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Unit of study_

MATH2061: Linear Mathematics and Vector Calculus

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.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH2061
Unit name Linear Mathematics and Vector Calculus
Session, year
? 
Intensive August, 2020
Attendance mode Block mode
Location Camperdown/Darlington, Sydney
Credit points 6

Enrolment rules

Prohibitions
? 
MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922
Prerequisites
? 
(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907)
Corequisites
? 
None
Available to study abroad and exchange students

No

Teaching staff and contact details

Coordinator Nathan Brownlowe, nathan.brownlowe@sydney.edu.au
Type Description Weight Due Length
Tutorial quiz Quizzes
2x Quizzes in Weeks 3 and 4
30% Multiple weeks 40 mins each
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14
Assignment Assignments
2x assignment due Weeks 2 and 3
10% Multiple weeks 1 week per assignment
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14
Final exam (Open book) Type C final exam Final Exam
Online open book without invigilation
60% Week 05 2 hours
Outcomes assessed: LO1 LO14 LO13 LO12 LO11 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Type C final exam = Type C final exam ?

Detailed information for each assessment can be found on Canvas.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Representing complete or close to complete mastery of the material.

Distinction

75 - 84

Representing excellence, but substantially less than complete mastery.

Credit

65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.

Pass

50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see sydney.edu.au/students/guide-to-grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, and the resources available to all students.

The University expects students and staff to act ethically and honestly and will treat all allegations of academic dishonesty or plagiarism seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic dishonesty. If such matches indicate evidence of plagiarism or other forms of dishonesty, your teacher is required to report your work for further investigation.

WK Topic Learning activity Learning outcomes
Week 01 Linear systems, Gaussian elimination, vector spaces and subspaces Block teaching (3 hr) LO1 LO2
Subspaces, linear combinations, span,linear dependence and independence Block teaching (3 hr) LO2 LO3 LO4 LO5
Linear dependence and independence, span, basis and dimension Block teaching (1 hr) LO3 LO4 LO5
Week 02 Linear dependence and independence, span, basis and dimension Block teaching (2 hr) LO3 LO4 LO5
Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity and linear transformations Block teaching (3 hr) LO5 LO6 LO7
Eigenvalues and eigenvectors, diagonalisation theorem and Leslie population model Block teaching (3 hr) LO8 LO9
Recurrence relations and systems of linear differential equations Block teaching (2 hr) LO9
Week 03 Vector equations of lines and curves (revision), arc length, two types of line integrals and work done by a force Block teaching (3 hr) LO10
Vector fields, grad and curl, normals to surfaces, conservative fields and potential functions Block teaching (3 hr) LO10 LO11
Double integrals, area, volume and mass. Div (divergence of a vector field), green’s theorem and flux across a curve Block teaching (3 hr) LO11 LO12 LO13 LO14
Week 04 Green’s theorem continued., surface area, surface integrals, flux across a surface, polar, cylindrical and spherical coordinates Block teaching (3 hr) LO11 LO12 LO13 LO14
Triple integrals., volume and mass revisited and Gauss’ divergence theorem Block teaching (3 hr) LO11 LO12 LO13 LO14
Triple integrals in cylindrical/spherical coordinates, stokes’ theorem and connections between different types of integrals Block teaching (1 hr) LO11 LO12 LO13 LO14
Triple integrals in cylindrical/spherical coordinates, stokes’ theorem and connections between different types of integrals Block teaching (2 hr) LO11 LO12 LO13 LO14
Revision Block teaching (7 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University’s graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. solve a system of linear equations
  • LO2. apply the subspace test in several different vector spaces
  • LO3. calculate the span of a given set of vectors in various vector spaces
  • LO4. test sets of vectors for linear independence and dependence
  • LO5. find bases of vector spaces and subspaces
  • LO6. find a polynomial of minimum degree that fits a set of points exactly
  • LO7. find bases of the fundamental subspaces of a matrix
  • LO8. test whether an n × n matrix is diagonalisable, and if it is find its diagonal form
  • LO9. apply diagonalisation to solve recurrence relations and systems of DEs
  • LO10. extended (from first year) their knowledge of vectors in two and three dimensions, and of functions of several variables
  • LO11. evaluate certain line integrals, double integrals, surface integrals and triple integrals
  • LO12. evaluate certain line integrals, double integrals, surface integrals and triple integrals
  • LO13. understand the physical and geometrical significance of these integrals
  • LO14. know how to use the important theorems of Green, Gauss and Stokes.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9
No changes have been made since this unit was last offered.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

  • No eating or drinking is allowed in any laboratory under any circumstances
  • A laboratory coat and closed-toe shoes are mandatory
  • Follow safety instructions in your manual and posted in laboratories
  • In case of fire, follow instructions posted outside the laboratory door
  • First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
  • As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.