Assumed Background

• This course will build on foundations that you have obtained in earlier courses: differential and integral calculus, linear algebra, vector analysis, and especially differential equations. In particular, you must have a sound working knowledge of all the material listed in the course summary for MATH2000. It is your responsibility to fill in any gaps in the assumed knowledge. You may need to undertake background reading to understand the lecture material. Chapters 1, 2, 6, 7, 8 and 9 of the set text (E Kreyszig, Advanced Engineering Mathematics, 8th Edition) cover most of the assumed background material.

Teaching Mode

• Three hours of lectures and one hour of tutorial per week.
  • Lectures:
    • Room 63-360, Monday, 8am.
    • Room 63-360, Tuesday, 12pm.
    • Room 63-360, Friday, 9am.
  • Tutorials :
    • Tut. a Room 5-213, Thursday, 12pm.
    • Tut. c Room 50-S201, Friday, 8am.
    • Tut. d Room 43-102, Friday, 2pm.
    • Tut. f Room 67-141, Friday, 3pm.
  • MATH2011 students: Please go to Tut. f. If this is impossible for you, please go to Tut. c.
  • There are no tutorials in the first week of lectures, that is no tutorials on Thursday, July 29 or Friday, July 30. And there are no tutorials in the week beginning September 6, that is no tutorials on Thursday, September 9 or Friday, September 10.

Mid-semester break: One week beginning September 27.

Examination period: Study week is November 1-5. Examination period is November 8-20.

Syllabus

• Topic 1. Systems of Ordinary Differential Equations (Kreyszig Chapter 3). Solutions to Homogeneous Linear Systems of ODE's with constant coeffcients using matrices. The Phase Plane for 2-Dimensional linear and some nonlinear systems. Critical Points and their stability properties. Nonhomogeneous Linear Systems.
• Topic 2. Laplace Transforms (Kreyszig Chapter 5). The Laplace Transform and its Inverse Transform. Linearity, Shifting, Convolution and the use of Partial Fractions. Transforms of Derivatives and Integrals. Use of Laplace Transforms to solve Linear Differential Equations including those involving discontinuous functions such as the Step Function and the Dirac Delta function.
• Topic 3. Fourier Series (Kreyszig Chapter 10). Fourier analysis, and of orthogonal periodic functions. Formulas for Fourier coefficients. When a Fourier expansion works. Even and odd functions and their expansions. When a Fourier expansion works. Even and odd functions and their expansions. Half-range sine and cosine series. Differentiation of Fourier series. Application of Fourier series to a forced oscillator. Concepts of scalar and vector fields. The operator del; grad, div and curl. Flux of a vector field. Idea of a flux integral. Gauss' divergence theorem. Conservation laws. The Laplacian operator. The heat, wave and Laplace's equation in 1, 2, and 3 dimensions.
• Topic 4. Partial Differential Equations (Kreyszig Chapter 11). Nature of solutions of PDEs. Superposition principle for PDEs. General solution of wave equation and d'Alembert's solution of the IVP. Examples. Fourier's method for wave equation. Green's function for the 1-d heat equation. Solution of IVP on whole line. Example. The error function and other examples. Heat conduction and diffusion. Temperature waves in the earth. Kelvin's estimation of the earth's age. Fourier's method for 1-d heat equation with source term. Short-cut when source is time-independent. Revisit 1-d wave equation with forcing. Fourier's method and Laplace's equation in 2-d rectangular region.Continuation: other BCs. Idea of conjugate harmonic functions. Heat stream function. Point source for Laplace's equation in 2-d. Images for point sources/sinks. Other applications of Laplace's equation: Fluid flow, electrostatics. Potentials and stream functions.

• Topic 1. Systems of Ordinary Differential Equations (Kreyszig Chapter 3).
• Topic 2. Laplace Transforms (Kreyszig Chapter 5).

• Topic 3. Fourier Series (Kreyszig Chapter 10).

  Lecture 19: Idea of Fourier analysis, and of orthogonal periodic functions. (Kreyszig Sec.10.1; pp 530, 531, 534)

  Lecture 20: Formulas for Fourier coefficients. (K Secs 10.1, 10.2, 10.3)

  Lecture 21: When a Fourier expansion works. Even and odd functions and their expansions. (K pp 534-5, 541-3)

  Lecture 22: Half-range sine and cosine series. Differentiation of Fourier series. (K pp 544-6).

  Lecture 23: Application of Fourier series to a forced oscillator. Concepts of scalar and vector fields. The operator del; grad, div and curl. (K Sec 10.6; pp 423-4, 427, 446-7, 453, 457)

  Lecture 24: Grad, div and curl. Flux of a vector field. Idea of a flux integral. Gauss' divergence theorem. (K p 481; Secs 9.7, 9.8)

  Lecture 25: Conservation laws. The Laplacian operator. The heat, wave and Laplace's equation in 1, 2, and 3 dimensions. (K p 451, pp 511-12, Secs 11.1, 11.2)

• Topic 4. Partial Differential Equations (Kreyszig Chapter 11).

  Lecture 26: Nature of solutions of PDEs. Superposition principle for PDEs. General solution of wave equation and d'Alembert's solution of the IVP. Examples. (K Secs 11.4, 11.1, 11.2)

  Lecture 27: Fourier's method for wave equation. Meaning of solution. (K Sec 11.3)

  Lecture 28: Fourier's method for 1-d heat equation. Interpretation. Examples. (K Secs 11.3, 11.5).

  Lecture 29: Green's function for the 1-d heat equation. Solution of IVP on whole line. Example. The error function. (K p 612).

  Lecture 30: More examples. method of images on semi-axis.

  Lecture 31: Heat conduction and diffusion. Temperature waves in the earth. Kelvin's estimation of the earth's age.

  Lecture 32: Fourier's method for 1-d heat equation with source term. Short-cut when source is time-independent. Revisit 1-d wave equation with forcing.

  Lecture 33: Fourier's method and Laplace's equation in 2-d rectangular region.

  Lecture 34: Continuation: other BCs. Idea of conjugate harmonic functions. Heat stream function. (K pp 605-9; 808; 673)

  Lecture 35: Point source for Laplace's equation in 2-d. Images for point sources/sinks.

  Lecture 36: Other applications of Laplace's equation: Fluid flow, electrostatics. Potentials and stream functions.

Course materials

• Course Notes: Hard copies of the lecture overheads will be distributed at the start of each lecture, and the overheads will be scanned into the course web page after lectures each week.
• Text: The compulsory text is

  Advanced Engineering Mathematics, 8th Edition by E Kreyszig (John Wiley & Sons).

  Some assignments will be set from this book. MATH2100 deals mainly with Chapters 3, 5, 10 and 11. (MATH2010 deals mainly with Chapters 3 & 5; MATH2011 deals mainly with Chapters 10 & 11.) If you have an earlier edition of Kreyszig's book, that will be fine for the theory in the course, but you may need to check the assignment questions each week with a copy of the 8th edition in the reserved section of the PS&E Library.

• References: There are many other books containing the course material, which forms a standard part of the mathematician's, physical scientist's and engineer's toolkit.

  Other books along the lines of Kreyszig may be found in the PS&E Library under the call number QA401.

  More specialised books may be found under QA371, QA372, QA404 and QA432. (See also Kreyszig, Appendix 1, for more references.)

  Some good specialised books are:

  P. Blanchard, R L Devaney and G R Hall Differential Equations QA371 .B58 1996.

  W E Boyce and R C DiPrima, Elementary Differential Equations, QA372.B3 1997.

  W T Thompson, Laplace Transformations, QA432.T5 1960.

  R V Churchill & J W Brown, Fourier Series and Boundary Value Problems, QA404.C6 1978.

  (The first threeo books are mainly for the first half of MATH2100, and for MATH2010; the fourth book is for the second half of MATH2100 and for MATH2011.)

  You may also find useful the lecture notes of Dr Phil Diamond, who previously taught this course under the name MT253, and also the lecture notes on ODEs by Dr Alan Jones.

Assessment

• For MATH2100, there will be 10 assignments, each worth 3.5%. The due dates are:
  • Assignment 1: Your tutorial on August 5 or 6.
  • Assignment 2: Your tutorial on August 12 or 13.
  • Assignment 3: Your tutorial on August 19 or 20.
  • Assignment 4: Your tutorial on August 26 or 27.
  • Assignment 5: Your tutorial on September 2 or 3.
  • Assignment 6: Your tutorial on September 16 or 17.
  • Assignment 7: Your tutorial on September 23 or 24.
  • Assignment 8: Your tutorial on October 7 or 8.
  • Assignment 9: Your tutorial on October 14 or 15.
  • Assignment 10: Your tutorial on October 21 or 22.
• For MATH2010, there will be 5 assignments, each worth 7%. The due dates are:
  • Assignment 1: Your tutorial on August 5 or 6.
  • Assignment 2: Your tutorial on August 12 or 13.
  • Assignment 3: Your tutorial on August 19 or 20.
  • Assignment 4: Your tutorial on August 26 or 27.
  • Assignment 5: Your tutorial on September 2 or 3.
• For MATH2011, there will be 5 assignments, each worth 7%. The due dates are:
  • Assignment 1: Your tutorial on September 16 or 17.
  • Assignment 2: Your tutorial on September 23 or 24.
  • Assignment 3: Your tutorial on October 7 or 8.
  • Assignment 4: Your tutorial on October 14 or 15.
  • Assignment 5: Your tutorial on October 21 or 22.

  Each assignment will be set in lectures, one week before the tutorial at which it is due to be handed in. So the first assignment for MATH2100/2010 will be set on the Tuesday or Friday of the first week of lectures, to be handed in by the end of your tutorial on the Thursday or Friday of the second week. The first assignment for MATH2011 (the 6th for MATH2100) will be due Thursday 16th or Friday 17th September. There are no tutorials on Thursday 29th July or Friday, 30th July, nor on Thursday 9th September or Friday 10th September.

Missed assessment items

Feedback on Assessment

You will receive feedback on assignments during the course in the form of marks and written comments on assignments. You will also be able to download model answers to assignment questions after each assignment has been marked, and handed back to students. Further feedback may be obtained from the course coordinator and the two specialist tutors.

Students may peruse examination 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=6

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

Plagiarism

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 palgiarism 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.

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

For more information on the University's policy on plagiarism, please refer to http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=40&s3=12.

Final Examination

• The final examination for MATH2100 will be closed book, 2 hours long, at the end of the semester. It will count 65% towards the final grade. Calculators will be permitted, but memory must be cleared before entering the exam room. There will be NO MID-SEMESTER examination.
• The final examination for MATH2010 will be closed book, 1 hour long, at the end of the semester. It will count 65% towards the final grade. Calculators will be permitted, but memory must be cleared before entering the exam room. There will be NO MID-SEMESTER examination.
• The final examination for MATH2011 will be closed book, 1 hour long, at the end of the semester. It will count 65% towards the final grade. Calculators will be permitted, but memory must be cleared before entering the exam room. There will be NO MID-SEMESTER examination.

Assessment Criteria

• Grade of 7: the student demonstrates an outstanding understanding of the theory of the topics listed in the syllabus, and outstanding ability to apply the asociated techniques to solve problems. Typically students must obtain a final percentage of at least 85 to be awarded a 7.
• Grade of 6: the student demonstrates a comprehensive understanding of the theory of the topics listed in the syllabus, and proficiency in applying the associated techniques to solve problems. Typically students must obtain a final percentage of 75 - 84 to be awarded a 6.
• Grade of 5: the student demonstrates an adequate understanding of the theory of the topics listed in the syllabus, and ability to apply the associated techniques to solve moderately difficult problems. Typically students must obtain a final percentage of 65 - 74 to be awarded a 5.
• Grade of 4: the student demonstrates an understanding of the theory of the topics listed in the syllabus, and the ability to apply the associated techniques to solve straightforward problems. Typically students must obtain a final percentage of 50 - 64 to be awarded a 4.
• Grade of 3: the student demonstrates some understanding of the theory of the topics listed in the syllabus, and the ability to apply the associated techniques to solve some straightforward problems. Typically students must obtain a final percentage of 45 - 49 to be awarded a 3.
• Grade of 2: the student demonstrates little understanding of the theory of the topics listed in the syllabus, and little ability to apply the associated techniques to solve problems. Typically students must obtain a final percentage of 20 - 44 to be awarded a 2.
• Grade of 1: the student demonstrates very little understanding of the theory of the topics listed in the syllabus, and very litle ability to apply the associated techniques to solve problems. Typically students must obtain a final percentage of 1 - 19 to be awarded a 1.

Graduate Attributes:

In-depth knowledge of the fields of study

• A comprehensive and well-founded knowledge of the mathematical techniques required to solve ODE's (MATH2010 and first half of MATH2100) and PDE's (MATH2011 and second half of MATH2100) by attending lectures and solving assignment problems.
• An understanding of how Biology, Physics, Chemistry and Engineering use Differential Equations to model various types of behaviour.
• An international perspective on the field of Differential Equations developed by using internationally accepted standards of mathematical rigour and notation, and a text-book recognised world-wide.

Effective Communication

• The ability to collect, analyse and organise information and ideas, and to convey these ideas clearly and fluently in written form, developed through tutorial assignments.
• The ability to interact effectively with others in order to work towards a common outcome, developed through cooperative problem solving strategies on assignments.
• The ability to select and use the appropriate level, style and means of communication, developed through assignments and tutorials.
• The ability to engage effectively and appropriately with information and communication technologies, developed through practical use of pen, ink, calculators and computers.

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, recognise when they are solvable, create solutions, and improve innovatively on current practices.

Critical Judgement

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

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, developed through the experience of a discipline where the concepts of right and wrong are suported by universal and absolute standards.
• A knowledge of other cultures and times, and an apprecaition of cultural diversity, developed by participating in tutorials and classes in a course 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

Personal Matters

• 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 free academic and personal support to students in a confidential environment. If appropriate, they will provide a letter to give to your Faculty Office which may help your case for a special exam. (There is no longer special consideration for examinations.) Do not leave it too late to seek help!. 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, lecturers prefer this course of action, as they are not qualified to assess medical evidence. The procedure outlined here accords with the University's policy on student privacy and confidentiality.

Student Liaison Officer

Dr Peter Adams, Room 547, Priestley Building, email: pa@maths.uq.edu.au is available to offer independent academic advice to help students resolve difficulties with MATH2100/2010/2011, for example if you are unhappy with the way lecture or tutorial materials are organised or presented.