Unit convenor and teaching staff |
Unit convenor and teaching staff
Other Staff
Li Ji
Contact via li.ji@mq.edu.au
E7A 211
Wednesday, Thursday or by appointment
Elena Vynogradova
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Credit points |
Credit points
3
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Prerequisites |
Prerequisites
MATH235 and (MATH232 or MATH236)
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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 develops the ideas and techniques of analysis important in many branches of pure and applied mathematics. Topics include the theory of ordinary differential equations, including linear and nonlinear systems and their stability. Some special functions are also discussed, together with important applications in various branches of mathematics.
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Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
On successful completion of this unit, you will be able to:
Name | Weighting | Due |
---|---|---|
Eight assignments | 20% | to be advised |
One Test | 20% | to be advised |
Final examination | 60% | University Examination Period |
Due: to be advised
Weighting: 20%
Due: to be advised
Weighting: 20%
Due: University Examination Period
Weighting: 60%
Lectures: you should attend two hours of each lecture stream each week, making a total of four hours.
ORDINARY DIFFERENTIAL EQUATIONS
SPECIAL FUNCTIONS
No single textbook is entirely satisfactory for this part of the course. Attendance of the lectures is strongly recommended.
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 in the Numeracy Centre (C5A 255).
Difficulties with your home computer or internet connection do not constitute a reasonable excuse for lateness of, or failure to submit, assessment tasks.
WEEK |
ODES |
SPECIAL FUNCTIONS |
1 |
Introduction. First order equations. |
Power series solutions to 2-nd order ODF with variable coefficients. |
2 |
Existence & uniqueness, successive approximations. |
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3 |
Second order linear equations, fundamental sets, reduction of order. |
Legendre equation. Legendre functions. |
4 |
Properties of Legendre functions. |
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5 |
Higher order linear equations. |
Frobenius method to solve ODE with variable coefficients. Bessel equation. |
6 |
Linear equations with constant coefficients. |
Bessel functions. Gamma function. |
MID-SESSION BREAK |
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7 |
First-order linear systems: fundamental set of solutions. Systems with constant coefficients |
cntd. Bessel functions. Gamma function. |
8 |
Critical points and stability. The phase plane and stability of linear systems. |
Classical Orthogonal polynomials. |
9 |
Sturm-Liouville problems. |
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10 |
Non-linear systems and stability. |
Eigen-values problems. Properties. |
11 |
Limit cycles and stability. |
Series expansions in special functions. |
12 |
Application to solving partial differential equations. |
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13 |
Revision |
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Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
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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.
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/
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