In physics, economics and engineering, we frequently encounter quantities (for example energy) that depend on many variables (such as position, velocity, temperature). Usually this dependency is expressed through a partial differential equation, and solving these equations is important for understanding these complex relationships.

In this course we will study first and second order partial differential equations. The solution methods studied in this course will include the method of characteristics, separation of variables, Fourier series and Fourier transforms.

This course will be useful for majors in economics, mathematical finance, engineering and physics. We will illustrate the theory with examples from these disciplines.

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.

Examination Material or equipment

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

Required Resources

A key resource is instructional time; please take full advantage through lecture and workshop attendance.

Recommended Resources

An introduction to Partial Differential Equations by Peter J. Olver

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.

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 office 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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Partial Differential Equations First order partial differential equations Second order partial differential equations The wave equation Initial and boundary conditions The diffusion equation Boundary value problems Fourier analysis Harmonic functions	Feedback is given through written assignments, the mid-semester exam, and workshop worksheets.
2	Complex Analysis Complex functions Differentiation Elementary functions Integration Conformal mappings	Feedback is given through written assignments, the mid-semester exam, and workshop worksheets.

Tutorial Registration

Students are required to enrol in a workshop group. Workshops for MATH2306 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	Learning Outcomes
Assignments	30 %	1,2,3,4
Mid-semester Examination	20 %	1,3
Workshop Presentations	10 %	1,2,3,4
Final Examination	40 %	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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

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 Skills website. 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

Students are expected to attend lectures and workshops.

Examination(s)

The course includes an in-class mid-semester examination and a final examination. More information is given in the assessment items. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and mode of exams.

Assessment Task 1

Assignments

There will be 10 assignments across the semester. They will be made available weekly, starting from Week 1 and excluding Weeks 3 and 12. Students are expected to use MATLAB to answer some components of most assignments. It is intended that the marked assignments will be returned within 7 days after submission. Assignment solutions will typically not be released but feedback and guidance will be provided on graded assignments. Further details can be found on the course Wattle site.

Assessment Task 2

Mid-semester Examination

A mid-semester examination is included in the assessment and will be taken in class in Week 4. Further details can be found on the course Wattle site.

If your score on the mid-semester exam is at least as good as your score on the final exam, then your mid-semester exam score determines 20% of your course grade and your final exam score determines 40% of your course grade; if your final exam score is better than your mid-semester exam score, then your mid-semester exam score determines 10% of your course grade and your final exam score determines 50% of your course grade.

Assessment Task 3

Workshop Presentations

Ten workshops will be held during the semester, starting in Week 2. A worksheet will be made available at least one week before your workshop. The questions on the worksheet will be similar to those on the assignments. 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:

up to 4 points for the first presentation;

up to 3 points for the second presentation;

and up to 3 points for the third presentation;

giving a total of up to 10 points. Students may nominate when they wish to give the presentations (to be discussed in tutorials).

Assessment Task 4

Final Examination

A final examination is included in the assessment. To pass the course, students are required to satisfy a hurdle requirement of scoring at least 40% of the available marks on the final exam. Specific details about the hurdle requirements are given in Wattle. Details about the examination will be made available in the examinations timetable. Further details can be found on the course Wattle site.

If your score on the mid-semester exam is at least as good as your score on the final exam, then your mid-semester exam score determines 20% of your course grade and your final exam score determines 40% of your course grade; if your final exam score is better than your mid-semester exam score, then your mid-semester exam score determines 10% of your course grade and your final exam score determines 50% of your course grade.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

You may 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. MATH2306 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

All assignment submission is electronic, through either Wattle or Gradescope, as discussed on the Wattle page.

Late Submission

Late submission of assessment tasks without an extension is penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after one or more of the following have elapsed: 5 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item, or after solutions or graded assignments have been made available to the class. Late submission is not accepted for examinations.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Assignments will be returned electronically.

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.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
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.

Distribution of grades policy

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).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Access and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students