Course Profile for MATH4403 Partial Differential Equations, 2003

(2 unit, 3L 1T)

Course Objective

• The course aims to introduce students to the theory of partial differential equations of the second order through careful motivation, mathematical methods and physical applications.

Contact and Advice

• The course coordinator is Dr J. Chabrowski, room 67-345in the Priestley Building, (building 67). If you have any comments or suggestions on the course or have questions on the course material, contact the coordinator by phone on 3365 3259 or by email at jhc@maths.uq.edu.au . You are welcome to ask any questions about the course during consultation hours. Unfortunately, tutors are not paid to answer queries out of class hours, so you should contact lecturers directly. If you have questions about your current or future program of study, contact the chief academic advisor, honours advisor or postgraduate advisor .

Assumed Background

• The formal prerequisite: MATH2400 or MT251. Specifically, based on these courses students should have a basic appreciation of multivariable calculus, and an appreciation of the basics of partial differential equations.

Teaching Mode

• Three hours of lectures and one hour of tutorial per week. In tutorials, students will be expected to solve tutorial problems. Solutions to all tutorial problems will be handed out at appropriate the time. Students should feel free to approach the lecturer at times other than consultation hours.
• Lectures: Monday 10-11, Tuesday 11-12, Thursday 9-10 in 67-641.
• Tutorials: Tuesday 2-3 in 67-641.
• There are no tutorials in week 1
• Examination period: The examination period is November 8-22, 2003.

Syllabus

• The maximum principle for differential equations,
• maximum principle for elliptic equations,
• Hopf's maximum principle,
• sub and superharmonic functions,
• Dirichlet problem,
• Harnack inequality,
• Perron method,
• irregular and regular boundary points,
• maximum principle for parabolic equations,
• boundary value problems for parabolic equations,
• Cauchy problem,
• boundary value problems for hyperbolic equations.

Information Changes

• Any changes to course information will be announced in lectures and the information will be reproduced on the web page ( http://www.maths.uq.edu.au/courses/MATH4403). It is your responsibility to keep up to date with all information presented in your lecture group.

Resources

• Course Notes: Lecture notes must be taken in the lectures.
• Text: There is no text
• References: The Physical Sciences and Engineering Library has plenty of suitable reference books. 1) Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice - Hall 1967, 2) Mark A. Pinsky, Partial differential equations and boundary value problems with applications, McGrow - Hill, Inc. 1991, 3) A. Friedman, Partial differential equations of parabolic type, Englewood Cliffs, N.J. Prentice - Hall Inc. 1964 4) D. Gilbarg and N.F. Trudinger, Elliptic partial differential equations of second order (second edition), Springer Verlag 1983
• Web: The course web page is at http://www.maths.uq.edu.au/courses/MATH4403. Information about the course and other resources are available there.

Assessment

• Assessment Scheme: There will be 2 assignments, which will contribute 30% to the final assessment. The remaining 70% will be derived from a 3 hour examination paper at the end of the semester. Students will be expected to display competence in both theoretical and practical areas of the syllabus. There is no mid-semester exam.
• Assignments and tutorials: You are expected to come to tutorials.
• Assignment submission: Your assignment should be handed to the tutor/lecturer at the end of the tutorial. Please mark your assignment with your name, student number, the date, the subject and assignment number and your student number. Assignments will be returned with marks and comments within two weeks. Ask at the tutorial if your marked assignment is not returned promptly or if you have any questions about the marking.
• If you miss an assessment item: In case of illness (or bereavement) you may be exempted from an assignment if a medical certificate (or other documentation) is received by the course co-ordinator within one week of the due date of the assignment. If you are exempted, then your assignment marks are weighted on a pro-rata basis. Note that ad hoc excuses (car trouble and the like!) will not be accepted; only documentation in connection with illness or bereavement . If you enrolled late then exemption will automatically be granted for anything missed before the date of enrolment.
• Plagiarism: Plagiarism is the act of using other author's ideas and words or solutions without acknowledgement. It is a form of cheating and is considered as misconduct under official university policy and may attract severe penalties. You must not engage in plagiarism in any of your assignments. For more information, consult the libarary UseIt on Plagiarism: http://www.library.uq.edu.au/ssah/useits/plaguseit.html.
• Midsemester Examination: Held in around week 6 in lecture time. It is worth 20%. The exam will be 1 hour long. Calculators without ASCII capabilities are permitted.
• Final Examination: The final exam is a closed book 3 hour exam. Calculators without ASCII capabilities are permitted. The exam will be held at a time to be advised by Examinations Section. Anything discussed in lectures is examinable. In addition problems from assignments, tutorial sheets and relevant sections of the references (where explicit reference has been made) as well as similar problems may form part of the written exam.
• Assessment Criteria:
  • To earn a Grade of 7, a st udent must achieve a final mark of at least 85% and demonstr ate an excellent understanding of all of the theory. This includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification.
  • To earn a Grade of 6, a student must achieve a final mark of at least 75% and demonstrate a comprehensive understanding of the theory of advanced analysis. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification.
  • To earn a Grade of 5, a student must achieve a final mark of at least 65% and demonstrate an adequate understanding of the course theory. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification.
  • To earn a Grade of 4, a student must achieve a final mark of at least 50% and demonstrate an understanding of the basic concepts of advanced analysi s. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate just ification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases.
  • To earn a Grade of 3, a student must achieve a final mark of at least 45% and demonstrate some knowledge of the basic concepts of advanced analysis. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems.
  • To earn a Grade of 2, a student must achieve a final mark of at least 20% and demonstrate some knowledge of the basic concepts of advanced analysis. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately.
  • A student will receive a Grade of 1 if they achieve a final mark of at most 19% or demonstrate extremely poor knowledge of the basic concepts in the course material. This includes attempts at answering some questions but showing an extremely poor understanding of the key concepts.

Personal Situation

• 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.
• Personal Crises: If you feel that problems in your life are interfering with your university performance, you should consult Student Support Services in the Student Union complex. They offer academic and personal support in a confidential environment for free to students. They can provide a letter to give to lecturers which will help your case for a special exam (there is no longer special consideration for examinations), but do not leave it too late. If you are concerned about privacy with regard to medical certificates, please contact the University Health Service. With your permission, the Director will contact your treating practitioner to clarify the extent of your medical condition or other incapacity, and provide lecturers with a report - the Director is bound by confidentiality obligations. In any case, we prefer this course of action, as we are not qualified to assess medical evidence. The procedure outlined here accords with the University's policy on student privacy and confidentiality.