University of Tasmania



|[pic] |

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|School of Mathematics & Physics |

|Faculty of Science, Engineering & Technology |

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|KMA252 / KME271 |

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|Calculus and Applications 2 / |

|Engineering Mathematics |

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|Semester 1, 2006 |

|Unit Outline |

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|Dr Michael Brideson |

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|CRICOS Provider Code: 00586B |

Contact details

Unit coordinator/lecturer

|Unit coordinator/lecturer: |Dr Michael Brideson |

|Campus: |Hobart |

|e-mail: |Michael.Brideson@utas.edu.au |

|Phone: |(6226) 2430 |

|Fax: |(6226) 2867 |

|Room number |454 – Physics Building |

|Consultation hours: |Just knock on the door |

|Campus |Hobart |

Unit details

|Campus: |Hobart |

|Unit Weight: |12.5% |

|Prerequisites: |For KMA252: One of KMA150, KMA154, KMA156, KMA172, KNT150 (or one of |

| |KMA152, KMA171 with permission of the Head of School) |

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| |For KME271: KMA150, or KMA156, or KMA152 and KMA154, or KMA171 and |

| |KMA172, or KNT150 |

|Teaching Pattern: |3x1hr lectures, 1-hr tutorial weekly |

© The University of Tasmania 2006

Contents

Unit description 2

Learning outcomes 2

Generic graduate attributes 3

Prior knowledge &/or skills 3

Learning resources required 3

Requisite texts 3

Recommended reading 3

E- (electronic) resources 4

Details of teaching arrangements 4

Lectures 4

Tutorials 4

Occupational health and safety (OH&S) 5

Unit schedule 5

Learning expectations and strategies 6

Expectations 6

Learning strategies 6

Specific attendance/performance requirements 6

Assessment 6

Assessment schedule 6

Assessment details 6

Submission of assignments 6

Requests for extensions 7

Penalties 7

Academic referencing 7

Plagiarism 7

Further information and assistance 8

Unit description

The calculus section of the subject(s) is focussed on dealing with functions of several variables; the typical case is [pic]. Functions like this are important because they describe many of the situations we encounter when applying mathematics to models of the real world. The graph of the function [pic] is a surface, and so might be used to describe roof sections, aeroplane fuselages, and so on. We need to be able to say how rapidly such a surface curves, and that immediately requires us to do calculus on functions of two (or more) variables.

We will also need to consider vectors that are functions of several variables. Some obvious examples of these are the velocity vector in a moving fluid, the heat-flow vector in a solid, and the electric and magnetic fields produced by an antenna. This will lead us to consider more advanced concepts, such as circulation, compressibility, divergence, and curl. Understanding this material is fundamental to the study of all areas of Engineering and (continuum) Applied Mathematics, and it underpins modern continuum mechanics and electromagnetic theory.

The Fourier-series section of the subject(s) is concerned with how to represent periodic functions. This is an important idea in all sorts of applications, such as acoustics and signal processing, and (perhaps surprisingly) can even be used to solve problems arising in heat-flow theory, fluid mechanics, and so on.

Learning outcomes

On completion of this unit, you should be able to understand and implement calculus related concepts that are fundamental to solving advanced problems in engineering, economics, and applied mathematics. You should be able to:

▪ Use graphs, cross-sections, and contour plots to analyse and manipulate functions of two or more variables.

▪ Perform vector operations, leading to an ability to work with parametric forms of curves, to describe circular motion, and to find lengths of curves.

▪ Construct partial derivatives and differentials, and extend the concept to gradients, directional derivatives, Taylor series approximations, and tangent plane approximations.

▪ Apply the method of Lagrange multipliers to optimisation problems.

▪ Integrate multi-variable functions to compute line, surface, and volume integrals.

▪ Understand the vector differential operator, and how to use it to compute gradient, divergence, and curl.

▪ Understand integral theorems such as Gauss’ Divergence Theorem, Stokes’ Theorem, and Green’s Theorem in the Plane.

▪ Find the Fourier Series expansion for periodic functions of a single variable.

These learning outcomes will be assessed with weekly assignments and an end of semester exam.

Generic graduate attributes

The University has defined a set of generic graduate attributes (GGAs) that can be expected of all graduates (see ). By undertaking this unit you should make progress in attaining the following attributes:

Knowledge: This unit provides you with the necessary mathematical tools to recognise, interpret, and solve calculus based problems. Such problems are fundamental to many areas of the physical sciences, engineering, finance, and economics.

Communication skills: Weekly assignments will provide you with the opportunity to develop and demonstrate your ability to communicate numerical and graphical information in a clear and accurate way. Group assignments will also enable you to develop effective communication in group-based environments.

Problem-solving skills: Weekly assignments will provide you with the opportunity to develop and demonstrate problem-solving skills. Group assignments will also enable you to develop the necessary problem-solving skills for group-based environments.

Global perspective: Mathematics is a global language. Whether you are building bridges in India, Somalia, or Australia, the governing mathematics is still the same. Similarly, the techniques of calculus learnt in this course are easily transportable to all branches of engineering and the physical sciences. With this course you can build yourself a mathematical toolbox that you can take anywhere.

Social responsibility: ?

Prior knowledge &/or skills

▪ Knowledge of basic concepts in single variable calculus.

▪ Sound independent study and research skills.

Learning resources required

Requisite texts

Either of the following two texts is applicable to this unit:

1. Calculus, 5e edition, J. Stewart (Brooks-Cole 2003).

2. Calculus: Single and Multivariable, 3rd edition, Hughes-Hallett et al (Wiley 2002).

These texts have been chosen as they have both recently been used for first-year Calculus here at UTas.

Recommended reading

You will also find a fair amount of the material for this unit in books such as:

1. Advanced Engineering Mathematics, 9th edition, E. Kreyszig (Wiley 2006).

2. Thomas’ Calculus, 11th edition, Weir et al (Pearson Education, 2005)

Kreyszig is an excellent reference book, which also does a good job in covering the Fourier series section of the unit (and many other topics, too).

There are quite a large number of text-books with the same or similar title, and you should be able to find some of these in the library.

E- (electronic) resources

Lecture notes can be downloaded from Michael Brideson’s homepage on the internal Mathematics website:

▪ Internal website: maths.utas.edu.au

Navigate to Michael Brideson’s homepage by clicking on “People” in the navigation bar.

Alternatively you can use the following link to go directly to the lecture notes:

▪ maths.utas.edu.au//People/Brideson/teaching/kma252lectureseries/

Notes:

1. The lecture notes do not contain any diagrams, but there are spaces for them. You will need to attend lectures to obtain the diagrams.

2. It is best that you do not print the entire document but print a few chapters at a time. The notes are constantly edited throughout the semester so newer versions may need to be downloaded as the semester progresses. The corrections made will be listed on the download webpage.

Details of teaching arrangements

Lectures

There are 3 lectures per week:

Tuesday 9am Physics Lecture Theatre 2

Wednesday 10am Physics Lecture Theatre 2

Friday 9am Physics Lecture Theatre 2

Tutorials

There are no tutorial sessions in the first week as it will be used to sort people into tute groups.

The tutorial sessions are available for analysing marked assignments, and for reviewing topics related to the lecture material.

Assignments will be given out at the end of each week’s lectures, and are to be submitted in the assignment mailboxes by midday on Friday of the following week. On some occasions the assignment will be solved in groups during a tutorial session. During these sessions the assignment may also be marked, so attendance is mandatory.

The purpose of the assignments is to give you the opportunity to practice solving problems related to the lecture material. This will enable you to become familiar with the various topics in the unit and their methods for solving. It will also enable you to see how the various topics are linked together, and how they link to your intended profession.

Practice problems, make mistakes, and learn from your mistakes – that’s the way to learn math!!!

Occupational health and safety (OH&S)

The University is committed to providing a safe and secure teaching and learning environment. In addition to specific requirements of this unit you should refer to the University’s policy at:

If access to Physics Lecture Theatre 2 or your designated tutorial room is likely to be a problem, please contact Dr Brideson.

Unit schedule

[pic]

There will be no lecture on Friday March 10.

Learning expectations and strategies

Expectations

The University is committed to high standards of professional conduct in all activities, and holds its commitment and responsibilities to its students as being of paramount importance. Likewise, it holds expectations about the responsibilities students have as they pursue their studies within the special environment the University offers ().

The University’s Code of Conduct for Teaching and Learning states:

Students are expected to participate actively and positively in the teaching/learning environment. They must attend classes when and as required, strive to maintain steady progress within the subject or unit framework, comply with workload expectations, and submit required work on time.

Learning strategies

If you need assistance in preparing for study please refer to Dr Brideson or your tutor.

For additional information refer to the Learning Development website :



Specific attendance/performance requirements

There are no specific attendance requirements for lectures. However, failure to attend lectures will result in incomplete lecture notes.

There are no specific attendance requirements for the majority of tutorials. Group assignments however, will be assessed on attendance.

Assessment

Assessment schedule

Except for week 1, there will be an assignment due at the end of every teaching week during the semester. The highest 10 marks from these assignments will count toward your final mark for the unit.

The final examination in this unit will be held during the November examination period and will be based on material covered in lectures and tutorials. The purpose of the final examination is to determine the extent to which you have achieved the Learning Outcomes as set out above. The entire semester's work is examinable.

Assessment details

For both KMA252 and KME271 there will be a 2 hour final exam worth 80% of the unit’s overall mark, and assignments worth 20% of the unit’s overall mark.

You must pass both the final exam and the assignments to gain a pass for the unit; e.g. you will not pass the unit if you get 100% for the final exam but not hand in any assignments.

Submission of assignments

Assignments must be submitted to the post boxes on Level 3 of the Physics Building by midday of the Friday that the assignment is due. The Post boxes will be labelled with the unit code, tutor’s name, and tutorial time. Make sure that you put your assignment in the correct box.

Assignments must be submitted with a signed cover sheet. The assignment sheet will double as a cover sheet, but separate cover sheets will also be available at the level 3 post boxes

Marked assignments will be returned in the next tutorial session.

Requests for extensions

Extensions will only be granted on the basis of consultation with Dr Brideson and your tutor before the due date. If you are ill, please provide a medical certificate.

Penalties

Late submission of assignments will incur a penalty of:

▪ 1 – business day late = 10% penalty

▪ 2 – 5 business days late = 25% penalty

▪ More than 5 business days = 100% penalty

Academic referencing

In your written work you will need to support your ideas by referring to scholarly literature, works of art and/or inventions. It is important that you understand how to correctly refer to the work of others and maintain academic integrity.

Failure to appropriately acknowledge the ideas of others constitutes academic dishonesty (plagiarism), a matter considered by the University of Tasmania as a serious offence.

For information on presentation of assignments, including referencing styles:



Please read the following statement on plagiarism. Should you require clarification please see your unit coordinator or lecturer.

Plagiarism

|Plagiarism is a form of cheating. It is taking and using someone else's thoughts, writings or inventions and representing them|

|as your own; for example, using an author's words without putting them in quotation marks and citing the source, using an |

|author's ideas without proper acknowledgment and citation, copying another student's work. |

|If you have any doubts about how to refer to the work of others in your assignments, please consult your lecturer or tutor for|

|relevant referencing guidelines, and the academic integrity resources on the web at |

|. |

|The intentional copying of someone else’s work as one’s own is a serious offence punishable by penalties that may range from a|

|fine or deduction/cancellation of marks and, in the most serious of cases, to exclusion from a unit, a course or the |

|University. Details of penalties that can be imposed are available in the Ordinance of Student Discipline – Part 3 Academic |

|Misconduct, see |

|The University reserves the right to submit assignments to plagiarism detection software, and might then retain a copy of the |

|assignment on its database for the purpose of future plagiarism checking. |

For further information on this statement and general referencing guidelines, see or follow the link under ‘Policy, Procedures and Feedback’ on the Current Students homepage.

Further information and assistance

If you are experiencing difficulties with your studies or assignments, have personal or life planning issues, disability or illness which may affect your course of study, you are advised to raise these with your lecturer in the first instance.

There is a range of University-wide support services available to you including Teaching & Learning, Student Services, International Services. Please refer to the Current Students homepage at:

Should you require assistance in accessing the Library visit their website for more information at

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