APP MTH 7088 - Applied Mathematics Topic F
North Terrace Campus - Semester 2 - 2020
General Course Information
Course Code APP MTH 7088 Course Applied Mathematics Topic F Coordinating Unit School of Mathematical Sciences 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 Coordinator: Michael Chen
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
In 2020 the title of this course will be: Practical asymptotics
Differential equation models of real world problems are often very complex. Perturbation methods and asymptotic techniques can be used to systematically derive simpler versions of these models by exploiting the presence of small (or large) parameters; the idea being that the new model is mathematically tractable and still describes the behaviour of the original. This is useful, for example, in problems which involve slender geometries, or for situations where both small and large time scales are important.
This course is a broad introduction to asymptotic techniques and their application. Topics covered include: asymptotic evaluation of integrals; perturbations methods; boundary-layer theory; asymptotic matching; multi-scale analysis and asymptotics beyond all orders. Case studies will be used to demonstrate the utility of these techniques for problems from fluid mechanics, biology and industry.
Assumed knowledge: Necessary material from previous courses will be briefly revised (solution of ODEs & PDEs; applied complex variables). Some MATLAB (or similar) is helpful, but not essential.
On successful completion of this course students will be able to
1. develop ODE and PDE models of real world problems;
2. understand the concept and properties of an asymptotic expansion;
3. derive reduced models via asymptotic and perturbation methods, and construct solutions;
4. interpret model solutions in terms of a physical 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)
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
Required ResourcesAll required materials will be provided.
Recommended ResourcesT. Witelski, M. Bowen, Methods of Mathematical Modelling: Continuous Systems and Differential Equations, Springer, 2015. (electronic version available from UoA library)
C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, 1999. (electronic version available from UoA library)
Online LearningMyUni 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.
Learning & Teaching Activities
Learning & Teaching ModesThe 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.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 Tutorials 6 18 Assignments 5 40 Project 1 8 Total 156
Learning Activities Summary
Learning activities summary
- develop models for real world applications;
- introductory perturbation methods;
- asymptotic techniques;
- multi-scale modelling and homogenisation theory.
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 Objective Assessed Assignments/Project 30% all Exam 70% all
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment item Distributed Due date Weighting Assignment 1 Week 1 Week 3 5% Assignment 2 Week 4 Week 6 5% Assignment 3 Week 7 Week 8 5% Assignment 4 Week 9 Week 10 5% Assignment 5 Week 10 Week 12 5% Project Week 6 Week 13 5%
SubmissionAll written assignments are to be submitted to the lecturer with a signed cover sheet attached. There will be a maximum two week turn-around time on assignments for feedback to students.
Late assignments will not be accepted, but students may be excused from an assignment for medical or compassionate reasons. In such cases, documentation is required and the lecturer must be notified as soon as possible before the fact.
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.
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.
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