Course Profile for MATH3102 - Methods and Models of Applied Mathematics B

2nd Semester, 2004

Brief Description

This course covers two main modules: 1. Vector analysis and complex analysis; 2. Models described in terms of partial differential equations and their solutions using the methods of separation of variables, Fourier and Laplace transforms.

You will learn how to model various types of `real-world' problems and how to solve these models by means of mathematical methods developed in the course. Main applications discussed in the unit are heat conduction/diffusion in solids, perfect fluid flow, potential theory and the spread of pollutants.

Staff (Course Coordinator): Dr. Yao-Zhong Zhang

Lecturers and Contact Details

• Name: Dr Yao-Zhong Zhang
• Room: 67-702, in Priestley Building, (building 67)
• Phone number: 336 53256
• Email: yzz@maths.uq.edu.au.
• Consultation hours: Tue 4-5pm, Wed 2-4pm

You are welcome to ask any questions about the course during consultation hours. Unfortunately, tutors are not paid to answer queries out of tutorial classes, so you should contact the lecturer directly.
If you have questions about your current or future program of study, contact the chief academic advisor , honours coordinator or postgraduate coordinator .

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/MATH3102 . 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 and Venue: 2 units, 3L, 1T

• Lectures: Tue 3-4pm 67-343, Wed 9-10am 67-341, Thu 11am-12pm 67-342
• Tutorial: Thu 12-1pm 67-342

Assumed Background

• Students should have taken MATH2100. A basic knowledge of vector analysis, PDE's, ODE's and complex variable methods (contour integrations) will be assumed. It is a student's own responsibility to fill in any gaps in their assumed knowledge. You may need to undertake background reading to understand the lecture material.

Course Goals/Objectives

• MATH3102 aims to consolidate students' knowledge and skills in vector analysis, complex analysis, Fourier and Laplace transformations, and their applications to various physical models. Main applications discussed in this unit are heat conduction/diffusion, perfect fluid flow, potential theory and spread of pollutants.

Graduate Attributes

The following graduate attributes will be developed in the course -

1. 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.

2. 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.
   • The ability to engage effectively and appropriately with information and communication technologies: - through practical use of pen, ink, and computers.

3. Independence and Creativity

   • The ability to work and learn independently.
   • The ability to generate ideas and adapt innovatively to changing environments.
   • The ability to identify problems, create solutions, innovate and improve current practices.

4. Critical Judgement

   • The ability to define and analyse problems.
   • The ability to apply critical reasoning to issues through independent thought and informed judgement.
   • The ability to evaluate opinions, make decisions and to reflect critically on the justifications for decisions.

5. Ethical and Social Understanding

   • An appreciation of the philosophical and social contexts of the discipline.
   • A knowledge and respect of ethics and ethical standards in relation to a major area of Study: - through the experience of a discipline where the concepts of right and wrong are supported by universal and absolute standards.
   • 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 .

Teaching and Learning Methods

• Three hours of lectures and one hour of tutorial per week.
• Lectures and Tutorials: See SI-net.
• There are no tutorials in week 1 and week 13.
• Public holidays: There are no lectures and tutorials on the public holidays.
• Examination period: Study week is November 1-7, 2004, Examination period is 8-21 November, 2004.

Students should attend all the lectures. In truth most people cannot follow immediately all the details of a mathematical lecture; but try to get at least a broad overview of the material. Afterwards work through the material carefully, using lecture notes (on the web) or the reference books. It is important to understand the examples discussed in lectures, and it is good idea to make sure you can do the examples by yourself with the solution covered up. Of course this does not mean memorizing the solution, rather it is a check that you understand the key steps involved.

Assignment sheets will be handed out in lectures every two weeks and are available on the web. The solutions to each assignment will also be handed out after its due date.

Resources (Textbook and References)

• Course Notes: Notes are available at the course web page.
• Text: There is no set textbook. Lecture notes must be taken in the lectures.
• References: The reference books are:
  • "Applied Vector Analysis" by H.P. Hsu, Harcourt Brace Jovanovich College outline series
  • "Advanced Engineering Mathematics", by E. Kreyszig, John Willy, PS & E Library QA401.K7 1999
  • "Advanced Calculus for Applications", by F.B. Hildebrand, Prentice-Hall, PS & E Library QA303.H55 1976
  • "Functions of a Complex Variable" by G.F. Carrier, M. Krook and C.E. Pearson, McGraw-Hill, PS & E Library QA331.C315 1996
  • "Fourier Series and Boundary Value Problems", by R.V. Churchill, McGraw-Hill, PS & E Library QA404.C6 1993
  • Many books can be found in the library under QA303, QA330, QA331, QA377, QA401, QA403, QA404 and QA433.
• Library contact: The liaison librarian for Earth Sciences/Maths/Physics 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.

Assessment

• Required Assessment Tasks: Assessment will be based on the following two components:

  Assessment Item	Brief Description	Weighting
  Assignments	5 assignments	40
  End of semester Exam	2 hours	60

• The due dates for assignments are:
  • Assignment 1: due 5pm, Thursday August 19.
  • Assignment 2: due 5pm, Thursday September 2.
  • Assignment 3: due 5pm, Thursday September 16.
  • Assignment 4: due 5pm, Thursday October 7.
  • Assignment 5: due 5pm, Thursday October 21.
• Failure to complete any part of any item of the assessment will result in your receiving a mark of 0 for that part of that item of the assessment.
  To determine your grade for MATH3102 we will use the the sum of marks from the assignments and end of semester exam and apply the ``ASSESSMENT CRITERIA'' listed in this guide.
• Collaboration on assignments is allowed, but must write out your own solutions in your own way. Identical assignment solutions will share the marks!
• Final Examination: Two hour written examination at the end of the semester. Anything discussed in lectures is examinable. In addition, problems from assignments and tutorials as well as similar problems may form part of the written exam.
• Criteria for the Award of Grades: Solutions will be marked for accuracy, appropriateness of mathematical techniques and clarity of presentation, as demonstrated by examples presented in lectures.
  • To earn a Grade of 7, a student must demonstrate an excellent understanding of the course material. 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. They will be able to apply techniques to completely solve both theoretical and practical problems.
  • To earn a Grade of 6, a student must demonstrate a comprehensive understanding of the course material. 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. They will be able to apply techniques to partially solve both theoretical and practical problems.
  • To earn a Grade of 5, a student must demonstrate an adequate understanding of the course material. 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. They will be able to apply techniques to solve fundamental problems.
  • To earn a Grade of 4, a student must demonstrate an understanding of the basic concepts of the course material. 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 justification. 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 demonstrate some knowledge of the basic concepts of the course material. 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 demonstrate some knowledge of the basic concepts of the course material. 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 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.
• Assessment Policy: As solutions to assignments are distributed promptly, credit cannot be given for late assignments. Students who miss assignments through bereavement or ill health should document their problems and discuss this with the lecturer of the course. An alternative due date may be negotiated between the student and lecturer. Allowance cannot be made for reasons such as sporting or social commitments, or overwork in other courses.
  Students should be familiar with the assessment rules in their degrees as well as general university policy such as found in the General Award Rules. These are all set out on the Program and Course Information page on the UQ website http://www.uq.edu.au/student/courses/ .

Plagiarism

Below is the University's definition of plagiarism Plagiarism is the action or practice of taking and using as one's own the thoughts or writings of another (without acknowledgement). The following practices constitute acts of plagiarism and are a major infringement of the University's academic values:

• (a) where paragraphs, sentences, a single sentence or significant part of a sentence which are copied directly, are not enclosed in quotation marks and appropriately footnoted;
• (b) where direct quotations are not used, but are paraphrased or summarised, and the source of the material is not acknowledged either by footnoting or other simple reference within the text of the paper;
• (c) where an idea which appears elsewhere in print, film or electronic medium is used or developed without reference being made to the author or the source of that idea.

Supplementary examinations

New University assessment rules relating to supplementary examinations are accessible at the following URL: http://www.uq.edu.au/student/GeneralRules2003/2003GARs.htm . In general, the effect of this rule is to provide for one supplementary examination to a student in his or her final semester of enrolment where a passing grade is required to complete the program. There are, however, exceptions to this rule and transition rules for some cohorts of students. You should check the program 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 within 14 days of the publication of results.

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.

Further Information

More information on the General Award Rules at the University can be found at http://www.uq.edu.au/student/GeneralRules2003/2003GARs.htm .

More information on the University's assessment policy may be found at http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=5 .

EPSA Faculty policy on the award of special and supplementary exams may be found at http://www.epsa.uq.edu.au/index.html?id=9329&pid=7564 .

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. ( http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=6 )

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 six 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/contents/view.asp?s1=3&s2=30&s3=5 .

EPSA Faculty policy on feedback and re-marking may be found at http://www.epsa.uq.edu.au/index.html?id=7674&pid=7564 .

For a remark on the final exam (after viewing the exam on a viewing day), students are to complete a "Request for assessment re-marking form".

The link to the policy is http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=2 .

The form may be downloaded from there -- section 3.6 of the policy at http://www.uq.edu.au/hupp-download/Request%20Assessment%20Re_Marking%20Form.pdf .

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.

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 will be Assoc Prof Peter Adams, Room 547 Priestley building, (email pa@maths.uq.edu.au ).

Course Schule: Program of Work for the Semester

• Elements of vector analysis:
  Gradient, divergence, curl, curvilinear coordinates, line integrals and surface integrals, Stoke's theorem, Gauss theorem and Green's theorem.
• Heat conduction in solids:
  Heat conduction equation, one-dimensional heat flow and its fundamental solution, generalized functions, convolution integrals.
• Inviscid/perfect fluid flow -- continuum mechanics:
  Spatial and material description of flow, continuity equation, incompressible fluid, potential flow, Euler's and Bernoulli's equations.
• Potential theory.
• Spread of pollutants:
  Convection-diffusion equation, steady one-dimensional problem, two-dimensional problem.
• Separation of variables and Sturm-Liouville theory.
• Review of complex variables:
  Analytic functions, multi-valued functions, Cauchy's residue theorem and contour integrals.
• Fourier transforms:
  Fourier transform of delta function, properties and applications of Fourier transforms, Green's functions and convolution theorem.
• Laplace transforms:
  Properties, Laplace transform and PDE's, Laplace transform convolution and applications to physical models.

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/MATH3102). It is your responsibility to keep up to date with all information presented in your lecture group.

MATH3102 Web Page.