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Unit of study_

MATH1933: Multivariable Calculus and Modelling (SSP)

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1923 Multivariable Calculus and Modelling (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH1933
Unit name Multivariable Calculus and Modelling (SSP)
Session, year
? 
Semester 2, 2020
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 3

Enrolment rules

Prohibitions
? 
MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923
Prerequisites
? 
None
Corequisites
? 
None
Assumed knowledge
? 

(HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent.

Available to study abroad and exchange students

Yes

Teaching staff and contact details

Coordinator Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s) Alexander Fish , alexander.fish@sydney.edu.au
Administrative staff MATH1933@sydney.edu.au Please send all email regarding MATH1933 to this address. It goes to the unit of study coordinator, the lecturers and administrative support.
Type Description Weight Due Length
Final exam (Open book) Type C final exam Final exam
multiple choice and written calculations
60% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO14 LO12 LO11 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 1
written calculations
4.5% Week 03
Due date: 07 Sep 2020

Closing date: 17 Sep 2020
10 days
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Online task Quiz 1
multiple choice or written answers
11.5% Week 06
Due date: 30 Sep 2020

Closing date: 30 Sep 2020
40 minutes
Outcomes assessed: LO3 LO4 LO5 LO6
Assignment Special Assignment 1
written calculations
4% Week 06
Due date: 15 Oct 2020

Closing date: 25 Oct 2020
10 days
Outcomes assessed: LO1 LO13 LO14
Assignment Assignment 2
Written calculations
4.5% Week 08
Due date: 19 Oct 2020

Closing date: 29 Oct 2020
10 days
Outcomes assessed: LO1 LO2 LO6 LO7 LO8 LO9
Online task Quiz 2
multiple choice or written answers
11.5% Week 11
Due date: 11 Nov 2020

Closing date: 11 Nov 2020
40 minutes
Outcomes assessed: LO7 LO8 LO9 LO10
Assignment Special Assignment 2
written calculations
4% Week 12
Due date: 19 Nov 2020

Closing date: 29 Nov 2020
10 days
Outcomes assessed: LO1 LO13 LO14
Type C final exam = Type C final exam ?
  • Quizzes: Two quizzes will be held online through Canvas. The quizzes are 40 Minutes and have to be submitted by the closing time of 23:59 on the due date. The quiz can be taken any time during the 24 hour period before the closing time. The better mark principle will be used for the quizzes so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that for each quiz, the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead.
  • Assignments:  All assignments must be submitted electronically, as one single typeset or scanned PDF file only, via Canvas by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly and that it is complete (check that you can view each page). Late submisions will receive a penalty.
  • Final Exam: There is one examination during the examination period at the end of Semester. Further information about the exam will be made available at a later date on Canvas.

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
Multiple weeks Special Topics Seminar (1 hr) LO13 LO14
Week 01 Introduction to models Lecture (2 hr) LO3
Week 02 First-order differential equations Lecture (2 hr) LO4 LO5
Week 03 Integrating factors and direction fields Lecture (2 hr) LO4 LO5
Week 04 Second-order differential equations. Boundary conditions Lecture (2 hr) LO6
Week 05 Systems of linear differential equations and interpretation through diagonalisation. Introduction to phase plane analysis Lecture (2 hr) LO6
Week 06 Functions of more than one real variable Lecture (2 hr) LO7
Week 07 Limits of functions of more than one real variable Lecture (2 hr) LO7
Week 08 Partial derivatives. Tangent planes. Linear approximation Lecture (2 hr) LO8 LO9
Week 09 Directional derivatives. Gradient vector and applications Lecture (2 hr) LO10
Week 10 Chain rule. Implicit differentiation Lecture (2 hr) LO10
Week 11 Optimising functions of two or more variables Lecture (2 hr) LO11
Week 12 Further optimisation and interpretation using diagonalisation Lecture (2 hr) LO12

Attendance and class requirements

  • Attendance: Students are expected to attend a minimum of 80% of timetabled activities for this unit, unless granted exemption by the Associate Dean. For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%.
  • Tutorial attendance: You should attend the tutorial given on your personal timetable. Attendance at tutorials will be recorded. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled. While there is no penalty if 80% attendance is not met we strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions.

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 3 credit point unit, this equates to roughly 60-75 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. apply mathematical logic and rigour to solving problems
  • LO2. express mathematical ideas and arguments coherently in written form
  • LO3. set up differential equations which arise from mathematical models of interest to scientists and engineers
  • LO4. understand the relationship between a first-order differential equation, its direction field, and its solution curves
  • LO5. solve separable and first-order linear differential equations
  • LO6. solve second-order homogeneous linear differential equations with constant coefficients
  • LO7. understand the concepts of limit and derivative for functions of more than one variable
  • LO8. calculate partial derivatives and understand their geometric significance
  • LO9. find equations of tangent planes to surfaces
  • LO10. calculate the direction derivative and gradient vector, and understand their physical significance
  • LO11. optimise functions of two or more variables
  • LO12. understand the connections between multivariable calculus and linear algebra
  • LO13. gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments
  • LO14. grasp new mathematical concepts beyond routine methods and calculations.

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.

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.