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MATH2061: Linear Mathematics and Vector Calculus (2019 - Semester 1)

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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
Versions for this Unit:
Campus: Camperdown/Darlington
Pre-Requisites: (MATH1011 OR MATH1001 OR MATH1901 OR MATH1906) AND (MATH1014 OR MATH1002 OR MATH1902) AND (MATH1003 OR MATH1903 OR MATH1907).
Prohibitions: MATH2001, MATH2901, MATH2002, MATH2902, MATH2961, MATH2067
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. 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.
Timetable: MATH2061 Timetable
T&L Activities: Lectures: Three 1 hour lectures, one 1 hour tutorial and one 1 hour practice class per week.

Practical Work:

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.

(1) Maths/ Science Methods and Tools (Level 2)
1. Be able to solve a system of linear equations
2. Be able to apply the subspace test in several different vector spaces
3. Be able to calculate the span of a given set of vectors in various vector spaces
4. Be able to find a polynomial of minimum degree that fits a set of points exactly
5. Be able to find bases of the fundamental subspaces of a matrix
6. Be able to test whether an n x n matrix is diagonalisable.
Assessment Methods:
# Name Group Weight Due Week Outcomes
1 Assignment No 5.00 Week 4 1,
2 Quiz No 30.00 Week 6 1,
3 Examination No 60.00 Exam Period 2, 3, 4, 5, 6,
4 Participation No 5.00 Multiple Weeks 1, 2, 3, 4, 5, 6,
Assessment Description: One 2 hour exam, assignments, quizzes (100%)

Note that the "Weeks" referred to in this Schedule are those of the official university semester calendar https://web.timetable.usyd.edu.au/calendar.jsp

Week Description
Week 4 Assessment Due: Assignment
Week 6 Assessment Due: Quiz
Exam Period Assessment Due: Examination

Course Relations

The following is a list of courses which have added this Unit to their structure.

Course Year(s) Offered
Aeronautical (till 2014) 2010, 2011, 2012, 2013
Civil (till 2014) 2010, 2011, 2012, 2013, 2014
Civil Engineering / Arts 2011, 2012, 2013, 2014
Civil Engineering / Commerce 2010, 2011, 2012, 2013, 2014
Civil Engineering / Design in Architecture 2010, 2011, 2012, 2013, 2014
Civil Engineering / Medical Science 2011, 2012, 2013, 2014
Civil Engineering / Project Management 2012, 2013, 2014
Civil Engineering / Science 2011, 2012, 2013, 2014
Civil (Construction Management) (till 2014) 2011, 2012, 2013, 2014
Civil (Environmental) (till 2014) 2011, 2012, 2013, 2014
Civil (Geotechnical) (till 2014) 2011, 2012, 2013, 2014
Civil Engineering / Law 2010, 2011, 2012, 2013, 2014
Civil (Structures) (till 2014) 2011, 2012, 2013, 2014
Computer Engineering (till 2010) 2010
Computer Engineering / Commerce 2010
Electrical (till 2014) 2010, 2011, 2012, 2013, 2014
Electrical Engineering / Arts 2011, 2012, 2013, 2014
Electrical Engineering / Commerce 2010, 2011, 2012, 2013, 2014
Electrical (Bioelectronics) (till 2012) 2011, 2012
Electrical Engineering (Bioelectronics) / Arts 2011, 2012
Electrical Engineering (Bioelectronics) / Commerce 2011, 2012
Electrical Engineering (Bioelectronics) / Medical Science 2011, 2012
Electrical Engineering (Bioelectronics) / Science 2011, 2012
Electrical Engineering (Bioelectronics) / Law 2011, 2012
Electrical Engineering / Medical Science 2011, 2012, 2013, 2014
Electrical Engineering / Project Management 2012, 2013, 2014
Electrical Engineering / Science 2011, 2012, 2013, 2014
Electrical (Computer) (till 2014) 2011, 2012, 2013, 2014
Electrical Engineering (Computer) / Arts 2011, 2012, 2013, 2014
Electrical Engineering (Computer) / Commerce 2011, 2012, 2013, 2014
Electrical Engineering (Computer) / Medical Science 2011, 2013, 2014
Electrical Engineering (Computer) / Science 2011, 2012, 2013, 2014
Electrical Engineering (Computer) / Law 2011, 2012, 2013, 2014
Electrical (Power) (till 2014) 2010, 2011, 2012, 2013, 2014
Electrical Engineering (Power) / Arts 2011, 2012, 2013, 2014
Electrical Engineering (Power) / Commerce 2010, 2011, 2012, 2013, 2014
Electrical Engineering (Power) / Medical Science 2011, 2012, 2013, 2014
Electrical Engineering (Power) / Project Management 2012, 2013, 2014
Electrical Engineering (Power) / Science 2011, 2012, 2013, 2014
Electrical Engineering (Power) / Law 2010, 2011, 2012, 2013, 2014
Electrical (Telecommunications) (till 2014) 2011, 2012, 2013, 2014
Electrical Engineering (Telecommunications) / Arts 2011, 2012, 2013, 2014
Electrical Engineering (Telecommunications) / Commerce 2011, 2012, 2013, 2014
Electrical Engineering (Telecommunications) / Medical Science 2011, 2012, 2013, 2014
Electrical Engineering (Telecommunications) / Science 2011, 2012, 2013, 2014
Electrical Engineering (Telecommunications) / Law 2011, 2012, 2013, 2014
Civil/ Project Management 2019
Civil 2015, 2016, 2017, 2018, 2019
Civil / Arts 2015, 2016, 2017, 2018, 2019
Civil / Commerce 2015, 2016, 2017, 2018, 2019
Civil / Design in Architecture 2015, 2016, 2017, 2018, 2019
Civil / Medical Science 2015, 2016, 2017
Civil / Music Studies 2016, 2017
Civil / Project Management 2015, 2016, 2017, 2018
Civil / Science 2015, 2016, 2017, 2018, 2019
Civil/Science (Health) 2018, 2019
Civil (Construction Management) 2015
Civil (Environmental) 2015
Civil (Geotechnical) 2015
Civil / Law 2015, 2016, 2017, 2018, 2019
Civil (Structures) 2015
Civil Mid-Year 2016, 2017, 2018, 2019
Electrical Mid-Year 2016, 2017, 2018, 2019
Electrical/ Project Management 2019
Electrical 2015, 2016, 2017, 2018, 2019
Electrical / Arts 2015, 2016, 2017, 2018, 2019
Electrical / Commerce 2015, 2016, 2017, 2018, 2019
Electrical / Medical Science 2015, 2016, 2017
Electrical / Music Studies 2016, 2017
Electrical / Project Management 2015, 2016, 2017, 2018
Electrical / Science 2015, 2016, 2017, 2018, 2019
Electrical/Science (Health) 2018, 2019
Electrical (Computer) 2015
Electrical (Computer) / Arts 2015
Electrical (Computer) / Commerce 2015
Electrical (Computer) / Medical Science 2015
Electrical (Computer) / Project Management 2015
Electrical (Computer) / Science 2015
Electrical (Computer) / Law 2015
Electrical / Law 2015, 2016, 2017, 2018, 2019
Electrical (Power) 2015
Electrical (Power) / Arts 2015
Electrical (Power) / Commerce 2015
Electrical (Power) / Medical Science 2015
Electrical (Power) / Project Management 2015
Electrical (Power) / Science 2015
Electrical (Power) / Law 2015
Electrical (Telecommunications) 2015
Electrical (Telecommunications) / Arts 2015
Electrical (Telecommunications) / Commerce 2015
Electrical (Telecommunications) / Medical Science 2015
Electrical (Telecommunications) / Project Management 2015
Electrical (Telecommunications) / Science 2015
Electrical (Telecommunications) / Law 2015
Mechanical (till 2014) 2010, 2011, 2012, 2013
Mechatronic (till 2014) 2010, 2011, 2012, 2013
Project Engineering and Management (Civil) (till 2012) 2010, 2011, 2012
Project Engineering and Management (Civil) / Arts 2011
Project Engineering and Management (Civil) / Commerce 2010, 2011
Project Engineering and Management (Civil) / Science 2011
Software Engineering (till 2014) 2010, 2011, 2012, 2013, 2014
Telecommunications (till 2010) 2010
Civil/Science (Medical Science Stream) 2018, 2019
Electrical/Science (Medical Science Stream) 2018, 2019
Bachelor of Computer Science and Technology 2015, 2016, 2017
Bachelor of Computer Science and Technology (Advanced) 2015, 2016, 2017
Bachelor of Computer Science and Technology (Computer Science) 2014 and earlier 2010, 2011, 2012
Bachelor of Computer Science and Technology (Information Systems) 2014 and earlier 2011, 2012, 2013, 2014
Bachelor of Computer Science and Technology (Information Systems)(Advanced) 2014 and earlier 2013, 2014
Bachelor of Computer Science & Tech. Mid-Year 2016, 2017
Aeronautical Engineering / Science 2011, 2012, 2013, 2014
Aeronautical Engineering (Space) / Science 2011, 2012, 2013, 2014
Biomedical Engineering / Science 2013, 2014
Chemical & Biomolecular Engineering / Science 2011, 2012, 2013, 2014
Aeronautical / Science 2015, 2016, 2017
Aeronautical (Space) / Science 2015
Biomedical /Science 2015, 2016, 2017
Chemical & Biomolecular / Science 2015, 2016, 2017
Mechanical / Science 2015, 2016, 2017
Mechanical (Space) / Science 2015
Mechatronic / Science 2015, 2016, 2017
Mechatronic (Space) / Science 2015
Software Mid-Year 2016, 2017, 2018, 2019
Software 2015, 2016, 2017, 2018, 2019
Software / Science 2015, 2016, 2017
Mechanical Engineering (Biomedical) / Science 2011, 2012
Mechanical Engineering / Science 2011, 2012, 2013, 2014
Mechanical Engineering (Space) / Science 2011, 2012, 2013, 2014
Mechatronic Engineering / Science 2011, 2012, 2013, 2014
Mechatronic Engineering (Space) / Science 2011, 2012, 2013, 2014
Software Engineering / Arts 2011, 2012, 2013, 2014
Software Engineering / Commerce 2010, 2011, 2012, 2013, 2014
Software Engineering / Medical Science 2011, 2012, 2013, 2014
Software Engineering / Project Management 2012, 2013, 2014
Software Engineering / Science 2011, 2012, 2013, 2014
Software Engineering / Law 2010, 2011, 2012, 2013, 2014
Bachelor of Information Technology 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Arts 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Commerce 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Medical Science 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Science 2015, 2016, 2017
Information Technology (Computer Science) / Science 2012, 2013, 2014
Bachelor of Information Technology (Information Systems) 2014 and earlier 2013, 2014
Information Technology (Information Systems) / Science 2012, 2013, 2014
Bachelor of Information Technology/Bachelor of Laws 2015, 2016, 2017
Bachelor of Project Management (Built Environment) 2018, 2016, 2017
Bachelor of Project Management (Civil Engineering Science) 2018, 2016, 2017
Bachelor of Project Management (Software) 2018, 2016, 2017
Bachelor of Project Management (Built Environment) Mid-Year 2016, 2017, 2018
Bachelor of Project Management (Civil Engineering Science) Mid-Year 2016, 2017, 2018
Bachelor of Project Management (Software) Mid-Year 2016, 2017, 2018

Course Goals

This unit contributes to the achievement of the following course goals:

Attribute Practiced Assessed
(1) Maths/ Science Methods and Tools (Level 2) No 100%

These goals are selected from Engineering & IT Graduate Outcomes Table 2018 which defines overall goals for courses where this unit is primarily offered. See Engineering & IT Graduate Outcomes Table 2018 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.