Students

MATH3905 – Mathematical Methods

2020 – Session 1, Weekday attendance, North Ryde

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Due to the Coronavirus (COVID-19) pandemic, any references to assessment tasks and on-campus delivery may no longer be up-to-date on this page.

Students should consult iLearn for revised unit information.

Find out more about the Coronavirus (COVID-19) and potential impacts on staff and students

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor/Lecturer
Stuart Hawkins
12WW 722
please refer to iLearn
Lecturer
Elena Vynogradova
12WW 709
please refer to iLearn
Frank Schoenig
Credit points Credit points
10
Prerequisites Prerequisites
(MATH2010 or MATH235) and (MATH2020 or MATH2110 or MATH236 or MATH232)
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description

This unit develops the ideas and techniques of analysis important in many branches of pure and applied mathematics. Topics include the theory of ordinary differential equations and the theory of special functions. The study of ordinary differential equations encompasses linear and nonlinear systems. While linear systems are important in their own right, they provide the key framework for analysing the stability of nonlinear systems. The theory of special functions will focus on some particularly widely used classes of special functions. We will see how to derive their properties, including asymptotics, from their series and integral representations. We will show how to employ generalised Fourier series and eigenfunction expansions utilising special functions in some important applications.

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:

  • ULO1: Demonstrate knowledge of the principles and concepts of the theory of Ordinary Differential Equations and the theory of Special Functions.
  • ULO2: Deduce the properties and various asymptotics of the functions from their series and integral representations.
  • ULO3: Demonstrate understanding of and proficiency with a variety of mathematical techniques used in pure and applied mathematics.
  • ULO4: Apply the ideas and techniques of the theory of Ordinary Differential Equations and the theory of the Special Functions to model a broad range of phenomena in science and in engineering.
  • ULO5: Construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning.

Assessment Tasks

Coronavirus (COVID-19) Update

Assessment details are no longer provided here as a result of changes due to the Coronavirus (COVID-19) pandemic.

Students should consult iLearn for revised unit information.

Find out more about the Coronavirus (COVID-19) and potential impacts on staff and students

General Assessment Information

ATTENDANCE and PARTICIPATION: Please contact the unit convenor as soon as possible if you have difficulty attending and participating in any classes. There may be alternatives available to make up the work. If there are circumstances that mean you will miss a class, you can apply for Special Consideration via ask.mq.edu.au

ASSIGNMENT SUBMISSION: Assignment submission will be online through the iLearn page.

Submit assignments online via the appropriate assignment link on the iLearn page. A personalised cover sheet is not required with online submissions. Read the submission statement carefully before accepting it as there are substantial penalties for making a false declaration.

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You may submit as often as required prior to the due date/time. Please note that each submission will completely replace any previous submissions. It is in your interests to make frequent submissions of your partially completed work as insurance against technical or other problems near the submission deadline.

LATE SUBMISSION OF WORK:  All assessment tasks must be submitted by the official due date and time. In the case of a late submission for a non-timed assessment (e.g. an assignment), if special consideration has NOT been granted, 20% of the earned mark will be deducted for each 24-hour period (or part thereof) that the submission is late for the first 2 days (including weekends and/or public holidays). For example, if an assignment is submitted 25 hours late, its mark will attract a penalty equal to 40% of the earned mark. After 2 days (including weekends and public holidays) a mark of 0% will be awarded. Timed assessment tasks (e.g. tests, examinations) do not fall under these rules.

FINAL EXAM POLICY: It is Macquarie University policy not to set early examinations for individuals or groups of students. All students are expected to ensure that they are available until the end of the teaching semester, that is, the final day of the official examination period. The only excuse for not sitting an examination at the designated time is because of documented illness or unavoidable disruption. In these special circumstances, you may apply for special consideration via ask.mq.edu.au.

If you receive special consideration for the final exam, a supplementary exam will be scheduled in the interval between the regular exam period and the start of the next session. By making a special consideration application for the final exam you are declaring yourself available for a resit during this supplementary examination period and will not be eligible for a second special consideration approval based on pre-existing commitments. Please ensure you are familiar with the policy prior to submitting an application.

You can check the supplementary exam information page on FSE101 in iLearn (bit.ly/FSESupp) for dates, and approved applicants will receive an individual notification one week prior to the exam with the exact date and time of their supplementary examination.

Delivery and Resources

Coronavirus (COVID-19) Update

Any references to on-campus delivery below may no longer be relevant due to COVID-19.

Please check here for updated delivery information: https://ask.mq.edu.au/account/pub/display/unit_status

Classes

Lectures: you should attend two hours of each lecture stream each week, making a total of four hours per week.

Required and Recommended Texts and/or Materials

ORDINARY DIFFERENTIAL EQUATIONS

  • Ordinary Differential Equations and Stability Theory David A. Sanchez, Dover
  • Ordinary Differential Equations and Stability Theory V.I. Arnold

SPECIAL FUNCTIONS

No single textbook is entirely satisfactory for this part of the course. Attendance of the lectures is strongly recommended.

  • Advanced Engineering Mathematics Erwin Kreyszig, John Wiley&Sons, various editions. QA401.K7
  • Partial differential Equations. An Introduction Walter A. Strauss, John Wiley&Sons, 1992. QA374.S86/1992
  • Equations of Mathematical Physics A.N. Tikhonov & A.A. Samarskii, Oxford University Press (also reprinted by Dover). QA401.T512/1963

Technology Used and Required

Students are expected to have access to an internet enabled computer with a web browser and Adobe Reader software. Several areas of the university provide wireless access for portable computers. There are computers for student use in the Library and MUSE.

Unit Schedule

Coronavirus (COVID-19) Update

The unit schedule/topics and any references to on-campus delivery below may no longer be relevant due to COVID-19. Please consult iLearn for latest details, and check here for updated delivery information: https://ask.mq.edu.au/account/pub/display/unit_status

Week ODEs

Special Functions

Task Due

1

First order ODEs Power series solutions to 2-nd order ODE with variable coefficients.  
2      
3 Existence and uniqueness Legendre equation. Legendre functions.  
4   Properties of Legendre functions.  
5 Higher order ODEs Frobenius method to solve ODE with variable coefficients. Bessel equation.  
6 Linear ODEs Bessel functions. Gamma function.  
7     Assignment 1
  Mid Semester Break    
8 Inhomogeneous linear ODEs Classical Orthogonal polynomials.  
9   Sturm-Liouville problems. Test
10 Laplace transform Eigenvalue problems. Properties.  
11 Linear Systems Series expansions in special functions. Application to solving partial differential equations.  
12     Assignment 2
13 Revision Revision  

 

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit the Student Policy Gateway (https://students.mq.edu.au/support/study/student-policy-gateway). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/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/study/getting-started/student-conduct​

Results

Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) 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 or if you are a Global MBA student contact globalmba.support@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 help you improve your marks and take control of your study.

The Library provides online and face to face support to help you find and use relevant information resources. 

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

If you are a Global MBA student contact globalmba.support@mq.edu.au

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

Changes since First Published

Date Description
18/02/2020 an amendment to the ULO's was updated in the CMS