Due to the university's COVID-19 response, the exam in this unit will be replaced with a 24 hour take-home exam.
Passing criteria: 40% of the available marks on the assessment
More details will be available in Moodle. Learning outcomes assessed will be unchanged.
Overview
In this unit, you will study topics in multivariable calculus - differential and integral calculus as applied to scalar and vector functions of more than one variable. After reviewing vectors and the geometry of space, you will investigate derivatives and integrals of vector functions with applications to arc length, curvature of space curves and motion in space. Partial differentiation is studied by defining limits and continuity in two dimensions, and is used to define tangent planes, linear approximations and differentials. The chain rule is developed for functions of more than one variable as well as directional derivatives and the gradient vector, which leads into multivariate optimisation with and without constraints. You will study multiple integrals by expanding the concept of single variable integrals to double and triple integrals which are evaluated as iterated integrals. These ideas are further developed to show you how to calculate volumes, surface areas, masses and centroids of very general regions in two and three dimensional space as well as probability for bivariate distributions. Finally you will investigate the calculus of vector fields, line integrals and surface integrals. The connection between these new types of integrals and multiple integrals is given in three theorems - Green’s Theorem, Stokes’ Theorem and the Divergence Theorem - which turn out to be higher-dimensional versions of the Fundamental Theorem of Calculus. Mathematical software is used to investigate and solve most problems in the unit.
Details
Pre-requisites or Co-requisites
Prerequisite: MATH12224 Anti-requisite: MATH12172
Important note: Students enrolled in a subsequent unit who failed their pre-requisite unit, should drop the subsequent unit before the census date or within 10 working days of Fail grade notification. Students who do not drop the unit in this timeframe cannot later drop the unit without academic and financial liability. See details in the Assessment Policy and Procedure (Higher Education Coursework).
Offerings For Term 1 - 2020
Attendance Requirements
All on-campus students are expected to attend scheduled classes - in some units, these classes are identified as a mandatory (pass/fail) component and attendance is compulsory. International students, on a student visa, must maintain a full time study load and meet both attendance and academic progress requirements in each study period (satisfactory attendance for International students is defined as maintaining at least an 80% attendance record).
Recommended Student Time Commitment
Each 6-credit Undergraduate unit at CQUniversity requires an overall time commitment of an average of 12.5 hours of study per week, making a total of 150 hours for the unit.
Class Timetable
Assessment Overview
Assessment Grading
This is a graded unit: your overall grade will be calculated from the marks or grades for each assessment task, based on the relative weightings shown in the table above. You must obtain an overall mark for the unit of at least 50%, or an overall grade of 'pass' in order to pass the unit. If any 'pass/fail' tasks are shown in the table above they must also be completed successfully ('pass' grade). You must also meet any minimum mark requirements specified for a particular assessment task, as detailed in the 'assessment task' section (note that in some instances, the minimum mark for a task may be greater than 50%). Consult the University's Grades and Results Policy for more details of interim results and final grades.
All University policies are available on the CQUniversity Policy site.
You may wish to view these policies:
- Grades and Results Policy
- Assessment Policy and Procedure (Higher Education Coursework)
- Review of Grade Procedure
- Student Academic Integrity Policy and Procedure
- Monitoring Academic Progress (MAP) Policy and Procedure - Domestic Students
- Monitoring Academic Progress (MAP) Policy and Procedure - International Students
- Student Refund and Credit Balance Policy and Procedure
- Student Feedback - Compliments and Complaints Policy and Procedure
- Information and Communications Technology Acceptable Use Policy and Procedure
This list is not an exhaustive list of all University policies. The full list of University policies are available on the CQUniversity Policy site.
Feedback, Recommendations and Responses
Every unit is reviewed for enhancement each year. At the most recent review, the following staff and student feedback items were identified and recommendations were made.
Feedback from Student evaluation
Students have positive comments on the textbook, assignment questions, videos and examples.
Continue to provide current learning and teaching support.
Feedback from Student evaluation
Students thought the exam was difficult.
This unit is challenging for most students. The previous fundamental mathematical knowledge and skills play a very important role in this unit, such as the basic algebra, 3-D geometry and calculus. In the previous take home exam, students have two weeks to finish. In the open book exam, they only have three hours and it is not possible to discuss with others. This caused a shift in the grade distribution to the lower part. Our recommendation is to add more tutorial examples for students to follow and increase the Zoom session attendance and engagement.
- Solve geometric problems in three dimensional space using vectors and their operators
- Differentiate and integrate of vector functions to solve problems involving arc length and curvature of space curves
- Apply the concept of the limit, continuity and partial derivative of a function of many variables to calculate tangent planes, linear approximations and differentials
- Optimise multivariable problems, either with or without constraints, using the chain rule, directional derivatives and the gradient vector
- Calculate double and triple integrals over general regions, and also in polar, cylindrical and spherical coordinates
- Simplify the evaluation of a double or triple integral by applying the change of variables technique
- Solve problems involving the curl and divergence of a vector field
- Investigate the calculus of vector fields, line integrals and surface integrals through Green’s theorem, Stokes’ Theorem and the Divergence Theorem
- Use mathematical software to visualise, analyse and solve problems in multivariable calculus.
Alignment of Assessment Tasks to Learning Outcomes
| Assessment Tasks | Learning Outcomes | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| 1 - Written Assessment - 25% | |||||||||
| 2 - Written Assessment - 25% | |||||||||
| 3 - Examination - 50% | |||||||||
Alignment of Graduate Attributes to Learning Outcomes
| Graduate Attributes | Learning Outcomes | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| 1 - Communication | |||||||||
| 2 - Problem Solving | |||||||||
| 3 - Critical Thinking | |||||||||
| 4 - Information Literacy | |||||||||
| 5 - Team Work | |||||||||
| 6 - Information Technology Competence | |||||||||
| 7 - Cross Cultural Competence | |||||||||
| 8 - Ethical practice | |||||||||
| 9 - Social Innovation | |||||||||
| 10 - First Nations Knowledges | |||||||||
| 11 - Aboriginal and Torres Strait Islander Cultures | |||||||||
Alignment of Assessment Tasks to Graduate Attributes
| Assessment Tasks | Graduate Attributes | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
| 1 - Written Assessment - 25% | |||||||||||
| 2 - Written Assessment - 25% | |||||||||||
| 3 - Examination - 50% | |||||||||||
Textbooks
Calculus : Concepts and Contexts
- Edition 4 (2018)
- Authors: Stewart, J.
- Brooks-Cole, Cengage Learning
- Belmont Belmont , CA , U.S.A.
- ISBN: 9781337687669
- Binding: Hardcover
Additional Textbook Information
Copies are available for purchase at the CQUni Bookshop here: http://bookshop.cqu.edu.au (search on the Unit code)
IT Resources
- CQUniversity Student Email
- Internet
- Unit Website (Moodle)
All submissions for this unit must use the referencing style: Harvard (author-date)
For further information, see the Assessment Tasks.
r.dodd@cqu.edu.au
y.wang2@cqu.edu.au
Week 1
Begin Date: 09 Mar 2020Module/Topic
Three Dimensional Coordinate Systems, Vectors, The Dot and Cross Product, Equations of Lines and Planes, Functions and Surfaces, Cylindrical and Spherical Coordinates
Chapter
All of Chapter 9
Events and Submissions/Topic
Week 2
Begin Date: 16 Mar 2020Module/Topic
Vector Functions and Space Curves, Derivatives and Integrals of Vector Functions, Arc Length and Curvature, Motion in Space
Chapter
Sections 10.1 to 10.4
Events and Submissions/Topic
Week 3
Begin Date: 23 Mar 2020Module/Topic
Parametric Surfaces, Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations
Chapter
Section 10.5 plus
Sections 11.1 to 11.4 (part)
Events and Submissions/Topic
Week 4
Begin Date: 30 Mar 2020Module/Topic
Differentials, The Chain Rule and Implicit Differentiation, Directional Derivatives and the Gradient Vector
Chapter
Sections 11.4 to 11.6
Events and Submissions/Topic
Week 5
Begin Date: 06 Apr 2020Module/Topic
Maximum and Minimum Values, Lagrange Multipliers
Chapter
Sections 11.7 & 11.8
Events and Submissions/Topic
Vacation Week
Begin Date: 13 Apr 2020Module/Topic
Chapter
Events and Submissions/Topic
Week 6
Begin Date: 20 Apr 2020Module/Topic
Double Integrals over Rectangles and General Regions, Double Iterated Integrals, Double Integrals in Polar Coordinates
Chapter
Sections 12.1 to 12.4
Events and Submissions/Topic
Week 7
Begin Date: 27 Apr 2020Module/Topic
Applications of Double Integrals, Surface Area
Chapter
Sections 12.5 & 12.6
Events and Submissions/Topic
Week 8
Begin Date: 04 May 2020Module/Topic
Triple Integrals and Triple Integrals in Cylindrical and Spherical Coordinates
Chapter
Sections 12.7 & 12.8
Events and Submissions/Topic
Week 9
Begin Date: 11 May 2020Module/Topic
Change of Variables in Multiple Integrals, Vector Fields, Line Integrals
Chapter
Section 12.9 plus
Sections 13.1 & 13.2
Events and Submissions/Topic
Week 10
Begin Date: 18 May 2020Module/Topic
The Fundamental Theorem for Line Integrals, Green's Theorem
Chapter
Sections 13.3 & 13.4
Events and Submissions/Topic
Week 11
Begin Date: 25 May 2020Module/Topic
Curl and Divergence, Surface Integrals
Chapter
Sections 13.5 & 13.6
Events and Submissions/Topic
Week 12
Begin Date: 01 Jun 2020Module/Topic
Stoke's Theorem, The Divergence Theorem, Summary
Chapter
Sections 13.7 to 13.9
Events and Submissions/Topic
Review/Exam Week
Begin Date: 08 Jun 2020Module/Topic
Chapter
Events and Submissions/Topic
Exam Week
Begin Date: 15 Jun 2020Module/Topic
Chapter
Events and Submissions/Topic
1 Written Assessment
Submit full worked solutions to Assignment 1 exercises. The exercises cover topics from Weeks 1 to 5 of the course. The selected exercises and other details are given on the Moodle website.
Week 6 Friday (24 Apr 2020) 11:00 pm AEST
Submit by 11pm on Friday of Week 6
Week 8 Friday (8 May 2020)
Results will be available to students approximately two weeks after the submission date.
The final mark is out of 25. Questions are awarded the full marks allocated if they are error-free, partial marks if there are some problems, and no marks if not attempted or contain so many errors as to render the attempt to be without value. To ensure maximum benefit, answers to all questions should be neatly and clearly presented and all appropriate working should be shown.
- Solve geometric problems in three dimensional space using vectors and their operators
- Differentiate and integrate of vector functions to solve problems involving arc length and curvature of space curves
- Apply the concept of the limit, continuity and partial derivative of a function of many variables to calculate tangent planes, linear approximations and differentials
- Optimise multivariable problems, either with or without constraints, using the chain rule, directional derivatives and the gradient vector
- Use mathematical software to visualise, analyse and solve problems in multivariable calculus.
- Communication
- Problem Solving
- Critical Thinking
- Information Literacy
- Information Technology Competence
- Ethical practice
2 Written Assessment
Submit full worked solutions to Assignment 2 exercises. The exercises cover topics from Weeks 6 to 9 of the course. The selected exercises and other details are given on the Moodle website.
Week 10 Friday (22 May 2020) 11:00 pm AEST
Submit by 11pm on Friday of Week 10
Week 12 Friday (5 June 2020)
Results will be available to students approximately two weeks after the submission date.
The final mark is out of 25. Questions are awarded the full marks allocated if they are error-free, partial marks if there are some problems, and no marks if not attempted or contain so many errors as to render the attempt to be without value. To ensure maximum benefit, answers to all questions should be neatly and clearly presented and all appropriate working should be shown.
- Calculate double and triple integrals over general regions, and also in polar, cylindrical and spherical coordinates
- Simplify the evaluation of a double or triple integral by applying the change of variables technique
- Use mathematical software to visualise, analyse and solve problems in multivariable calculus.
- Communication
- Problem Solving
- Critical Thinking
- Information Literacy
- Information Technology Competence
- Ethical practice
Examination
Calculator - all non-communicable calculators, including scientific, programmable and graphics calculators are authorised
As a CQUniversity student you are expected to act honestly in all aspects of your academic work.
Any assessable work undertaken or submitted for review or assessment must be your own work. Assessable work is any type of work you do to meet the assessment requirements in the unit, including draft work submitted for review and feedback and final work to be assessed.
When you use the ideas, words or data of others in your assessment, you must thoroughly and clearly acknowledge the source of this information by using the correct referencing style for your unit. Using others’ work without proper acknowledgement may be considered a form of intellectual dishonesty.
Participating honestly, respectfully, responsibly, and fairly in your university study ensures the CQUniversity qualification you earn will be valued as a true indication of your individual academic achievement and will continue to receive the respect and recognition it deserves.
As a student, you are responsible for reading and following CQUniversity’s policies, including the Student Academic Integrity Policy and Procedure. This policy sets out CQUniversity’s expectations of you to act with integrity, examples of academic integrity breaches to avoid, the processes used to address alleged breaches of academic integrity, and potential penalties.
What is a breach of academic integrity?
A breach of academic integrity includes but is not limited to plagiarism, self-plagiarism, collusion, cheating, contract cheating, and academic misconduct. The Student Academic Integrity Policy and Procedure defines what these terms mean and gives examples.
Why is academic integrity important?
A breach of academic integrity may result in one or more penalties, including suspension or even expulsion from the University. It can also have negative implications for student visas and future enrolment at CQUniversity or elsewhere. Students who engage in contract cheating also risk being blackmailed by contract cheating services.
Where can I get assistance?
For academic advice and guidance, the Academic Learning Centre (ALC) can support you in becoming confident in completing assessments with integrity and of high standard.
What can you do to act with integrity?
