- Lecturer contact details
- Lecture times
- Unit outline
- Reference books
- Tutorials
- Assignments
- Plagiarism
- Tests
- Learning Outcomes
- Assessment
- Withdrawal from Unit
- Student Feedback
- Expected Participation
- Special Consideration
Mathematics IIA Study Guide Semester 2, 2004
Lecturer contact details
 Rod Yager (Linear Algebra) Room E7A 404 Phone 02 9850 8934 Email rody@maths.mq.edu.au |
 Tanya Schmah (Vector Calculus) Room E7A 416 Phone 02 9850 8949 Email schmah@maths.mq.edu.au |
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Lecture Times
Linear Algebra Lectures: Monday 6pm-8pm in E7B 100Vector Calculus Lectures: Wednesday 6pm-8pm in E6A 102
On occassions, it will be necessary to interchange these lectures to accomodate the lecturers other committments.
Unit Outline
Linear Algebra
- Inner product spaces
- Fourier series
- Change of basis
- Orthogonal diagonalization
- Applications to least squares approximation and quadratic forms
- Linear transformations
- Matrix representation of linear transformations
- Complex vector spaces
- Jordan canonical forms (time permitting)
Vector Calculus
- Calculus as a tool for understanding the properties of functions with n inputs and m outputs
- Limits and continuity of such functions
- Differential calculus:
- partial derivatives
- the derivative as a local linear approximation
- chain rule
- directional derivatives
- gradients
- Jacobians
- Applications to:
- Taylor series
- implicit and inverse functions
- critical points
- extrema
- Lagrange multiplier methods
- Integral Calculus:
- Multiple Integrals
- iterated integrals
- change of variables in multiple integrals.
Reference Books
Linear Algebra
WWL Chen, Linear Algebra MATH 235Vector Calculus
Marsden & Tromba, "Vector Calculus", 3rd Edition, (1988) W.H. FreemanWWL Chen, Multivariable Analysis MATH 235
Tutorials
Tutorials commence in Week 2. There are three time slots:- Monday 5pm in E68 108
- Monday 8pm in E8A 188
- Wednesday 5pm in E7B 163
During the tutorials you will have the opportunity to ask your tutor for help with these or any other questions. To get the most out of the tutorials, you should spend some time attempting to solve the questions prior to the tutorial session.
Assignments
There will be five (5) assignments. Each will contain questions from both strands of the unit. Make a serious attempt on all questions. Start working on the questions well before the due date, you may need several attempts before you can solve the problems. Do not be discouraged if you cannot solve them at your first attempt. Firstly devise a plan, then try to carry it out, then check it out; if it wasn't successful choose another plan, repeat the cycle. Assignments are due by 12noon on the following days:- Assignment 1: week 3 Monday 15 March
- Assignment 2: week 5 Monday 29 March
- Assignment 3: week 8 Monday 3 May
- Assignment 4: week 10 Monday 17 May
- Assignment 5: week 12 Monday 31 May
Plagiarism
It is permissible, and indeed you are encouraged, to discuss the assignment questions withother people, but you must then write out your solutions independently, without reference to anyone else's work. If in the course of writing up your answer, you realise you need more help, then you may get that help, but you should ensure that the end result is that you have understood your entire answer and are able to reproduce it independently.Students who are found to have participated in deliberate copying will be subject to disciplinary action which may include the forfeiture of all assignment marks or failure in the unit. Please see the section concerning plagiarism on pages 42-43 in the 2004 Handbook of Undergraduate Studies.
Tests
There will be two (2) tests, conducted in Weeks 5 and 10. Test 1: Friday 2 April in the 12noon lecture in E6A102.Test 2: Friday 21 May in the 12noon lecture in E6A102.You are expected to attempt both of these tests. Please contact one of the lecturers in case of difficulty over this. Warning: see Expected Participation.
Learning Outcomes
In this unit, you are expected to develop a good understanding of the topics listed under Unit Outline. You should improve your skills in the following areas common to all mathematical studies:- Solving problems, including:
- formulating a precise mathematical question from a "real world" problem;
- identifying and applying appropriate mathematical techniques.
- Understanding logical arguments and recognising any gaps or faults in such arguments.
- Expressing yourself clearly and logically in writing.
More broadly, you are expected to improve your generic skills in the following areas: literacy and numeracy, self-awareness and interpersonal skills, communications, critical analysis, problem solving and creative thinking.
By the end of this unit, you should be able to give clear and complete answers to questions of a similar level of difficulty to those on your assignments. This includes being able to formulate logical arguments more complex than have been expected of you in earlier mathematical units. Your grades will reflect your understanding of the subject and your ability to answer questions clearly and logically. For an explanation of the interpretation of grades, please see Rule 10 of Bachelor Degree Rules, on pages 88-89 in the 2004 Handbook of Undergraduate Studies.
Assessment
The 5 assignments will count for 10% of the final grade. The two tests will count for 20% of the final grade. The final exam will count for 70% of the final grade.Note that a grade of at least a P in MATH235 is a prerequisite for the unit MATH236 and for some 300-level Mathematics units. This prerequisite will not be waived.
Withdrawal from Unit
Your attention is drawn to the following deadline: Tuesday 31 August: Last day for students to lodge a "Change of Program" form to discontinue the unitand to be regarded as not effectively enrolled (NE). See page 89 of the 2004 Macquarie University Handbook of Undergraduate Studies.If you submit a form to withdraw after 31 August, you will be awarded the grade FW. A grade of W(withdrawal without academic penalty) will only be awarded in the case of fully documented "unavoidable disruption". See pages 36 & 89 of the 2004 Macquarie University Handbook of Undergraduate Studies.
Student Feedback
There will be a formal evaluation of the unit towards the end of the semester. You are also encouraged to give feedback to the lecturers during the semester; in particular, any comments like "I can't read your writing" should be made as early as possible!Expected Participation
Students are expected to submit all 5 assignments and to sit both tests. Requests for "special consideration" will not be looked on with favour if the student making the request has not submitted reasonable attempts on at least 4 assignments and sat both tests. Please contact one of the lecturers in case of difficulty over the participation requirements. Past experience clearly indicates that students who do not attempt assignments throughout the semester rarely perform well in the final examination.Special Consideration
If illness or misadventure makes it impossible for you to sit for the final examination, or interferes significantly with your performance in the examination, then you are permitted to request "special consideration". If you have demonstrated satisfactory participation (see above), and if we are satisfied (eg, by your previous performance in the unit, or by the quality of work you have been able to produce in the examination) that there is evidence that you have not been able to show your true ability, then we may decide to invite you to sit for a special examination to resolve your grade for the unit. You should note the following:- See Rule 9 (1) and 9 (2) of Bachelor Degree Rules, concerning examinations, on page 88 in the 2004 Handbook of Undergraduate Studies.
- Every student is entitled to apply for special consideration, and each application is considered on its merits. However, it is the decision of the Division whether to offer a special examination or not. As a general rule, a special examination is offered if illness or misadventure interferes with an otherwise satisfactory performance. Consequently, a special examination is not offered unless all criteria concerning expected participation have been satisfied.
- The examination period for this semester is between 16-06-2004 and 30-06-2004. Please note that special consideration cannot be made for those who have merely made inappropriate travel arrangements.
- It is essential that you lodge the request for special consideration by 2 December 2004, accompanied by any appropriate documentary evidence. The appropriate forms and instructions on how to apply can be obtained from here. It is also advisable for you to let the lecturers know informally that you have applied for special consideration.
- The purpose of the special examination is to resolve the temporary difficulty caused by your illness or misadventure, not to give you an advantage over other students by allowing you extra time to study. We will therefore hold the special examination as soon as possible. In determining your grade from a special examination, we may also take into account the possibility of extra study time available to you.
- In view of the previous paragraph, you must make sure that you are readily available to be contacted, andmust hold yourself available to attend the special examination at short notice on the date and time the Division sets. This is provisionally set for 16-07-2004.
- If you elect to be away from Sydney during the special examination, or cannot be contacted, or are unavailable to attend the special examination, then the Division will accept this as a firm indication that any request you may have submitted for special consideration does not apply to this unit.