Unit convenor and teaching staff |
Unit convenor and teaching staff
Other staff
Garry Lawson
Unit convenor
Chris Meaney
Contact via 9850 8922
e7a207
Lecturer
Michael Batanin
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Credit points |
Credit points
3
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Prerequisites |
Prerequisites
MATH133 or MATH136
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Corequisites |
Corequisites
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Co-badged status |
Co-badged status
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Unit description |
Unit description
The idea of a vector space first introduced in MATH136 and MATH133 is enriched in this unit by the introduction of an inner product. This leads to the important notion of orthogonality that underpins many areas of mathematics. The idea of linear transformations which transfer linearity from one space to another is also discussed. The results and techniques are then applied to problems such as approximation, quadratic forms and Fourier series. Differential and integral calculus involving functions of several real variables are discussed in greater depth than in MATH136 and MATH133. The ideas here are central to the development of mathematics in many different directions.
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Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
On successful completion of this unit, you will be able to:
Name | Weighting | Due |
---|---|---|
5 Assignments | 20% | weeks 4, 6, 8, 10, and 12 |
Exam | 60% | Exam period |
One Test | 20% | Week 7 |
Quizzes | 0% | Week 3 |
Due: weeks 4, 6, 8, 10, and 12
Weighting: 20%
Due in weeks 4, 6, 8, 10, and 12.
Due: Exam period
Weighting: 60%
Due: Week 7
Weighting: 20%
To be held in week 7.
Due: Week 3
Weighting: 0%
In order to obtain a passing grade in this unit, students are required to demonstrate their mastery of the required basic skills and techniques by passing both on-line quizzes. Students who do not meet this requirement will have their grade capped at F 49.
The required text for MATH235 is available for download on
You should download and study these. The online notes are intended primarily as a source of reference. These are not intended to be treated as the only source for learning. The following texts provide useful references for various sections of the course:
Other similar texts are available in the Library.
Week | Algebra | Calculus |
1 | Complex linear algebra | Sets and functions. Euclidean spaces. |
2 | Transformations in Euclidean spaces | Continuity and limits. |
3 | Finite-dimensional vector spaces and linear transformations | Continuity and limits. |
4 | Basis and dimension. Rank-nullity theorem. | Directional and partial derivatives. Derivatives. |
5 | Eigenvalues and eigenvectors. | Directional and partial derivatives. Derivatives. |
6 | Real inner product spaces. | Derivatives of vector-valued functions. |
7 | Gram-Schmidt orthogonalization process. Orthonal projections. | The inverse function theorem. |
8 | Gram-Schmidt orthogonalization process. Orthonal projections. | The implicit function theorem |
9 | Change of basis in inner product spaces | Critical points & extrema. |
10 | Orthonormal diagonalization | Lagrange multipliers. |
11 | Applications of real inner product spaces | Multiple integrals. |
12 | Complex inner product spaces | Multiple integrals: Fubini's theorem and change of variables |
13 | Revision | Revision |
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Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
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No extensions will be granted. Students who have not submitted the task prior to the deadline will be awarded a mark of 0 for the task, except for cases in which an application for special consideration is made and approved.
In order to obtain a passing grade in this unit, students are required to demonstrate their mastery of the required basic skills and techniques by passing both on-line quizzes. Students who do not meet this requirement will have their grade capped at F 49.
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In order to obtain a passing grade in this unit, students are required to demonstrate their mastery of the required basic skills and techniques by passing both on-line quizzes. Students who do not meet this requirement will have their grade capped at F 49.
Satisfactory performance on supervised assessment tasks, such as tests and the final exam, is necessary to pass this unit. If there is a significant difference between a student's marks on supervised assessment tasks and on unsupervised assessment tasks, the scaling of these tasks may be adjusted when determining the final grade, to reflect more appropriately that student's performance on supervised tasks.