Turing patterns, diffusion-driven instability (6 lectures)

Domain growth, free boundary problems, avascular tumour models, development of the necrotic core (4 Lectures).

Summary (1 Lecture).

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

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

Assessment Summary

Assessment task	Task type	Weighting	Learning outcomes
Assignments	Formative and summative	30%	All
Exam	Summative	70%	All

Assessment Related Requirements

An aggregate score of 50% is required to pass the course.

Assessment Detail

There will be four assignments worth 30% of the total mark. The remaining 70% will come from the exam

Submission

Assignments must be handed in person to the lecturer or submitted in the assigned assignment box if they are to be marked.

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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