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

2nd Semester, 2003

(2 unit, 3L 1T)

Course Objective

• 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.

Contact and Advice

• The course coordinator is Dr. Yao-Zhong Zhang, room 67-702 in 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 33653256 or by email at yzz@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

• 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.

Teaching Mode

• Three hours of lectures and one hour of tutorial per week.
• Lectures: Mon 9-10am 67-342, Wed 8-9am 67-343, Fri 9-10am 8-212
• Tutorials: Tue 3-4pm 67-342
• There are no tutorials in week 1
• Public holidays: 13 August, 2003.
• Examination period: 10-22 November, 2003.

Syllabus

• 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.

Resources

• Course Notes: Notes are available at the course web page. There are no set textbooks. 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.
• Web: The course web page is at http://www.maths.uq.edu.au/courses/MATH3102. Information about the course and other resources are available there.

Assessment

• Assessment Scheme: 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

• 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 at the end of 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!
• Two hour written examination at the end of the semester held at a time to be advised by Examinations Section.
• 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.
• 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.
• Assessment Criteria:
  • 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.

Graduate Attributes

The University has a statement of Graduate Attributes ( http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=20&s3=5) which describes core attributes to be developed in an undergraduate program.

The following graduate attributes will be developed in this course:

• In-Depth Knowledge of the Field of Study
  • A comprehensive and well-founded knowledge of the field of study.
• 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.
  • The ability to interact effectively with others in order to work towards a common outcome.
  • The ability to select and use the appropriate level, style and means of communication.
  • The ability to engage effectively and appropriately with information and communication technologies.
• Independence and Creativity
  • The ability to identify problems, create solutions, innovate and improve current practices.
• 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.

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.