Students
PHYS701 – Mathematical Methods in Physics
2015 – S1 Day
General Information
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| Unit convenor and teaching staff |
Unit convenor and teaching staff
Unit Convenor
Dominic Berry
Contact via dominic.berry@mq.edu.au
E6B 2.408
11 am - 5 pm
Lecturer
Gavin Brennen
Contact via gavin.brennen@mq.edu.au
E6B 2.611
Wednesday 2 - 5 pm
Gavin Brennen
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| Credit points |
Credit points
4
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| Prerequisites |
Prerequisites
Admission to MRes
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| Corequisites |
Corequisites
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| Co-badged status |
Co-badged status
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| Unit description |
Unit description
This unit covers topics in mathematical physics including: differential equations and group theory. The aim is to develop effective problem solving strategies, and where possible, the examples will be taken from the physical sciences. In the first topic the primary focus is on ordinary differential equations covering topics from first order equations and how to classify and solve them, through to higher order equations and more general techniques such as reduction of order, Laplace transforms, Green functions and series solutions. The second topic covers discrete groups and continuous Lie groups and Lie algebras. Group representations are introduced with the examples from Abelian and non-Abelian groups. Irreducible representations, unitary representations, Shur’s Lemma, and orthogonality relations are covered in the context of discrete groups. Compact and non-compact Lie groups and their generating Lie algebras are presented with several examples making the connection between symmetries and conservation laws, e.g. space-time symmetries and the Poincare group.
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Important Academic Dates
Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
Learning Outcomes
On successful completion of this unit, you will be able to:
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to find series solutions of differential equations about ordinary or singular points.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Understand discrete groups, continuous Lie groups and Lie algebras, and representation theory.
- Demonstrate ability to apply methods through explanation of tutorial and assignment questions at the whiteboard.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
- Recognise the relations between symmetries and conservation laws.
Assessment Tasks
| Name | Weighting | Due |
|---|---|---|
| Assignments | 35% | Biweekly |
| Tutorial engagement | 15% | Weekly |
| Final Examination | 50% | Exam weeks |
Assignments
Due: Biweekly
Weighting: 35%
The assignments will comprise of 3-4 questions designed to engage the students with the material as
it's covered. The difficulty of the questions will be set so that the assignment would take on average
around 7 hours to complete.
On successful completion you will be able to:
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to find series solutions of differential equations about ordinary or singular points.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Understand discrete groups, continuous Lie groups and Lie algebras, and representation theory.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
- Recognise the relations between symmetries and conservation laws.
Tutorial engagement
Due: Weekly
Weighting: 15%
Each tutorial session, several students will present their attempts at either previous assignment
questions or tutorial problems at the whiteboard.
Students will be assessed on the degree to which they have engaged with the problem, their ability to
explain their thinking, and ability to draw on ideas and techniques from the course. The correctness of
the final answer is secondary to these other issues.
Each student will be expected to present at the whiteboard on at least 3 occasions. All students will be
expected to engage in the class discussion around these problems.
Grades will be announced periodically as we cycle through the class.
On successful completion you will be able to:
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to find series solutions of differential equations about ordinary or singular points.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Understand discrete groups, continuous Lie groups and Lie algebras, and representation theory.
- Demonstrate ability to apply methods through explanation of tutorial and assignment questions at the whiteboard.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
- Recognise the relations between symmetries and conservation laws.
Final Examination
Due: Exam weeks
Weighting: 50%
Three hour written examination.
On successful completion you will be able to:
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to find series solutions of differential equations about ordinary or singular points.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Understand discrete groups, continuous Lie groups and Lie algebras, and representation theory.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
- Recognise the relations between symmetries and conservation laws.
Delivery and Resources
Classes
Mixed Lecture and Tutorial/discussion
The timetable for classes can be found on the University web site at: http://www.timetables.mq.edu.au/
Required and Recommended Texts
The recommended text is "Physical Mathematics" by Kevin Cahill. It will be used as a frequent reference but will not be followed through in a chapter-by-chapter approach.
Some secondary textbooks are "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence, and "Elements of Green's Functions and Propagation" by Barton.
Teaching and Learning Strategy
The theoretical aspects of this unit are taught in lectures and tutorials with fortnightly assignments to strengthen the understanding of the material. The material is heavily mathematical in nature, and often abstract, and true understanding can only be achieved through testing and refining understanding through problem solving.
Unit Schedule
One half of this course is on Green's functions, series solutions, and eigengunction methods, and is given by Dominic Berry. The other half is on group theory, and is given by Gavin Brennen.
First lecture: Monday, 23 February.
Last lecture: Thursday, 4 June.
Lecture times and location
All lectures are in EMC-G230 Faculty Tute Rm
Monday: 11:00-13:00
Tuesday: 17:00-18:00
Thursday: 14:00-15:00
Policies and Procedures
Macquarie University policies and procedures are accessible from Policy Central. Students should be aware of the following policies in particular with regard to Learning and Teaching:
Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html
Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
Grading Policy http://mq.edu.au/policy/docs/grading/policy.html
Grade Appeal Policy http://mq.edu.au/policy/docs/gradeappeal/policy.html
Grievance Management Policy http://mq.edu.au/policy/docs/grievance_management/policy.html
Disruption to Studies Policy http://www.mq.edu.au/policy/docs/disruption_studies/policy.html The Disruption to Studies Policy is effective from March 3 2014 and replaces the Special Consideration Policy.
In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.
Student Code of Conduct
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/
Results
Results shown in iLearn, or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au.
Student Support
Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/
Learning Skills
Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.
Student Services and Support
Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.
Student Enquiries
For all student enquiries, visit Student Connect at ask.mq.edu.au
IT Help
For help with University computer systems and technology, visit http://informatics.mq.edu.au/help/.
When using the University's IT, you must adhere to the Acceptable Use Policy. The policy applies to all who connect to the MQ network including students.
Graduate Capabilities
PG - Discipline Knowledge and Skills
Our postgraduates will be able to demonstrate a significantly enhanced depth and breadth of knowledge, scholarly understanding, and specific subject content knowledge in their chosen fields.
This graduate capability is supported by:
Learning outcomes
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to find series solutions of differential equations about ordinary or singular points.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Understand discrete groups, continuous Lie groups and Lie algebras, and representation theory.
- Demonstrate ability to apply methods through explanation of tutorial and assignment questions at the whiteboard.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
- Recognise the relations between symmetries and conservation laws.
Assessment tasks
- Assignments
- Tutorial engagement
- Final Examination
PG - Critical, Analytical and Integrative Thinking
Our postgraduates will be capable of utilising and reflecting on prior knowledge and experience, of applying higher level critical thinking skills, and of integrating and synthesising learning and knowledge from a range of sources and environments. A characteristic of this form of thinking is the generation of new, professionally oriented knowledge through personal or group-based critique of practice and theory.
This graduate capability is supported by:
Learning outcomes
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Demonstrate ability to apply methods through explanation of tutorial and assignment questions at the whiteboard.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
- Recognise the relations between symmetries and conservation laws.
Assessment tasks
- Assignments
- Tutorial engagement
- Final Examination
PG - Research and Problem Solving Capability
Our postgraduates will be capable of systematic enquiry; able to use research skills to create new knowledge that can be applied to real world issues, or contribute to a field of study or practice to enhance society. They will be capable of creative questioning, problem finding and problem solving.
This graduate capability is supported by:
Learning outcomes
- Be able to apply Green's functions to solve partial differential equations in 1 or multiple dimensions.
- Be able to find series solutions of differential equations about ordinary or singular points.
- Be able to use eigenfunctions to find solutions of differential equations, and the properties of common cases.
- Demonstrate ability to apply methods through explanation of tutorial and assignment questions at the whiteboard.
- Be able to infer discrete and continuous symmetries from the properties of physical systems.
Assessment tasks
- Assignments
- Tutorial engagement
- Final Examination
PG - Effective Communication
Our postgraduates will be able to communicate effectively and convey their views to different social, cultural, and professional audiences. They will be able to use a variety of technologically supported media to communicate with empathy using a range of written, spoken or visual formats.
This graduate capability is supported by:
Learning outcome
- Demonstrate ability to apply methods through explanation of tutorial and assignment questions at the whiteboard.
Assessment task
- Tutorial engagement