Note: This unit is an archived version! See Overview tab for delivered versions.
MATH2061: Linear Mathematics and Vector Calculus (2010 - Summer Main)
| Unit: | MATH2061: Linear Mathematics and Vector Calculus (6 CP) |
| Mode: | Normal-Day |
| On Offer: | Yes |
| Level: | Intermediate |
| Faculty/School: | School of Mathematics and Statistics |
| Unit Coordinator/s: | |
| Session options: | Semester 1, Summer Main |
| Versions for this Unit: | |
| Site(s) for this Unit: |
http://www.maths.usyd.edu.au/u/UG/IM/ |
| Campus: | Camperdown/Darlington |
| Pre-Requisites: | None. |
| Brief Handbook Description: | This unit starts with an investigation of linearity: linear functions, general principles relating to the solution sets of homogeneous and inhomogeneous linear equations (including differential equations), linear independence and the dimension of a linear space. The study of eigenvalues and eigenvectors, begun in junior level linear algebra, is extended and developed. Linear operators on two-dimensional real space are investigated, paying particular attention to the geometrical significance of eigenvalues and eigenvectors. The unit then moves on to topics from vector calculus, including vector-valued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; path-independent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals; polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, though cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem and Stokes' Theorem. |
| Assumed Knowledge: | None. |
Attributes listed here represent the key course goals (see Course Map tab) designated for this unit. The list below describes how these attributes are developed through practice in the unit. See Learning Outcomes and Assessment tabs for details of how these attributes are assessed.
| Attribute Development Method | Attribute Developed |
| Extends maths skills in linearity and a variety of vector calculus topics. | Fundamentals of Science and Engineering (Level 2) |
For explanation of attributes and levels see Engineering/IT Graduate Attribute Matrix 2009.
Learning outcomes are the key abilities and knowledge that will be assessed in this unit. They are listed according to the course goal supported by each. See Assessment Tab for details how each outcome is assessed.
Fundamentals of Science and Engineering (Level 2)| Assessment Methods: |
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| Assessment Description: | Exact balance between quizzes and assessment is not confirmed. Handbook entry reports assessment comprising exam and quizzes but breakdown is not specified. Likely to be either 30:70 or 20:80 based on pattern followed in other units. |
| Online Course Content: | http://www.maths.usyd.edu.au/u/UG/IM/ |
| Note on Resources: | This outline is a brief extract only. See School of Mathematics and Statistics or the Intermediate Mathematics website for a more complete outline. |
Course Relations
The following is a list of courses which have added this Unit to their structure.
Course Goals
This unit contributes to the achievement of the following course goals:
| Attribute | Practiced | Assessed |
| Fundamentals of Science and Engineering (Level 2) | Yes | 100% |
These goals are selected from Engineering/IT Graduate Attribute Matrix 2009 which defines overall goals for courses where this unit is primarily offered. See Engineering/IT Graduate Attribute Matrix 2009 for details of the attributes and levels to be developed in the course as a whole. Percentage figures alongside each course goal provide a rough indication of their relative weighting in assessment for this unit. Note that not all goals are necessarily part of assessment. Some may be more about practice activity. See Learning outcomes for details of what is assessed in relation to each goal and Assessment for details of how the outcome is assessed. See Attributes for details of practice provided for each goal.
