APP MTH 4051 - Applied Mathematics Topic E - Honours
North Terrace Campus - Semester 2 - 2023
General Course Information
Course Code APP MTH 4051 Course Applied Mathematics Topic E - Honours Coordinating Unit Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 2.5 hours per week Available for Study Abroad and Exchange Y Restrictions Honours students only Course Description This course is available for students taking an honours degree in Mathematical Sciences. The course will cover an advanced topic in applied mathematics. For details of the topic offered this year please refer to the Course Outline.
Course Coordinator: Dr Edward GreenThis is the same course as APP MTH 7087 - Applied Mathematics Topic E
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 2023 the topic of this course is Mathematical Biology and Physiology.
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:
-ion transport and propagation of signals in nerve cells (Hodgkin-Huxley equations)
-model development using conservation laws
-models for cell movement
-development of patterns in tissues (Keller-Segel model, Turing patterns)
Assumed knowledge for the course is a basic understanding of ODEs and PDEs, e.g. as covered in Modelling with ODEs III and Waves and PDES III.
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)
Attribute 1: Deep discipline knowledge and intellectual breadth
Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.
Attribute 2: Creative and critical thinking, and problem solving
Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.
Attribute 3: Teamwork and communication skills
Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.
Attribute 8: Self-awareness and emotional intelligence
Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.
Required ResourcesAccess to the internet and University intranet.
Recommended ResourcesL. Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics, 2005.
J. P. Keener and J. Sneyd, Mathematical Physiology, Springer 2008.
J. D. Murray, Mathematical Biology (two volumes), Springer, 2002.
Online LearningThis course uses MyUni for providing electronic resources, such as assignments and handouts, and for making course announcements. It is recommended that students make appropriate use of these resources. Link to MyUni login page:
Learning & Teaching Activities
Learning & Teaching ModesStudents work through the course material with support from the lecturer. 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 Study 30 90 Assignments 5 66 Total 156
Learning Activities Summary
Learning activities summary
- Enzyme catalysed reactions, the Law of Mass Action, Michaelis-Menten kinetics
- Ion transport, excitable systems, the Hodgkin-Huxley equations
- Conservation laws, cell movement, reaction-advection diffusion equations, age-structured models
- Fisher's equation, travelling waves
- Pattern formation, Keller-Segel model, linear stability analysis, Turing patterns, diffusion-driven instability
- Domain growth, free boundary problems, avascular tumour models, development of the necrotic core
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.
Component Weighting Task type Learning outcomes assessed Assignments 30% Summative and formative all Exam 70% Summative all
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment item Distributed Due date Weighting Assignment 1 Week 2 Week 4 6% Assignment 2 Week 4 Week 6 6% Assignment 3 Week 6 Week 8 6% Assignment 4 Week 8 Week 10 6% Assignment 5 Week 10 Week 13 6%
Assignments are to be submitted online; exact dates and times and detailed instructions will be posted on MyUni.
SubmissionAll written assignments are to be submitted via MyUni.
Students requiring an extension or exemption for an assignment for medical or compassionate reasons should contact the lecturer as early as possible, and certainly before the deadline for the assignment in question.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M11 (Honours Mark Scheme) Grade Grade reflects following criteria for allocation of grade Reported on Official Transcript Fail A mark between 1-49 F Third Class A mark between 50-59 3 Second Class Div B A mark between 60-69 2B Second Class Div A A mark between 70-79 2A First Class A mark between 80-100 1 Result Pending An interim result RP Continuing Continuing CN
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.
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