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MATH336 – Partial Differential Equations

2017 – S2 Day

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Lecturer
Christopher Lustri
12 Wally's Walk, 714
Wednesday 3-4pm
Lecturer
Ji Li
12 Wally's Walk, 710
Tuesday 10-11am
Ji Li
Credit points Credit points
3
Prerequisites Prerequisites
MATH235 and (MATH232 or MATH236)
Corequisites Corequisites
MATH331 or MATH332 or MATH335 or MATH339
Co-badged status Co-badged status
Unit description Unit description
Partial differential equations form one of the most fundamental links between pure and applied mathematics. Many problems that arise naturally from physics and other sciences can be described by partial differential equations. Their study gives rise to the development of many mathematical techniques, and their solutions enrich both mathematics and their areas of origin. This unit explores how partial differential equations arise as models of real physical phenomena, and develops various techniques for solving them and characterising their solutions. Special attention is paid to three partial differential equations that have been central in the development of mathematics and the sciences – Laplace's equation, the wave equation and the diffusion equation.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at http://students.mq.edu.au/student_admin/enrolmentguide/academicdates/

Learning Outcomes

  1. Knowledge of the principles and concepts of a basic theory of partial differential equations.
  2. Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  3. Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  4. Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  5. Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  6. Preparing students to further studies in the areas of partial differential equations and advanced analysis.

General Assessment Information

HURDLES

This unit has no hurdle requirements. This means that there are no second chance examinations and assessments if you happen to fail at your first attempt, and your final grade is determined by adding the marks obtained for your examinations and assessments. Students should aim to get at least 60% for the course work in order to be reasonably confident of passing the unit.

SUPPLEMENTARY EXAMINATIONS

IMPORTANT: If you apply for Disruption to Study for your final examination, you must make yourself available for the week of December 11 – 15, 2017 for a supplementary examination.  If you are not available at that time, there is no guarantee an additional examination time will be offered. Specific examination dates and times will be determined at a later date

Assessment Tasks

Name Weighting Due
Assignment 1 10% Week 4
Assignment 2 10% Week 8
Assignment 3 10% Week 12
Mid-term Test 20% Week 9
Final Exam 50% Exam Period

Assignment 1

Due: Week 4
Weighting: 10%

Assignment based on work from Weeks 1-3.


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assignment 2

Due: Week 8
Weighting: 10%

Assignment based on work from Weeks 4-7.


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assignment 3

Due: Week 12
Weighting: 10%

Assignment based on work from Weeks 8-11.


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Mid-term Test

Due: Week 9
Weighting: 20%

Class test based on work from Weeks 1-8.


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Final Exam

Due: Exam Period
Weighting: 50%

Final examination based on all course material.


This Assessment Task relates to the following Learning Outcomes:
  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Delivery and Resources

Classes

Lectures: you should attend two hours of each lecture stream each week, making a total of four hours.

Required and Recommended Texts and/or Materials

No single textbook is entirely satisfactory for MATH336. The following text is not required, but can provide useful references for various sections of the course:

  • W. A. Strauss Partial Differential Equations, an introduction.  Wiley 2008

Technology Used and Required

Students are expected to have access to an internet enabled computer with a web browser and Adobe Reader software. Several areas of the university provide wireless access for portable computers. There are computers for student use in the Library.

Difficulties with your home computer or internet connection do not constitute a reasonable excuse for lateness of, or failure to submit, assessment tasks.

Unit Schedule

Week Stream A (Tuesday) Stream B (Wednesday)
1

Introduction to PDE (partial differential equations), first order PDE methods: characteristic lines, changing of coordinates.

Introductory modelling: flows, vibrations, and diffusions.
2 First order PDE: general case, constant coefficients, function coefficients. Initial and boundary conditions.
3

Second order linear PDE: general forms and classifications: hyperbolic, parabolic, and elliptic.

Waves equation with initial conditions: d'Alembert's methods.
4 Second order linear PDE: canonical forms, and reduction of the general forms to canonical forms. Wave equation with initial conditions: energy methods.
5

Boundary value problems for heat equations: Dirichlet, Neumann, and Robin conditions.

The diffusion equation, maximal principle, uniqueness, stability.
6 Boundary value problems for heat equations: Dirichlet, Neumann, and Robin conditions. The diffusion equation on the whole line and half line.
7 Fourier series: coefficients; even, odd, and periodic functions; completeness; convergence. Reflection of waves: Dirichlet problem on the half-line, finite interval,
8 Inhomogeneous wave and heat equations. Diffusion with a source: the inhomogeneous diffusion equation on the whole line with initial conditions.
9 Laplace equations, maximal principle, fundamental solutions, Wave with a source: inhomogeneous wave equation on the whole line with initial conditions.
10 Laplace equations in specific domains: rectangles, disc, wedges, annuli. Finite-difference methods: explicit and implicit numerical schemes.
11 Laplace equations in general domains : Green's identity, Green's functions. Finite-difference methods: numerical stability, application to canonical equations.
12 Laplace equations in upper-half space: Green's identity, Green's functions. Advanced numerical methods: irregularly shaped domains, finite element method.
13 Revision Revision

 

Learning and Teaching Activities

Lectures

There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central. Students should be aware of the following policies in particular with regard to Learning and Teaching:

Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html

Assessment Policy http://mq.edu.au/policy/docs/assessment/policy_2016.html

Grade Appeal Policy http://mq.edu.au/policy/docs/gradeappeal/policy.html

Complaint Management Procedure for Students and Members of the Public http://www.mq.edu.au/policy/docs/complaint_management/procedure.html​

Disruption to Studies Policy http://www.mq.edu.au/policy/docs/disruption_studies/policy.html The Disruption to Studies Policy is effective from March 3 2014 and replaces the Special Consideration Policy.

In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/

Results

Results shown in iLearn, or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au.

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.

Student Enquiry Service

For all student enquiries, visit Student Connect at ask.mq.edu.au

Equity Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

Graduate Capabilities

Discipline Specific Knowledge and Skills

Our graduates will take with them the intellectual development, depth and breadth of knowledge, scholarly understanding, and specific subject content in their chosen fields to make them competent and confident in their subject or profession. They will be able to demonstrate, where relevant, professional technical competence and meet professional standards. They will be able to articulate the structure of knowledge of their discipline, be able to adapt discipline-specific knowledge to novel situations, and be able to contribute from their discipline to inter-disciplinary solutions to problems.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Problem Solving and Research Capability

Our graduates should be capable of researching; of analysing, and interpreting and assessing data and information in various forms; of drawing connections across fields of knowledge; and they should be able to relate their knowledge to complex situations at work or in the world, in order to diagnose and solve problems. We want them to have the confidence to take the initiative in doing so, within an awareness of their own limitations.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Effective Communication

We want to develop in our students the ability to communicate and convey their views in forms effective with different audiences. We want our graduates to take with them the capability to read, listen, question, gather and evaluate information resources in a variety of formats, assess, write clearly, speak effectively, and to use visual communication and communication technologies as appropriate.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Capable of Professional and Personal Judgement and Initiative

We want our graduates to have emotional intelligence and sound interpersonal skills and to demonstrate discernment and common sense in their professional and personal judgement. They will exercise initiative as needed. They will be capable of risk assessment, and be able to handle ambiguity and complexity, enabling them to be adaptable in diverse and changing environments.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Critical, Analytical and Integrative Thinking

We want our graduates to be capable of reasoning, questioning and analysing, and to integrate and synthesise learning and knowledge from a range of sources and environments; to be able to critique constraints, assumptions and limitations; to be able to think independently and systemically in relation to scholarly activity, in the workplace, and in the world. We want them to have a level of scientific and information technology literacy.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Creative and Innovative

Our graduates will also be capable of creative thinking and of creating knowledge. They will be imaginative and open to experience and capable of innovation at work and in the community. We want them to be engaged in applying their critical, creative thinking.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Commitment to Continuous Learning

Our graduates will have enquiring minds and a literate curiosity which will lead them to pursue knowledge for its own sake. They will continue to pursue learning in their careers and as they participate in the world. They will be capable of reflecting on their experiences and relationships with others and the environment, learning from them, and growing - personally, professionally and socially.

This graduate capability is supported by:

Learning outcomes

  • Knowledge of the principles and concepts of a basic theory of partial differential equations.
  • Ability to use the ideas and techniques of the theory of partial differential equations to a model broad range of phenomena in science and and engineering (in particular using the heat and wave equations).
  • Understanding of the breadth of the theory of partial differential equations and its role in other fields.
  • Ability to construct logical, clearly presented and justified mathematical arguments incorporating deductive reasoning especially in the context of the theory of partial differential equations
  • Demonstrate efficient use of Fourier analysis techniques in the theory of partial differential equations.
  • Preparing students to further studies in the areas of partial differential equations and advanced analysis.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Mid-term Test
  • Final Exam

Learning and teaching activities

  • There will be two, two hours long lectures per week. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

Changes since First Published

Date Description
21/07/2017 Added information about supplementary exams
14/07/2017 Fixed wording in first section