## APP MTH 7045 - Applied Mathematics Topic B

### North Terrace Campus - Semester 1 - 2017

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 7045 Applied Mathematics Topic B Mathematical Sciences Semester 1 Postgraduate Coursework North Terrace Campus 3 Y Ongoing assessment 30%, exam 70%
##### Course Staff

Course Coordinator: Dr Luke Bennetts

##### Course Timetable

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

• Learning Outcomes

## Course learning outcomes

The course title is Nonlinear PDEs and Waves.

Waves impact on every facet of our experience. The simple acts of seeing and hearing rely on electromagnetic and sound waves. Traffic flows in waves. Waves carry the information required for our technological society to function. Earthquake and tsunami waves cause enormous devastation to our world.

PDEs are used to model all these manifestations of waves. This course builds on Modelling with ODEs and PDEs & Waves, with a focus on nonlinear PDEs and the associated phenomena caused by the nonlinearity. This will include: dissipative shocks in gas dynamics and traffic flow, produced by Burgers equation; solitons in shallow-water waves and acoustics, produced by the Korteweg de Vries equation; and breathers in deep-water waves and optical fibres, produced by the Schrödinger and sine-Gordon equations. Analytical and numerical mathematical methods will be used to find the solutions. Where practicable, the PDEs will be derived to emphasise connections to the applications.

Assumed knowledge: Modelling with ODEs; PDEs & Waves.

#### Learning outcomes

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

1. interpret several canonical nonlinear PDEs as models in different application areas;
2. describe fundamental nonlinear wave phenomena predicted by PDEs;
3. use analytical methods to obtain solutions to certain PDEs;
4. use asymptotic methods in appropriate regimes to derive approximate solutions;
5. employ appropriate numerical methods to solve nonlinear PDEs.

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
all
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
None.
##### Recommended Resources
Billingham, J. and King, A.C. Wave Motion, Cambridge Uni Press, 2000.
##### 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.

• Learning & Teaching Activities
##### Learning & Teaching Modes
This course relies on lectures and exercises as the primary learning mechanism for the material. A sequence of written and/or online assignments provides assessment opportunities for students to gauge their progress and understanding.

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 4 24 Project 1 24 Total 156
##### Learning Activities Summary
1. Burgers equation and the split-step method
2. Korteweg de Vries equation and the inverse scattering transform
3. Schrödinger and sine-Gordon equations
4. Stoke's waves and perturbation methods
• 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
 Component Weighting Objective Assessed Assignments+project 30% all Exam 70% all
##### Assessment Related Requirements
An aggregate score of 50% is required to pass the course.
##### Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1 Week 2 Week 4 4% Assignment 2 Week 4 Week 6 4% Assignment 3 Week 7 Week 9 4% Assignment 4 Week 9 Week 11 4% Project Week 6 Week 7 14%
##### Submission
Assignments and projects must be left in the course hand-in box or given to the lecturer in person by the specified deadline. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty.

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

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

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