Note:  The information in plain text is for inclusion in the course profile, the italicised text

 

 

 

 

Ordinary Differential Equations

 

 

 

 

 

 

 

 

 

 

 

 

School of Physical Sciences

 

 

 

 

 

 

MATH4402/MATH7402 

 

 

 

 

 

 

 

Dr Min-Chun Hong

 

 

 

 

 

 

 

 

 

Course Code: MATH4402/MATH7402

Course Title: Ordinary Differential Equations III/IVH IIIIVH

Semester  1 2006

 

 

1.  GENERAL COURSE INFORMATION

 

Brief description of course content:

 

Background analysis. Gronwall's inequality. Initial value problems for systems: existence & extendability of solutions. Periodic solutions: first integrals, Morse theorem, attractors; Brouwer's fixed point theorem & degree theory; Floquet's theorem. Perturbation theory: Poincare-Lindstdt method for periodic solutions.

 

 

Staff:

 

Lecturers:

 

Name  Dr Min-Chun Hong  

 

Campus: St Lucia

Room number/ Building :  Room 67-549,  Priestley Building

Phone number: 334-69036

Email: hong@maths.uq.edu.au

Consultation hours or Office hours: 2pm-4pm, Thursday

 

 

Tutorial Coordinator: Dr Min-Chun Hong  

 

 

 

Web page       The course profile and course material can be found on the web at the following address: :  http://www.maths.uq.edu.au/courses/MATH4402

 

This also contains up-to-date news about the course material and announcements for students.   Please check this regularly during the semester.

 

Class contact hours:     3L, 1T

 

Timetable:

Timetables are available on mySI-net.

New Search
 

 

This information is accurate as at 03-FEB-06. Room allocations may change and it is important you check your timetable prior to the start of classes.

 

 

 

 

 

 

MATH4402 Ordinary Differential Equations III/IVH - Timetable

 

Location

Group

Day

Start

End

Building

Room

Start - End Date

Class not taught on the specified date(s)

St Lucia

L

 MON

 11:00am

 11:50am

 67

 342

 27/02 - 03/06

 

 

L

 TUE

 10:00am

 10:50am

 67

 341

 27/02 - 03/06

 

 

L

 FRI

 10:00am

 10:50am

 67

 342

 27/02 - 03/06

 

 

T

 THU

 11:00am

 11:50am

 09

 642

 27/02 - 03/06

 02/03

 

 

Assumed background:

 

 

 

 

2.  AIMS, OBJECTIVES AND GRADUATE ATTRIBUTES

 

Course Aims:

 

The subject aims to introduce students to rigorous examination of some basic concepts of MATH4402 will cover the following topics:.

 

 

 

Learning Objectives:

On successfully completing this course students will be able to:

 

 

 

 

Graduate Attributes: 

 

 

For more information on the University policy on development of graduate attributes in courses, refer to the web http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=20&s3=5

 

The following graduate attributes will be developed in the course –

 

In-Depth Knowledge of the Field of Study:

 

·        A comprehensive and well-founded knowledge of the field of study:- through solving problems.

·        An understanding of how other disciplines relate to the field of study:- through applying the mathematical techniques of the course to simple problems from other disciplines..

·        An international perspective on the field of study:- through using internationally accepted standards of mathematical rigour and notation.

 

Effective Communication:

 

·        The ability to collect, analyse, and organise information and ideas, and to convey those ideas clearly and fluently, in both written and spoken forms:- through tutorial participation.

·        The ability to interact effectively with others in order to work towards a common outcome:-  through cooperative learning strategies in tutorials .

·        The ability to select and use the appropriate level, style and means of communication:- through assignments and tutorials.

·        The ability to engage effectively and appropriately with information and communication technologies:- through practical use of pen, ink, and computers.

 

 

Independence and Creativity:

 

·        The ability to work and learn independently:- through assignments and tutorials.

·        The ability to generate ideas and adapt innovatively to changing environments:- through solving problems..

·        The ability to identify problems, create solutions, innovate and improve current practices:- through assignments and tutorials..

 

Critical Judgement:

 

 

·        The ability to define and analyse problems:- through solving problems.

·        The ability to apply critical reasoning to issues through independent thought and informed judgement:- through solving problems in  assignments and tutorial questions.

·        The ability to evaluate opinions, make decisions and to reflect critically on the justifications for decision-: through learning lectures.

Ethical and Social Understanding:

 

·        An understanding of social and civic responsibility - through cooperative learning strategies in tutorials and lectures

·        An appreciation of the philosophical and social contexts of a discipline:-  through the

     experience of a discipline where the concepts of right and wrong are supported by    

      universal and absolute standards

·        A knowledge and respect of ethics and ethical standards in relation to a major area of

       study-through tutorial participation in a subject taken by students with diverse backgrounds and interests

·        A knowledge of other cultures and times and an appreciation of cultural diversity-through tutorial participation in a subject taken by students with diverse backgrounds and interests

 

For more information on the University policy on development of graduate attributes in courses, refer to the web http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=20&s3=5.

 

 

3.  LEARNING RESOURCES

 

Required Resources: 

No  textbook.

 

Recommended Resources:

Reference book:

1. Ferdnand Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer Verlag, New York, 1990

2. J. Hale, Ordinary Differential Equations, Wiley-Interscience, New York, 1969

 

 

The University offers a range of resources and services to support student learning.  Details are available on the myServices website (https://student.my.uq.edu.au/)

 

Library contact:

The liaison librarian for the physical sciences disciplines is located in the Physical Sciences and Engineering Library in the Hawken Building and may be consulted for assistance in the course:

 

                                 Leith Woodall

                                 Email: l.woodall@library.uq.edu.au

                                 Extension: 52367

 

 

 

 

4.  TEACHING AND LEARNING ACTIVITIES

 

 

Three hours of lectures and one hour of tutorials per week. There are no tutorials in week 1 and week 13. An extra tutorial in week 13 can be held by special arrangements with lecturer.

 Students should attend all their lectures. Since the theory presented in this course is developed logically, it is necessary to study lecture notes from previous lectures prior to attending each subsequent lecture. By following this procedure, you will find this course both enjoyable and informative.

 

There are 9 tutorial sheets. Tutorial sheets will be handed out in lectures. Solutions to tutorial problems will be available in the following week at tutorials. You should aim to do as many problems as possible on the tutorial sheet before the tutorial and ask about anything you do not understand at the tutorial and lecture.

 

If you do not work through the tutorial sheets, then you will have difficulty with the assignments. You can get help with any difficulties from lecturer  (or another student) at the tutorials.  But check you understand the answers to the problems by writing out your own solution by yourself.  (Students who work through the problems and make sure they understand any slips they made are very unlikely to have problems with this subject.)  Although we are happy to give help on the tutorial sheets, lecturer will not give help on the assignments that are to be handed in. These should be entirely your own work.  

 

Questions can be answered outside tutorial hours by visiting the lecturer in their contact hours. 

 

 

 

 

 

 

 

 

5.  ASSESSMENT

 

Required assessment tasks:

 

The assessment will be based on two assignments each worth 20 marks, and an end of semester examination. The final exam 60 marks. 

 

 

Assessment Item

%

Due date

Assignment 1 (due to week 7)

20%

13 April

Assignment 2 (due week 12)

20%

26 May

The end of   semester exam (departmental)

60%

June

 

 
 
Assignments

 

There will be two assignments containing problems that demand analytical solution.  The assignments will be available on the web at least 2 weeks before they are due, and are to be submitted at the end of weeks 7 and 13.  Students should solve the assignments on their own, without the direct assistance of lecturers, or other students.  Students whose solutions are copied from other students are violating the University’s plagiarism policy (given below); even if they rewrite the solution sentence by sentence, or change notation in the mathematics or code.   Students who copy solutions from the web or from books without referencing the

original source are violating the University’s policy on plagiarism (given below).  Students whose work does not display an independent approach in an assignment will not receive credit for the assignment. 

 

 

Final Exam

 

There will be a closed-book two-hour  exam in the examination period at the end of first semester ( June 2006).  The final exam counts 60% towards the final mark. 

The lecture notes and tutorial sheets are not allowed   for the final exam.  Any pocket calculators are permitted but contents of memory must be erased.

 

 

 

 

Assessment criteria

 

Answers to written examination questions for the  final examination will be assessed in terms of the extent to which they demonstrate the ability of the student to:

·        Define, explain and interrelate main concepts involved in the course.

·        Present proofs of the key theorems developed in the course.

·        Apply the theory to solve some practical questions.

 

Answers to both assignments will be assessed in terms to which they demonstrate the ability to apply theory to solve some practical questions.

 

Criteria for the award of grades:

 

Grades will be awarded according to the following scale:

 

1%

-

24%

marks

grade 1

25%

-

44%

marks

grade 2

45%

-

49%

marks

grade 3

50%

-

64%

marks

grade 4

65%

-

74%

marks

grade 5

75%

-

84%

marks

grade 6

85%

-

100%

marks

grade 7

 

 

 

Your grade for this course will be determined by which of the following levels of achievement that you consistently display in the items of summative assessment.

 

Grade of 7: (85% - 100% )  the student demonstrates an excellent understanding of the theory of the topics listed in the course outline and is highly proficient in applying the techniques to solve both theoretical and practical problems. 

 

Grade of 6: (75% - 84%)  the student demonstrates a comprehensive understanding of the theory of the topics listed in the course outline and is proficient in applying the techniques to solve both theoretical and practical problems.

 

Grade of 5: (65% - 74%)  the student demonstrates a good understanding of the theory of the topics listed in the course outline and can apply the techniques to solve problems.

 

Grade of 4: (50 – 64%)  the student demonstrates an understanding of the theory of the topics listed in the course outline and demonstrates a knowledge of the techniques used to solve problems.

 

Grade of 3: (45% - 49%) the student demonstrates some understanding of the
theory of the topics listed in the course outline and demonstrates some
knowledge of the techniques used to solve problems, but fails to satisfy all
of the basic requirements for a pass.

Grade of 2: (25 – 44%) the student demonstrates limited understanding of the theory of the topics listed in the course outline and demonstrates limited knowledge of the techniques used to solve problems.  This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately.

 

Grade of 1: (1 – 24%) the student demonstrates very limited understanding of the theory of the topics listed in the course outline and of the basic concepts in the course material.  This includes attempts at answering some questions but demonstrating very limited understanding of the key concepts.

 

 

6.  POLICIES & GUIDELINES

 

Assessment policy:

An overview of the University’s assessment-related policies can be found on myAdvisor link (http://www.uq.edu.au/myadvisor/index.html?page=2910).  Students should refer to section 3.30 Assessment in the University Handbook of Policies and Procedures link http://www.uq.edu.au/hupp/index.html?page=25108&pid=25075) for full details on all assessment-related policies.

 

As solutions to assignments are distributed promptly, credit cannot be given for late assignments.  Students who miss assignments through bereavement, ill health, or other serious unavoidable problems should document their problems and discuss this with Min-Chun Hong.  An alternative assessment scheme may be negotiated with the student.

Allowance cannot be made for reasons such as sporting fixtures (unless you are representing Queensland or Australia in open competition), social commitments (unless at least one Hilton sister will be present), or overwork in other courses. 

 

Students should be familiar with the rules which relate to assessment in their degrees as well as general university policy such as found in the General Award Rules.  These are all set out on the myAdvisor page on the UQ website

http://www.uq.edu.au/student/GeneralRules2006/2006GARs.htm

 

Plagiarism: 

 

 

The University has adopted the following definition of plagiarism:

“Plagiarism is the action or practice of taking and using as one’s own the thoughts or writings of another, without acknowledgment. The following practices constitute acts of plagiarism and are a major infringement of the University's academic values:

When a student knowingly plagiarises someone’s work, there is intent to gain an advantage and this may constitute misconduct.

 

Students are encouraged to study together and to discuss ideas, but this should not result in students handing in the same or similar assessment work.  Do not allow another student to copy your work.  While students may discuss approaches to tackling a tutorial problem, care must be taken to submit individual and different answers to the problem.  Submitting the same or largely similar answers to an assignment or tutorial problem may constitute misconduct.

 

The results of the assessment may be annulled and other action may be taken as is considered appropriate in the circumstances of the case.

 

For more information on the University policy on plagiarism, please refer to

http://www.uq.edu.au/hupp/index.html?page=25128&pid=25075

 

 

Supplementary examinations:

 

A supplementary examination may be awarded in one course to students who obtain a grade of 2 or 3 in the final semester of their program and require this course to finish their degree.  You should check the rules for your degree program for information on the possible award of supplementary examinations.  Applications for supplementary examinations must be made to the Director of Studies in the Faculty.

 

Special examinations:

 

If a student is unable to sit a scheduled examination for medical or other adverse reasons, she/he can and should apply for a special examination. Applications made on medical grounds should be accompanied by a medical certificate;  those on other grounds must be supported by a personal declaration stating the facts on which the application relies.

 

Applications for special examinations for central and end-of-semester exams must be made through the Student Centre.  Applications for special examinations in school exams are made to the course coordinator.

 

More information on the University’s assessment policy may be found

http://www.uq.edu.au/hupp/index.html?page=25109&pid=25075

 

EPSA Faculty policy on the award of special and supplementary exams may be found via the Faculty Guidelines on Examinations from the EPSA student page

http://www.epsa.uq.edu.au/index.html?page=9329&pid=0 for special exams and http://www.epsa.uq.edu.au/index.html?page=7675&pid=0 for supplementary exams.

 

 

Feedback on assessment:   

 

You may request feedback on assessment in this course progressively throughout the semester from the course coordinator.  Feedback on assessment may include discussion, written comments on work, model answers, lists of common mistakes and the like.

 

Students may peruse examinations scripts and obtain feedback on performance in a final examination provided that the request is made within six months of the release of final course results.  After a period of twelve months following the release of results, examination scripts may be destroyed.

 

Information on the University’s policy on access to feedback on assessment may be found at

http://www.uq.edu.au/hupp/index.html?page=25114&pid=25075

 

EPSA Faculty policy on assessment feedback and re-marking may be found at

http://www.epsa.uq.edu.au/index.html?page=7674&pid=7564 

 

Students with disabilities:

 

Any student with a disability who may require alternative academic arrangements in the course is encouraged to seek advice at the commencement of the semester from a Disability Adviser at Student Support Services.  Refer to the University policy – Students with A Disability (Disability Action plan) HUPP 3.40.6

 

Assistance for Students:

 

Students with English language difficulties should contact the course coordinator or tutors for the course.

 

Students with English language difficulties who require development of their English skills should contact the Institute for Continuing and TESOL Education on extension 56565.  

 

The Learning Assistance Unit located in the Relaxation Block in Student Support Services.  You may consult learning advisers in the unit to provide assistance with study skills, writing assignments and the like.  Individual sessions are available.  Student Support Services also offers workshops to assist students.  For more information, phone 51704 or on the web http://www.sss.uq.edu.au/index.html.

 

Student Liaison Officer:

 

The School of Physical Sciences has a Student Liaison Officer as an independent source of advice to assist students with resolving academic difficulties.

 

The Student Liaison officer during 2006 will be Prof.  Peter Adams, Room 547 Priestley Building, (email pa@maths.uq.edu.au)

 

Other Policies and Guidelines:

 

Working with Children:  Students who will be required to work with children as part of their studies should refer to the University policy – Working with Children Check – “Suitability Card” HUPP 1.60.7

 

Occupational Health and Safety:  Students should be familiar with the University policy on Occupational Health and Safety in the Laboratory (Undergraduate Student) HUPP 2.30.14

 

 

Course Learning Summary:

 

The week plan is:

Week 1: Statement of the initial value problem (IVP) for first order systems and equivalence with a system of integral equations. Background analysis including normed spaces and the Banach Contraction Mapping Principle.

Week 2: Existence for the IVP with lipschitz right side. Gronwall's inequality and variants. Differentiability with respect to parameters.

Week 3: Extendability of solutions.

Week 4: Linear systems, variation of parameters. Constant coefficient systems and Jordan forms. Linearised stability.

Week 5: Stability by Lyapunov's direct method.

Week 6: Periodic solutions. First integrals, the Morse Theorem and Attractors.

Week 7: Two dimensional homogeneous systems: phase plane analysis.

Week 8: Poincare-Bendixson Theory.

Week 9: Periodic solutions via Brouwer's Fixed Point Theorem and

Week 10: Degree Theory.

Week 11: Floquet's Theorem

Week 12: Perturbation Theory and the Poincare--Lindstedt method for periodic solutions.