• Class Number 3795
• Term Code 3130
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• LECTURER
• Dr Vanessa Robins
• Class Dates
• Class Start Date 22/02/2021
• Class End Date 28/05/2021
• Census Date 31/03/2021
• Last Date to Enrol 01/03/2021
SELT Survey Results

Applied Mathematical Methods in Physics (PHYS4301)

The purpose of this course is to give an in-depth introduction to mathematical methods used in modern physics. This course concentrates on different approaches and techniques which help to solve a variety of problems in theoretical and applied areas of physics. It will review and develop methods of Complex Analysis and their applications to calculation of integrals, finding and analysing solutions of differential equations which appear in physical problems. It will give a basic introduction to groups and their representations which appear in physical problems including rotation group, Lorentz group and simple unitary groups. Asymptotic methods used in modern quantum theory will also be explored. The course will provide strong integration of conceptual and applied elements from the physicists' point of view. All methods will be illustrated by working computational examples in Mathematica, so that students could get practical experience of application of mathematical methods to various problems in physics.

## Learning Outcomes

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

1. Demonstrate accurate and efficient use of complex analysis in physical problems.
2. Explain fundamental concepts of group theory and its use for analysis of physical symmetries.
3. Apply knowledge of methods and practical skills in solving differential equations and their role in physical applications.
4. Demonstrate effective use of asymptotic methods in physical problems.
5. Demonstrate high level communication skills in oral and written formats.

## Research-Led Teaching

This course aims to develop and improve mathematical skills of students and their ability to apply such skills for solving applied problems in research environment. It will review and develop methods of Complex Analysis, role fo symmetries and techniques of group theory for analysis of physical problems, different methods of solving differential equations and asymptotic methods used in modern quantum and classical physics. The course will provide strong integration of conceptual and applied elements from the physicists' point of view.

## Required Resources

"Essentials of Math Methods for Physicists" by H.J. Weber and G.B. Arfken, 5th Edition, ISBN: 9780120598779

Wolfram Mathematica, free for ANU students

"Mathematical Methods of Physics" by J. Mathews and R.L. Walker, 2nd Edition, ISBN: 978-0805370027

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:

• feedback to whole class, groups, individuals, focus group etc

## 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 Topics will include: Basics of complex analysis (CA), analytic functions Branch cuts, multi-valued functions and analytic continuation Applications of CA, conformal maps Role of symmetries in physics, basics of the group theory Lie groups and algebras, basics of representation theory Rotation group, Lorentz group and conformal group. Unitary groups U(1), SU(2), SU(3) and their representations. Partial differential equations, major clasification Methods in PDEs: Separation of variables, Fourier transform, conformal transformations, Green functions Asymptotic methods: Steepest descent, WKB approximation, applications Special functions of mathematical physics

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Online quizzes 20 % * * 1,2,3,4
Assignment 1 10 % 22/03/2021 29/03/2021 1,2,3,4
Assignment 2 10 % 23/04/2021 30/04/2021 1,2,3,4
Assignment 3 10 % 24/05/2021 31/05/2021 1,2,3,4
Presentation 10 % 27/05/2021 * 1,2,3,4,5
End of semester exam 30 % 03/06/2021 01/07/2021 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

This course has been adjusted for remote participation. All lectures will be supplied as pdf files together with live or ZOOM video recordings. All assessment will be done online including quizzes, assignments and presentation. Examinations will be in dual mode: in class and via ZOOM sessions. Remote students are requested to provide uninterrrupted video in ZOOM during the exam. They need to scan and upload on Wattle their workings after the exam.

## Examination(s)

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Value: 20 %
Learning Outcomes: 1,2,3,4

Online quizzes

There are online quizzes due at the end of each week. They will be marked automatically upon completion.

There are approximately 12 of each tasks due over the semester. Further details can be found on the course Wattle site.

Value: 10 %
Due Date: 22/03/2021
Return of Assessment: 29/03/2021
Learning Outcomes: 1,2,3,4

Assignment 1

Students are expected to contribute on an on-going basis throughout the semester. Each assignment will test students' understanding of the studied material. They will be submitted online and the marked assignments will be returned one week after submission.

Value: 10 %
Due Date: 23/04/2021
Return of Assessment: 30/04/2021
Learning Outcomes: 1,2,3,4

Assignment 2

Students are expected to contribute on an on-going basis throughout the semester. Each assignment will test students' understanding of the studied material. They will be submitted online and the marked assignments will be returned one week after submission.

Value: 10 %
Due Date: 24/05/2021
Return of Assessment: 31/05/2021
Learning Outcomes: 1,2,3,4

Assignment 3

Students are expected to contribute on an on-going basis throughout the semester. Each assignment will test students' understanding of the studied material. They will be submitted online and the marked assignments will be returned one week after submission.

Value: 10 %
Due Date: 27/05/2021
Learning Outcomes: 1,2,3,4,5

Presentation

The presentation will test student's ability for independent research work as well as oral and written communication skills.

The due date for oral or written presentation will be the last week. It is anticipated that oral presentations will be given during the last tutorial.

Value: 30 %
Due Date: 03/06/2021
Return of Assessment: 01/07/2021
Learning Outcomes: 1,2,3,4

End of semester exam

The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location exam.

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. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

## Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

## Late Submission

Late submission permitted. Late submission of assessment tasks without an extension are 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 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.

## 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.

## 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

Resubmission is not permitted.

## 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

### Research Interests

Mathematical Physics

Statistical mechanics

Quantum field theory

Classical and quantum integrable systems

Quantum groups and representation theory

Conformal field theory

Random matrices

Special functions and their q-deformations

Linear q-difference equations

 Friday 12:00 13:00 By Appointment

## Instructor

 Dr Vanessa Robins 61252747 Vanessa.Robins@anu.edu.au