APP MTH 7049 - Applied Mathematics Topic D

North Terrace Campus - Semester 2 - 2024

This course is available for students taking a Masters 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.

• General Course Information
Course Details
Course Code APP MTH 7049 Applied Mathematics Topic D Mathematical Sciences Semester 2 Postgraduate Coursework North Terrace Campus 3 Y Ongoing assessment, exam
Course Staff

Course Coordinator: Professor Yvonne Stokes

Course Timetable

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

• Learning Outcomes
Course Learning Outcomes
This year, the topic of this course is Mathematical modelling using perturbations methods.

Synopsis

Many different physical problems can be modelled using differential equations with applicable initial and boundary conditions, which feature a small parameter. This course concerns the development and solution of simplified models for such problems using perturbation methods which exploit this small parameter. The solution is represented as an asymptotic expansion in the small parameter, of which a few terms are determined, somewhat like approximating a function by a few terms of its Taylor series. Perturbation methods will be considered in the context of some different applications such as laser drilling and fibre drawing. It will be seen that the solutions obtained give excellent understanding, not readily obtained by brute force numerical simulation.

Use will be made of analytical and numerical solution techniques. Ability to use Matlab ODE solvers and graphical tools will be beneficial.

The course will be run mainly on active learning principles; in-person attendance is expected and there will be no video recordings of lectures.

Learning Outcomes

On successful completion of this course, students will be able to:
1. Identify the type of problems for which perturbation methods are applicable;
2. Derive simplified models from more complex ones using appropriate asymptotic expansions;
3. Obtain analytical/numerical solutions, as appropriate, to the models derived;
4. Understand and explain the physical insight given by these models;
5. Understand the limitations of these models.

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.

all

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.

all

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.

1,5

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.

all
• Learning Resources
Required Resources
Course materials will be provided via the course's MyUni site.
Recommended Resources
References
• Mark H. Holmes, Introduction to perturbation methods, 2nd ed., Springer (2013). Available online through the Barr Smith Library.
Online Learning
The course will have an active MyUni website. However in-person attendance at workshops is expected and these will not be recorded.
• Learning & Teaching Activities
Learning & Teaching Modes
The learning in this course will be, predominantly, by active, discovery-based learning. Oral presentations and written assessments will also be employed.

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

 Activity Quantity Workload Hours Workshops (includes presentations, and prior work) 24 96 Assignments 4 60 Total 156
Learning Activities Summary
There will be two workshop sessions per week, run in student-centred mode, coupled with prior readings, working of problems and preparation of presentations.

Formal assignments will also be submitted on which feedback will be given.
• 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
A guide is given below; this will be finalised before commencement of the course.

 Assessment Task Type Weighting Learning Outcomes Assignments (4) Formative and Summative 30% All Active participation Formative and Summative 10% All Presentations Formative and Summative 10% All Final exam (2 hours) Summative 50% All
Assessment Detail

No information currently available.

Submission

No information currently available.

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

M10 (Coursework Mark Scheme)
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
• Fraud Awareness

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