• Class Number 6073
• Term Code 3260
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Dr Sean Harris
• LECTURER
• Noa Kraitzman
• Class Dates
• Class Start Date 25/07/2022
• Class End Date 28/10/2022
• Census Date 31/08/2022
• Last Date to Enrol 01/08/2022
SELT Survey Results

Partial Differential Equations, Fourier Analysis and Complex Analysis (MATH6406)

Many physical processes such as vibrating strings, diffusion of heat and fluid flows are well modelled by partial differential equations and/or integral equations. This course provides an introduction to methods for solving and analysing standard partial differential equations and integral equations, including an introduction to complex analytic techniques.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of partial differential equations and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of Fourier series, complex analysis and integral transform techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from partial differential equations and complex analysis
4. Apply problem-solving using Fourier series, complex analysis and integral transform techniques applied to diverse situations in physics, engineering and other mathematical contexts.
5. Explain the use and applications of partial differential equations and/or complex analysis to some topic related to undergraduate study, employment or other experience.

UG Version

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of partial differential equations and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of Fourier series, complex analysis and integral transform techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from partial differential equations and complex analysis
4. Apply problem-solving using Fourier series, complex analysis and integral transform techniques applied to diverse situations in physics, engineering and other mathematical contexts.

## Examination Material or equipment

Information about examination material will be made available through the Examinations timetable.

## Required Resources

Partial Differential Equations: An Introduction by Walter A. Strauss (available for free online via the ANU Library)

Partial Differential Equations, Student Solutions Manual: An Introduction by Julie L. Levandosky, Steven P. Levandosky, and Walter A. Strauss.

An Introduction to Complex Analysis by Ravi P. Agarwal, Kanishka Perera and Sandra Pinelas.

Recommended student system requirements

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

## Staff Feedback

Students will be given feedback in the following forms in this course:

• Written comments on the assignments.
• Practice problems handed out as part of the workshops.
• Presentation of solutions during the workshops.
• Individual feedback may be given during the lecturer's of ce hours.

## Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Partial Differential Equations First order equations partial differential equations Second order partial differential equations The wave equation Fourier transform Initial and boundary conditions The diffusion equation Boundary value problems Fourier series Harmonic functions Feedback is given through written assignments as well as workshop worksheets.
2 Complex Numbers Introduction Differentiation Elementary functions Integration Conformal mappings Feedback is given through written assignments as well as workshop worksheets.
3 Advanced Topic Students will be required to undertake an Advanced Topic. The topic will be confirmed at the start of the course. Last year's Advanced Topic was the numerical solution of conservation equations. Feedback is given through written assignments.

## Tutorial Registration

Students are required to enrol in a workshop group. Workshops for MATH6406 start in Week 2. Workshop registration will be via MyTimetable. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Assignments 14 % * * 1,2,3,4
Mid-semester examination 22 % * * 2,3
Final Examination 30 % 03/11/2022 01/12/2022 2,3
Workshop Presentations 4 % * * 1,2,3,4
Advanced Topic 25 % * * 1,2,3,4,5
Online Lectures Questions 5 % * * 1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

## Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

## Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

## Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

## Participation

Remote participants will have access to online lectures, participate in workshops via Zoom, and take exams on Wattle. More information can be found on the Wattle page.

## Examination(s)

The course includes a mid-semester and final examination. More information is given in the assessment items.

Please note, that where a date range is used in the Assessment Summary in relation to the final exam, the due date and return date indicate the start of the official end of semester exam period and the date results are returned to students (official end of Semester results released on ISIS). Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and mode of exams.

Value: 14 %
Learning Outcomes: 1,2,3,4

Assignments

Assignments will be handed out weekly starting from Week 1. There are 10 assignments over the semester. The best 9 out 10 assignments will count towards the course grade. Students are expected to use MATLAB to answer some of the assignment questions.

It is intended that the marked assignments will be returned within 7 days after submission.

This year's assignment solutions will not be released as we will be including questions from the assignments in the exams. We will however release previous year's assignments and solutions, prior to the due dates, to give feedback and guidance on how to set out assignment solutions.

Further details can be found on the Course Wattle site.

Value: 22 %
Learning Outcomes: 2,3

Mid-semester examination

A mid-semester examination is included in the assessment. Exams will be conducted using Proctorio. We aim for the examination to be held in Week 6 or Week 7. Details about the examination will be made available at the Examinations timetable. Further details can be found on the Course Wattle site.

Value: 30 %
Due Date: 03/11/2022
Return of Assessment: 01/12/2022
Learning Outcomes: 2,3

Final Examination

A final examination is included in the assessment. Students are required to satisfy a hurdle requirement. Specific details about the hurdle requirements are given in Wattle. Details about the examination will be made available at the Examinations timetable. Further details can be found on the Course Wattle site.

Value: 4 %
Learning Outcomes: 1,2,3,4

Workshop Presentations

Ten tutorials will be held during the semester. The tutorials will start in Week 2.

A tutorial worksheet will be made available at least one week before your tutorial. The questions on the worksheet will be similar to those on the assignments, so it is an advantage to have a go at the worksheets. To encourage people to work through the worksheets, grades will be given for presenting a solution to one of the worksheet questions. The grades are

2 points for the first presentation,

1 points for the second presentation,

1 points for the third presentation,

giving a total of 4 points. Students may nominate when they wish to give the presentations.

Students will present on different dates which will be discussed in class.

Value: 25 %
Learning Outcomes: 1,2,3,4,5

Details of the assessment items for the Assessment Topic will be given on Wattle. The type of assessment items offered previously have included assignments as well as in class presentations.

Value: 5 %
Learning Outcomes: 1,2,3,4

Online Lectures Questions

Each week, we will have 4 online lectures and one in-class lecture. You are required to watch lecture videos before coming to the in-class lecture.

To encourage people to work while watching the videos, you will be asked to answer questions in most videos.

Once a video lecture is available, you will have 14 days to answer the questions in that video.

Further details can be found on the Course Wattle site.

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

## Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. MATH6406 does not use Turnitin, having been granted an exemption.

## Hardcopy Submission

Hard copies may be required to be submitted for the Advanced Topic part of the course. This will be discussed with the lecturer for the Advanced Topic.

Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

## Late Submission

Where an assignment is submitted after the due date, students are penalised by five per cent of the possible marks available for the assessment task per working day or part thereof. This is inline with the official university policy. As we want graded submissions to be returned in a timely fashion, and it is not fair to accept assignments after graded submission have been returned, there will be a cut-off time of less than a week. The cut-off time will depend on the workshop times. Details will be posted on wattle.

The late submission rules for the remaining assessment items will be discussed with the lecturer for the Advanced Topic.

## Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

## Returning Assignments

Assignments submitted under Assessment Task 1 will be returned electronically through the Wattle assignment tool.

## Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

## Resubmission of Assignments

Assignments may not be resubmitted.

## Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

## Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

## Convener

 Dr Sean Harris u5349004@anu.edu.au

### Research Interests

My research interests lie in harmonic and functional analysis, operator algebras and non-commutative geometry.

### Dr Sean Harris

 By Appointment

## Instructor

 Noa Kraitzman Sean.Harris@anu.edu.au