cosc3x11

Faculty of Science

School of Physics

COSC3X11: Scientific Computing / Scientific Computing(Adv)

Semester 1 , 2015 | 6 Credit Points | Coordinator: A/Prof Mike Wheatland([email protected])

1 IntroductionCOSC 3011/3911 Scientific Computing is a 6-credit point unit available to Senior students in a variety ofdegree programs, and is a core unit in the Computational Science (COSC) major. This unit provides aSenior-level treatment of problem solving using computers, with applications in physics and related areas ofscience. Students will learn to apply a variety of numerical schemes for solving ordinary and partialdifferential equations. Emphasis is placed on the suitability of particular methods to particular problems, andon the understanding of numerical accuracy and stability. The module will involve a mix of lectures andcomputational lab sessions. All coding is done in MATLAB and basic programming experience is assumed.

Students enrolled in the Advanced unit/module encounter a selection of more challenging laboratory andassignment questions, and the written examination contains a question for Advanced students only. The labsessions, assignments, and project provide practical experience in scientific programming and inimplementing numerical methods to solve science problems.

1.1 Assumed Knowledge and Prohibitions Assumed Knowledge

MATH2061 or MATH2961 or MATH2067 or equivalentSome programming experience in MATLAB

2 Course Aims, Learning Objectives andGraduate Attributes

2.1 Course AimsAfter taking this course, you should have sound knowledge of a range of methods for numerical solution ofOrdinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), as well as understanding

of the accuracy and stability of those methods. Advanced students are expected to gain a deeperunderstanding and the ability to understand more complex and/or new methods. A core aim is to train you toimplement the methods in code yourself in MATLAB. To this end, much of the course is spent in hands-onproblem solving in the lab, and in the project, which provides an opportunity to test your skills on newproblems and methods.

2.2 Learning Outcomes After successfully completing this unit, you should be able to demonstrate:

1.

Understanding of the different types of numerical error (rounding and range error, and localand global truncation error), and the ability to estimate when these errors become important innumerical calculations.

2.

Understanding of the general form of the Ordinary Differential Equations (ODEs) describingdynamics problems, and an ability to solve these problems numerically using Eulers methodand other elementary methods.

3. Understanding of non-dimensionalisation, and the ability to non-dimensionalise new problems.4. Understanding of, and the ability to implement, elementary methods for numerical solution ofdynamics ODEs.5. Understanding of, and the ability to implement, the Verlet method for numerical solution ofdynamics ODEs. Appreciation of this method as an example of a symplectic integrator.6. Understanding of the general coupled first order form for ODEs appropriate for numericalsolution, and the ability to convert a higher order ODE into this form (and vice versa).7.

Understanding of Taylor series methods including the ability to derive a second orderRunge-Kutta scheme, and the ability to implement fourth order Runge-Kutta (RK4) in code.Understanding of, and ability to implement, an adaptive time-stepping integration method.Understanding of stiff ODEs, and the ability to solve them using implicit schemes.

8. Understanding of and ability to use a modularised form of RK4 to solve a range of problems.9.

Understanding of ODE two-point boundary value problems including eigenvalue problems, andunderstanding of their solution using finite differencing and relaxation (via power iteration orinverse power iteration), and the ability to implement these methods. Understanding of the useof deflation and Successive Over Relaxation (SOR) to solve these problems.

10. Understanding of the classification of PDEs and associated Initial Value Problems (IVPs) andBoundary Value Problems (BVPs).11.

Understanding of the form and properties of parabolic PDES, in particular the diffusionequation, and the ability to implement and solve 1-D and 2-D diffusion problems usingForward-Time Centred Space (FTCS) discretisation and time-stepping.

12. Understanding of the numerical stability of the FTCS scheme for the diffusion equation basedon the matrix approach.13. Understanding of the form and properties of hyperbolic PDEs, in particular the wave equationand advection equations.14. Recognition of the failure of the FTCS method in application to the advection equation, andunderstanding of and ability to implement the Lax and method for numerical solution.15. Understanding of, and ability to analytically apply, von Neumann stability analysis to linearnumerical schemes.16.

Understanding of, and ability to implement, the Lax-Wendroff method for numerical solution oflinear and nonlinear advection equation. Understanding of these methods as FTCSdiscretisations of advection-diffusion equations.

17. Understanding of the properties of, and an ability to derive, a fluid model for traffic, and theability to numerically solve IVPs for this model using nonlinear Lax-Wendroff.18. Understanding of the form and properties of elliptic PDEs, in particular the Laplace andPoisson equations.19. Understanding of, and ability to implement the Jacobi, Gauss-Seidel, and Successive

19.

Understanding of, and ability to implement the Jacobi, Gauss-Seidel, and SuccessiveOver-Relaxation (SOR) methods for numerical solution of elliptic PDEs. Understanding of, andthe ability to implement Fourier methods for the solution of elliptic PDEs.

20. Understanding of the convergence rates for the numerical methods of solution of elliptic PDEs.21. Understanding of the order and accuracy of PDE solution methods, and understanding of, andability to implement implicit schemes. Understanding of stencils.22. Understanding of issues in solution of nonlinear PDEs, and other more general PDEs.

2.3 Graduate Attributes

Graduate Attributes are generic attributes that encompass not only technical knowledge but additionalqualities that will equip students to be strong contributing members of professional and social communitiesin their future careers. The overarching graduate attributes identified by the University relate to a graduatesattitude or stance towards knowledge, towards the world, and towards themselves. These are understoodas a combination of five overlapping skills or abilities, the foundations of which are developed as part ofspecific disciplinary study. For further details please refer to the Science faculty website at:http://www.itl.usyd.edu.au/graduateAttributes/facultyGA.cfm?faculty=Science

Graduate Attributes LearningOutcomes

A Research and Inquiry

A1. Apply scientific knowledge and critical thinking to identify, define andanalyse problems, create solutions, evaluate opinions, innovate andimprove current practices.

A2. Gather, evaluate and deploy information relevant to a scientificproblem.

B Information Literacy

B1. Use a range of searching tools (such as catalogues and databases)effectively and efficiently to find information.

B2. Access a range of information sources in the science disciplines, forexample books, reports, research articles, patents and companystandards.

B3. Critically evaluate the reliability and relevance of information in ascientific context.

B5. Use information technology to gather, process, and disseminatescientific information.

C Communication

C1. Explain and present ideas to different groups of people in plain English.

C2. Write and speak effectively in a range of contexts and for a variety ofdifferent audiences and purposes.

C4. Present and interpret data or other scientific information using graphs,tables, figures and symbols.

C5. Work as a member of a team, and take individual responsibility withinthe group for developing and achieving group goals.

C6. Take a leadership role in successfully influencing the activities of agroup towards a common goal.

D Ethical, Social and Professional Understanding

D1. Demonstrate an understanding of the significance and scope of ethicalprinciples, both as a professional scientist and in the broader socialcontext, and a commitment to apply these principles when makingdecisions.

E Personal and Intellectual Autonomy

E1. Evaluate personal performance and development, recognise gaps inknowledge and acquire new knowledge independently.

E2. Demonstrate flexibility in adapting to new situations and dealing withuncertainty.

E4. Set achievable and realistic goals and monitor and evaluate progresstowards these goals.

2.4 Threshold Learning Outcomes

The Threshold Learning Outcomes (LTOs) are the set of knowledge, skills and competencies that a personhas acquired and is able to demonstrate after the completion of a bachelor degree program. The TLOs arenot equally weighted across the degree program and the numbering does not imply a hierarchical order ofimportance.

Threshold Learning Outcomes LearningOutcomes

1 Understanding science

2 Scientific knowledge

2.1 Demonstrating well-developed knowledge in at least one disciplinaryarea

3 Inquiry and problem solving

3.1 Gathering, synthesising and critically evaluating information from arange of sources

3.3 Selecting and applying practical and/or theoretical techniques or toolsin order to conduct an investigation

3.4 Collecting, accurately recording, interpreting and drawing conclusionsfrom scientific data

4 Communication

4.1 Communicating scientific results, information or arguments, to a rangeof audiences, for a range of purposes, and using a variety of modes

5 Personal and professional responsibility

5.1 Being independent and self-directed learners

5.2 Working effectively, responsibly and safely in an individual or teamcontext

5.3 Demonstrating knowledge of the regulatory frameworks relevant totheir disciplinary area and personally practising ethical conduct

3 Study Commitment

This module consists of 10 lectures, 10 labs, the work associated with them, and a three-week project. Asuggested study commitment might be as follows:

In class activities Hours

Lectures (10 @ 1 hr each) 10

Computer Lab Session (10 @ 3hr each)

30

Total 40

Independent Study Hours

Reading of text for lectures (10 @ 0.5 hreach) 5

Reading of lecture notes after lectures ([email protected] hr each) 5

Pre-reading and or work for Labs (10@ 0.5 hreach) 5

Assignments (2 @ 4 hr each) 8

Project 30

Exam Preparation 8.5

Total 61.5

Study TipsYou are in control of your own study strategy, and as an adult learner it is up to you to devise a study planthat best suits you. If you attend classes regularly you should gain a good understanding of the coursework. Our experience indicates that not all students attend lectures regularly and this has a considerablenegative impact on their exam preparation and performance.

Good study habits are also very important - we offer some suggestions on our Learning Physics web page(http://sydney.edu.au/science/physics/current/learningphysics.shtml).

4 Learning and Teaching Activities

Class timetabling

Lectures

There will be 20 lectures starting on Monday 2 March and ending Monday 13 May.

Venue and Times: Carslaw Lab 177 Monday 9am and Monday 12pm

Computer Lab Session

There will be 10 labs starting on Wednesday 4 March and ending Wednesday 15 May. Labs start in week1.

Venue and Times: Carslaw Lab 177 Wednesday 1pm - 4pm

5 Teaching Staff and Contact Details

UnitCoordinator Email

A/ProfMikeWheatland

[email protected]

TeachingStaff Email Room Phone Note

A/ProfMikeWheatland [email protected]

H90Rm223

93515965

ComputationalPhysics andScientificComputing

6 Learning ResourcesReference (Normal and Advanced)

There is no textbook for the unit.

The book Numerical Methods for Physics (Second Edition) by Alejandro Garcia is a recommendedreference, and sections of this text are followed by parts of the unit. However, the unit contains additionalmaterial and the lecture presentation is self-contained. Students are not expected to buy this book, butcopies are available at the Co-op bookshop, and have been placed in the 2-hour collection at the SciTechLibrary.

The recommended reference on numerical methods is the Numerical Recipes: The Art of ScientificComputing series (second edition) by Press, Teukolsky, Vetterling, and Flannery. Chapters of these booksare available for download (subject to some restrictions) at www.nrbook.com.au, and copies have beenplaced in the 2-hour collection at the SciTech Library.

This unit uses MATLAB for computation, and basic programming experience in MATLAB is assumed.MATLAB is available on the computers in the Computational Physics Laboratory (Room 177 inCarslaw). Swipe-card access to the Computational Physics Lab is provided to all students during normalbuilding hours. University ICT provides student access to MATLAB on and off campus on personally-ownedcomputers (see http://sydney.edu.au/ict/student/software/download.shtml for details). I If you wish topurchase your own copy of MATLAB, a student version is available from the Co-op bookshop for $100,including documentation on DVD.

A recommended reference on MATLAB programming is Essential MATLAB for Scientists and Engineers byHahn and Valentine. This book is available from the university library as an electronic resource, andchapters of the book may be downloaded free of charge. The second chapter, covering MATLABFundamentals, is available directly from the eLearning pages for this subject. A variety of reference materialis also available online for MATLAB, including the documentation accessible via the help browser commandin MATLAB or online at the MathWorks site ( www.mathworks.com).

If you lack programming experience, I recommend that you work through a section of a suitable reference(i.e. a text) covering the basics of programming, in your own time. It is important to try a lot of examples:attempt any exercises in the reference. Chapter 2 of Numerical Methods for Physics by Garcia is oneoption. More coverage is provided by chapter 2 of Essential MATLAB for Scientists and Engineers by Hahnand Valentine. The first Lab in week 1 is a MATLAB refresher using examples from this chapter .

COURSE CONTENT (Normal/Advanced)

The following outline lists the topics covered each week in the lectures and labs, the science problems usedto illustrate the topics, and lists the relevant sections of the recommended references. Material unique to theCOSC3011/3911 unit is flagged.

Week 1Lectures/labs: Review of MATLAB; Types of numerical error rounding and range error, truncation error;An introduction to Computational Science (COSC3x11); Numerical error and floating point revisited(COSC3x11); Review of matrix algebra (COSC3x11)

Science problem:

Refs: Hahn & Valentine chapter 2; Numerical Recipes sections 1.3, 2.1, 2.11, 20.1; Garcia section 1.5.

Week 2Lectures/labs: Ordinary Differential Equations or ODEs dynamics problems; Non-dimensionalisation;Eulers method for dynamics; Local and global truncation error; The midpoint and Euler-Cromer methods fordynamics (COSC3x11)

Science problem: Projectile motion

Refs: Garcia sections 1.2. 1.4, 1.5, and 2.1; Numerical Recipes sections 1.3, 2.1, 2.11, 20.1

Week 3Lectures/labs: Dynamical ODEs continued the Kepler problem; Non-dimensionalisation of the problem;Elementary numerical methods applied to the problem; The Verlet method; Properties of the Verlet method;Verlet and symplecticity (COSC3x11)

Science problem: Keplerian orbits

Refs: Garcia section 3.1; Numerical Recipes section 5.7

Week 4 Lectures/labs: General form of ODEs for numerical solution; Runge-Kutta (Taylor series) methods; Fourthorder Runge-Kutta (RK4); Deriving second order Runge-Kutta (RK2); Adaptive time steps (COSC3x11);Stiff problems the implicit Backwards Euler method (COSC3x11)

Science problem: Simple pendulum

Refs: Garcia sections 2.1, 3.2, and 3.3; Numerical Recipes sections 16.0, 16.1, 16.2, 16.6

Week 5Lectures/labs: Modularizing RK4; Two-point BVPs and solution via finite differencing and relaxation;Eigenvalue problems; The quantum SHO (direct solution and solution for the ground state by inverse poweriteration); Deflation, and application to the quantum SHO (COSC3x11); Accelerated convergence byover-relaxation (COSC3x11)

Science problems: stationary states of a quantum system

Refs: Garcia pages 283285

Week 6 Lectures/labs: Partial Differential Equations or PDEs; Classification of PDEs (Initial Value Problems or IVPsand BVPs); Parabolic PDEs and the diffusion equation; Forward-Time Centred Space discretisation, andsolution for diffusion, numerical stability of FTCS for 1-D diffusion; 2-D diffusion (COSC3x11)

Science problem: the spread of heat

Refs: Garcia sections 6.1 and 6.2; Numerical Recipes section 19.0

Week 7Lectures/labs: Hyperbolic PDEs and the wave and advection equations; FTCS applied to advection; vonNeumann stability analysis; Lax method for advection; Lax-Wendroff method for advection (COSC3x11);Interpreting Lax and Lax Wendroff as advection-diffusion equations (COSC3x11).

Science problem: the advection of a pulse

Refs: Garcia sections 7.1 and 9.1; Numerical Recipes sections 19.1 and 19.2

Week 8Lectures/labs: Compressible fluid model for traffic; Analytic analysis of the traffic model (nonlinear advectionspeed, shock waves/traffic jams, method of characteristics); Cars starting from a set of traffic lights.COSC3x11: Same material, in some greater depth.

Science problems: various problems to do with traffic flow

Refs: Garcia: Section 7.2

Week 9 Lectures/labs: 2-D elliptic PDEs and the Laplace and Poisson equations; Jacobi and Gauss-Seidel methodsof relaxation for elliptic PDEs; Successive Over-Relaxation or SOR for elliptic PDEs; Convergence rates ofelliptic methods; Fourier methods for elliptic PDEs (COSC3x11)

Science problem: the electric fields around electrical charges

Refs: Garcia sections 8.1 and 8.2; Numerical Recipes sections 19.4 and 19.5

Week 10Lectures/labs: Order/accuracy of PDE solution methods; Implicit methods for diffusion (Crank-Nicolson);More general diffusion problems; Stencils (COSC3x11); Numerical solution of the time-dependentSchrdinger equation (COSC3x11)

Science problem: heat diffusion revisited; evolution in time of a quantum wave packet (COSC3x11)

Refs: Garcia sections 9.2 and 9.3; Numerical Recipes section 19.2 (COSC3x11)

Week 11 - 13There are no formal lectures or laboratory for COSC3x11 students this is time to work on the project.

Web ResourcesThe lecturer's notes will be avalable on Blackboard (elearning.sydney.edu.au), usually accessed bystudents through MyUni (sydney.edu.au/myuni), the student portal providing University information andsevices. Access to MyUni and Blackboard requires a Unikey username and password that is issued withyour confirmation of enrolment. The University provides computer facilities described on the Student ITpages (http://sydney.edu.au/ict/student). Email The University provides you with email access based on your username. We will use this email address toprovide you with important information regarding this unit of study. We expect you to periodically readyour email account or to forward mail from it to an account you do read (e.g. a gmail account).

Where to go for HelpIf you need help, you can:

as a first step, always check your unit Blackboard site for information, documents and links.go to the Physics Office, Room 210 in the Physics Building, or phone 02 9351 3037.ask your lecturerconsult one of the many services provided by the University. These can be found athttp://sydney.edu.au/current_students/student_services/ or through your MyUni pages(http://myuni.usyd.edu.au).email the Senior Physics Coordinator: A/Prof Mike Wheatland ([email protected])

Equity and Access StatementThe School of Physics is strongly committed to providing equity of access and opportunity to all students,and to make our environment supportive for everyone. If you feel you have not been treated fairly,discriminated against or disadvantaged in any way, you are encouraged to talk to any member of thePhysics staff . Any student who feels she/he may need an accommodation based on the impact of adisability should contact Disability Services http://sydney.edu.au/current_students/disability/ who can helparrange support.

7 Assessment Tasks

You are responsible for understanding the University policy regarding assessment andexamination, which can be found in the University Policy Register at http://sydney.edu.au/policies/ To achieve good results, students in physics must be able to express themselves accurately by clear,efficient use of the English language in their written work. Spelling, grammar, punctuation and correct use oflanguage will be taken into account when written reports and examination work are assessed. You shouldrefer to the Universitys WriteSite (http://writesite.elearn.usyd.edu.au/) if you are looking for guidance ongrammar and other aspects of academic and professional writing. AssessmentAssessment of this unit of study is based on an understanding of the Course Contentdemonstrated in a combination of assessments - a final examination, project, computationallaboratory work, and assignments spaced through the semester. Note that a result is returned for the entire unit of study, not this module separately. Late AssignmentsAssessments submitted late without permission will incur an immediate late penalty equalto 10% of the maximum mark. 24 hours later a further 20% penalty will be imposed forassignments between 1 and 7 days late, with extra 20% penalties imposed after each oneweek period from the due date until the assessment is submitted or submissions are closed.For example, on an assessment given a mark of 7/10, the penalty would be 1 mark ifsubmitted up to 24 hours late, resulting in a final mark of 6/10. If the assessment issubmitted up to 1 week late, the final mark would be 4/10. An assessment will notordinarily be accepted after a solution for the assessment is released or marked assessmentsare returned to other students.

7.1 Summative Assessments

AssessmentTask

PercentageMark Due Date Learning Outcomes

Assignment 1 12.5 Week 6 Friday, 17 April 2015

1, 2, 3, 4, 5, 6, 7, 8, 9

Assignment 2 12.5 Week 11 Monday, 18 May 2015

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

Laboratory 10 Weekly (weeks: 1, 2, 3,4, 5, 6, 7, 8, 9 and 10)

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

Project 25 Week 13 Friday, 05 June 2015

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

FinalExamination

35 Exam Period 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

Pre-lab onlinequizzes

5 Weekly 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

Descriptions of Summative Assessments

Assignment 1There will be two assignment question sheets available from the Blackboard site. Students submit individual(not group) responses to assignments. Each assignment must have a coversheet, which is available fromthe Blackboard site or the Physics Office (Room 210).

We encourage students to discuss assignments, but we will NOT accept assignments that are simplycopied between students or from any other source. You should write your final answers independently,expressing the answers in your own words and with your own working. Allowing your work to be copied isunfair to other students and ultimately, does not help the student copying from your work.

Copying the work of another person without acknowledgement is plagiarism and contrary to Universitypolicies, By signing the coversheet you are certifying that you have read and understood the University ofSydney Academic Dishonesty and Plagiarism in Coursework Policy athttp://sydney.edu.au/policies/showdoc.aspx?recnum=PDOC2012/254&RedndNum=0.

You are reminded that, whilst it is acceptable to collaborate on an assignment with other students, you mustwrite your own version of the answer. For codes this means the new working parts of the code needed for aproblem must be your own work. Submitting the same code as your lab partner (as if it is your own work) isunacceptable. Doing so fails to show that you have the understanding and skills needed for the task, andfails to acknowledge the contribution of another student.

Assignments must be submitted no later than 5pm on the due date. They must be handed in at the PhysicsOffice (Room 210) or, if electronic submission is permitted, to the email address provided.

The School of Physics does not take responsibility for lost assignments. You are advised to keep a copyof all assignments submitted.

The assignments consist of a number of questions, requiring you to write codes to solve science problems.There are two assignments, worth a total of 25% of the total mark.

Assignment 1 is due at 5pm on Friday end of week 6.Assignment 2 is due at 5pm on Monday start of week 11.

LaboratoryThe first laboratory session is a refresher in MATLAB, based on chapter 2 of Hahn and Valentine, EssentialMATLAB for Scientists and Engineers. This Lab is mandatory. The laboratory sessions from weeks 2-10consist of sets of exercises requiring you to modify the codes introduced in the lectures (available via theeLearning site), and to write your own codes. The tasks involve implementing numerical methods andsolving science problems. The laboratory sessions support the lecture material, and are a crucial part of theunit. Students work in pairs, with assistance from tutors and a supervisor. You will be provided withswipe-card access to the Computational Physics Laboratory (Room 177 in Carslaw) which will give youaccess during normal building hours. This will provide you with additional time using the lab computers towork on your assignments, and more generally to practice your skills and use the computers for work inother modules. You will be given your own computer account so that you can work independently onassignments, and as needed through semester.

The lab sessions account for 10% of the course. The mark is based on satisfactory completion of theexercises for each week. The work must be done during the lab class: work done outside the lab class timewill not be marked. The tutor or supervisor will assess completion of the exercises, and record this duringthe laboratory class. You must get the tutor or supervisor to sign off on your work and record a mark toreceive the marks for the week. It is your responsibility to do this.

You are required to keep a logbook recording the results of your computations. Your logbook need only behandwritten, but should include brief answers to the exercises in the laboratory sessions so that a tutor candetermine that you have satisfactorily completed the exercises. Include relevant derivations, numericalresults, explanatory text, and sketches of any important graphs. The tutor or supervisor will determine andrecord completion of the exercises based on discussion with you and reference to your logbook, during theclass. You need to supply the logbook.

ProjectThe project is a substantial part of the COSC3011/3911 unit, involving three weeks of work (there are nolectures or labs in weeks 11-13, to allow work on the project), and comprising 25% of the mark. The projectis due Friday 5 June at 5pm, i.e. the end of week 13, and should be handed in to the Physics Office, Room210. A one paragraph summary of the project topic is due Friday 22 May, i.e. the end of week 11. You mayrevise the topic at a later date, but failure to submit a one-paragraph summary on time may result in adeduction of 5% from your project mark. The one-paragraph summary should be e-mailed to the lecturer([email protected]).

Project scope and the choice of a topic: The project is an opportunity for you to extend the skillsdeveloped in the laboratory sessions, and to pursue your own interests. You are encouraged to design yourown topic, using your general scientific knowledge, or by drawing on one of the suggestions below.However, please ensure that the scientific model you are solving makes sense. Do not construct your ownmodel, unless you are sure that it is correct. The project must use MATLAB and should apply and/or extendupon the material covered in lectures. The project must involve numerical solution of ODEs or PDEs. Theproject should be associated with a problem in science, although the emphasis may be more towards thescience or towards the numerical methods applied. The report must provide references, listing anyresources or materials used. The one-paragraph summary (due 22 May) is a chance to obtain initialfeedback via e-mail about the suitability and difficulty of your chosen topic. The summary should bee-mailed to the lecturer, who will provide some preliminary advice, recommendations for reading, etc.However, after that initial feedback the project choice and the work itself should be your own. The level ofhelp provided in the lab sessions is not provided for the project work.

Assessment of the project is via a written report that should be not more than 10 pages in length, excludingappendices. It may be shorter. The report should introduce the scientific area, explain the modelling andnumerical methods applied, and present a discussion of the results obtained. You should include, as anappendix to the report, all relevant MATLAB codes. If you use codes other than ones you write yourself, this

must be acknowledged and explained. The lecturer will provide examples of excellent past student projectreports for inspection during the Computational lab sessions.

As part of your project submission, you may perform a demonstration of your codes in the laboratory duringweek 13. Please arrange with the lecturer if you want to do this.

The recommended references on numerical methods (Garcia and Numerical Recipes) are possible sourcesof material for interesting problems. However, you are expected to do additional reading and research toidentify and learn about a topic. Your report must cite all references you have consulted. Your project topiccould be a (significant) extension of one or more of the laboratory exercises, or a scientific system notconsidered in the course. As starting points, the lecturer will take a number of books with suitable topics tothe Computational lab sessions.

Past student projects have covered diverse topics including the motion of charged particles in specifiedelectromagnetic fields (orbit theory), solution of the Black-Scholes equation describing financial markets, thethree-body problem for orbital motion, solution of Burgers equation describing nonlinear advection, solutionof the Korteweg-de Vries equation describing solitons, solution of the wave equation in 2-D to describe avibrating drum skin, multigrid methods, the Generalised Minimum Residual method, and Chebyshevmethods. Other possibilities include modeling the spread of a disease, modeling the evolution of the agestructure of a population (using a more realistic model than the Leslie model), investigating a particularnonlinear system, and investigating symplectic methods.

Details of report assessment: The report is assessed according to: clarity of presentation (20%);understanding of topic and methods (30%); quality of results (30%), difficulty/novelty of topic (10%); and ona brief self-reflective statement (10%). Note that the difficulty/novelty category rewards projects involving asignificant extension beyond the course material.

The emphasis in assessment is on the quality of the work and not the quantity. A report may be significantlyshorter than 10 pages and receive high marks. Two crucial points are that that the science problem shouldmake sense, and that you must correctly implement numerical methods. Do not invent your own model for asystem unless you are certain that it provides a sensible description. It is important to get your codes to workcorrectly, and to provide evidence that the codes work correctly, e.g. in application to simple test cases. Ifthere is aberrant behaviour, you need to work out what is going wrong.

Marks will be awarded in the different categories according to the general guidelines given in the tablebelow. Note that not all of the points listed may be relevant for a given project, depending on the topic andmethods chosen.

Projects submitted late without permission are subject to the same late policy as assignments.

Final ExaminationThe written exam is a one-hour exam. The exam is held in an exam room and is not a practical test inthe lab. The emphasis is on the formal/theory aspects of the unit, i.e. numerical methods, including thestability and accuracy of the methods, the application to science problems, and aspects of basic sciencemodeling. It is a closed book exam: no notes may be taken into the exam room.

You will be asked to write descriptive answers to questions, to explain physical principles and to answerquantitative questions, all aimed at demonstrating your progress in achieving the goals of the unit. An abilityto memorise formulae and manipulate them without understanding the associated concepts will not berewarded. Proof of identification is required at all examinations. Note that you must bring your ownnon-programmable calculator to the examination. See the University policy on calculators at http://www.usyd.edu.au/current_students/student_administration/examinations/students.shtml#calculators

Pre-lab online quizzesMultiple choice quizzes are available under eLearning, to be completed before the Lab each week. Thesequizzes test your understanding of the lecture material and should help prepare you for Lab. They are worth5% of the course.

7.2 Assessment GradingFinal grades in this unit are awarded at levels of HD (High Distinction), DI (Distinction), CR (Credit), PS(Pass) and FA (Fail) as defined by the Academic Board Assessment Policy. These achievement levels aredescribed below. Details of the policy are available on the Universitys Policy Online website at http://www.sydney.edu.au/policies/.

Assessment tasks are moderated to ensure their appropriateness, their consistency with the achievementlevel descriptors below and equity of grade distributions across the units offered by the Faculty of Science.In Senior Physics, our aim is to give everyone a chance of a high grade, irrespective of their unit of study. Toachieve this, we compare student marks with student AAMs, and compare Normal and Advanced units byhaving some assessment tasks in common. We use this comparison to ensure one class isn't beingdisadvantaged by, say, a difficult assessment task. The result of this moderation process is a higherpercentage of HDs and DIs in the Advanced unit (as you might expect), however the process also ensuresthere are HDs and DIs awarded in the other units of study to students who excel.

Grades:

High Distinction (HD)At HD level, a student demonstrates a flair for the subject and comprehensive knowledge and understandingof the unit material. A High Distinction reflects exceptional achievement and is awarded to a student whodemonstrates the ability to apply subject knowledge to novel situations.

Distinction (DI)At DI level, a student demonstrates an aptitude for the subject and a solid knowledge and understanding ofthe unit material. A Distinction reflects excellent achievement and is awarded to a student whodemonstrates an ability to apply the key ideas of the subject.

Credit (CR)At CR level, a student demonstrates a good command and knowledge of the unit material. A Credit reflectssolid achievement and is awarded to a student who has a broad understanding of the unit material but hasnot fully developed the ability to apply the key ideas of the subject.

Pass (PS)At PS level, a student demonstrates proficiency in the unit material. A Pass reflects satisfactoryachievement and is awarded to a student who has threshold knowledge of the subject.

Assessed exercises may not be revised and resubmitted for re-marking. If you wish to appeal an academicdecision, you should refer to the University Policy at:http://sydney.edu.au/policies/showdoc.aspx?recnum=PDOC2011/188&RendNum=0 (Student Grievances,Appeals and Applications for Review Policy) and http://sydney.edu.au/policies/showdoc.aspx?recnum=PDOC2012/253&RendNum=0 (Student Appealsagainst Academic Decisions)

8 Learning and Teaching Policies

ACADEMIC DISHONESTY/PLAGIARISMThe School of Physics will NOT accept assessments that are simply copied. Copying the work of anotherperson without acknowledgment is plagiarism and contrary to University policies on Academic Dishonestyand Plagiarism as described on the University Policy Register web site https://sydney.edu.au/policy/). Anoutline of what constitutes Academic Dishonesty and Plagiarism can be found at

https://sydney.edu.au/science/physics/local/acadhonesty.shtml.

CONSIDERATION OF FACTORS AFFECTING YOUR STUDYIf your academic performance in a Science Faculty unit of study is adversely affected by illness or someother serious event, such as an accident or important commitment, you should complete an Applicationfor Special Consideration or an Application for Special Arrangements and submit it with accompanyingdocumentation to the Faculty of Science Office (level 2 of the Carslaw building) within relevant time limits.

These two forms of Consideration should cover most allowable circumstances. However, if you haveanother reason for requiring the School of Physics to take account of your circumstances, you should notifythe School of Physics Student Services Office immediately.

tYou should not submit an application of any type if

there is no assessment associated with a missed class, oryou have a reasonable opportunity to make up any work you missed.

More detailed information on Special Consideration and Special Arrangements is available from https://sydney.edu.au/science/physics/local/consideration.shtml

Relevant forms are available on the Faculty Forms and Procedures web site atsydney.edu.au/science/cstudent/ug/forms.shtml

For full details of applicable university policies and procedures, see the University Policy Register web siteat sydney.edu.au/policy.

Replacement assessments for end of semester examinationsStudents who apply for and are granted either special arrangements or special consideration for end ofsemester examinations in units offered by the Faculty of Science will be expected to sit any replacementassessments in the two weeks immediately following the end of the formal examination period. Later datesfor replacement assessments may be considered where the application is supported by appropriatedocumentation and provided that adequate resources are available to accommodate any later date.