Overview
The unit covers topics in single variable integral calculus and linear algebra. The fundamental theorem of calculus is studied as well as various techniques for evaluating integrals like the substitution rule, integration by parts, trigonometric substitution, and various numerical approximations. A number of applications of integral calculus are investigated including finding the area between curves, the volume of solids and cylindrical shells, the length of a curve, the average value of a function, as well as applications in physics and engineering. Modelling real world problems with differential equations is studied along with techniques for solving first order differential equations using direction fields and Euler’s method, or using methods for separable equations. The use of differential equations to formulate exponential and logistic models of various growth and decay processes is also investigated. Matrices are revisited with particular focus on the determinant of a matrix and how it can be used to solve linear systems of equations. Finally, infinite sequences and series are studied along with methods of determining if they converge or diverge. The use of power series to integrate and differentiate functions is investigated with particular emphasis on the Taylor and Maclaurin series representation of a function. Mathematical software is also used to analyse and solve most problems studied in the unit. Note: If you have completed unit MATH11164 then you cannot take this unit.
Details
Pre-requisites or Co-requisites
Prerequisite: MATH12223 Calculus and Linear Algebra A
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 2 - 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
Another practice exam would be benefical.
Two practice exam papers have already been provided. The 2019 Standard Exam paper will be included as an additional 'practice exam' in 2020. This stock of practice exam papers will grow annually.
Feedback from Student evaluation
Students appreciated the comparison between University mathematics units and the modern senior school mathematics syllabus that helped to contextualise coursework.
Continue this practice.
Feedback from Student evaluation
Sufficient explanation and worked examples helped students in understanding and learning mathematics.
Continue this practice.
- Assess and apply the fundamental theorem of calculus
- Evaluate definite and indefinite integrals using the substitution rule, integration by parts, trigonometric substitution and other numerical approximations
- Critically analyse and apply integral calculus to problems of calculating areas, volumes, lengths, average values and other applications in physics and engineering
- Model problems with differential equations with a particular focus on exponential and logistic models
- Solve first order differential equations using direction fields and Euler’s method, or using methods for separable equations
- Use the determinant of a matrix to solve a system of linear equations
- Analyse the convergence and divergence of infinite sequences or series with particular focus on power series
- Calculate a Taylor or Maclaurin series representation of a function and use it to integrate or differentiate a function
- Use mathematical software to visualise, analyse, and solve problems in single variable integral calculus and linear algebra.
Alignment of Assessment Tasks to Learning Outcomes
| Assessment Tasks | Learning Outcomes | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| 1 - Written Assessment - 20% | |||||||||
| 2 - Written Assessment - 20% | |||||||||
| 3 - Take Home Exam - 60% | |||||||||
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 - 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 | |
| 1 - Written Assessment - 20% | ||||||||||
| 2 - Written Assessment - 20% | ||||||||||
| 3 - Take Home Exam - 60% | ||||||||||
Textbooks
There are no required textbooks.
Additional Textbook Information
As MATH12223 is the prerequisite for MATH12224, those students who passed MATH12223 in Term 1 of 2019/20 can keep using the same textbook for MATH12224 in Term 2 of 2020.
For students who passed MATH12223 prior to 2019, you may choose to use the extracted PDF file on Moodle or purchase a copy of the textbook from the Bookshop: "Essentials and Examples of Applied Mathematics" (1st edn, ISBN 9781488623820) by William Guo, Pearson Australia (2018). Paper copies are available on the CQUni Bookshop here: http://bookshop.cqu.edu.au (search MATH11160)
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.
w.guo@cqu.edu.au
Module/Topic
Unit Introduction
Review of Differentials
Fundamentals of Indefinite integrals
Chapter
Section 11.3.1 Differentials of Functions
Section 12.1 Fundamentals of Indefinite integrals
Events and Submissions/Topic
Read Sections 11.3.1 & 12.1
Complete Week 1 exercises
Module/Topic
Integration by Substitution
Chapter
Section 12.2.1 Integration by Substitution
Events and Submissions/Topic
Read Section 12.2.1; complete Week 2 exercises
Module/Topic
Integration by Parts
Chapter
Section 12.2.2 Integration by Parts
Events and Submissions/Topic
Read Section 12.2.2; complete Week 3 exercises
Module/Topic
Integration by Complete Differentials and Partial Fractions
Chapter
Sections 12.2.3-12.2.4 Integration by Complete Differentials and Partial Fractions
Events and Submissions/Topic
Read Sections 12.2.3-12.2.4; complete Week 4 exercises
Module/Topic
Applications of Indefinite Integration
Chapter
Section 12.3 Applications of Indefinite Integration
Events and Submissions/Topic
Read Section 12.3; complete Week 5 exercises
Module/Topic
Chapter
Events and Submissions/Topic
Module/Topic
Essentials of Definite Integration
Chapter
Section 13.1 Essentials of Definite Integration
Events and Submissions/Topic
Read Section 13.1; complete Week 6 exercises
Assignment 1 Due: Week 6 Wednesday (26 Aug 2020) 11:59 pm AEST
Module/Topic
Applications of Definite Integration (I)
Chapter
Section 13.2.1 Applications of Definite Integration
Events and Submissions/Topic
Read Section 13.2.1; complete Week 7 exercises
Module/Topic
Applications of Definite Integration (II)
Chapter
Sections 13.2.1-13.2.2 Applications of Definite Integration
Events and Submissions/Topic
Read Sections 13.2.1-13.2.2; complete Week 8 exercises
Module/Topic
Numeric Integration
Chapter
Section 16.3 Numeric Integration
Events and Submissions/Topic
Read Section 16.3; complete Week 9 exercises
Module/Topic
Solving Systems of Linear Equations (I)
Chapter
Sections 15.1 and 15.2.1 Solving Systems of Linear Equations
Events and Submissions/Topic
Read Sections 15.1 & 15.2.1; complete Week 10 exercises
Module/Topic
Solving Systems of Linear Equations (II)
Chapter
Sections 15.2.2 and 15.2.3 Solving Systems of Linear Equations
Events and Submissions/Topic
Read Sections 15.2.2 & 15.2.3; complete Week 11 exercises
Module/Topic
Examination preview and preparation
Chapter
Events and Submissions/Topic
Module/Topic
Chapter
Events and Submissions/Topic
Module/Topic
Chapter
Events and Submissions/Topic
1 Written Assessment
This is an individual assignment.
This assignment is to test student's learning outcomes of topics studied in Weeks 1-5. The assignment details are provided on the Moodle website.
Week 6 Wednesday (26 Aug 2020) 11:59 pm AEST
Week 8 Wednesday (9 Sept 2020)
It is envisaged that feedback and solutions will be available in two weeks, or as soon as the process is completed.
The final mark is out of 20. 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. Assignments will receive NO marks if submitted after the solutions are released.
- Assess and apply the fundamental theorem of calculus
- Evaluate definite and indefinite integrals using the substitution rule, integration by parts, trigonometric substitution and other numerical approximations
- Use mathematical software to visualise, analyse, and solve problems in single variable integral calculus and linear algebra.
- Communication
- Problem Solving
- Critical Thinking
- Information Literacy
- Information Technology Competence
- Ethical practice
2 Written Assessment
This is an individual assignment.
This assignment is to test student's learning outcomes of topics studied in Weeks 6-11. The assignment details are provided on the Moodle website.
Week 12 Wednesday (7 Oct 2020) 11:59 pm AEST
It is envisaged that feedback and solutions will be available prior to sitting the standard examination.
The final mark is out of 20. 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. Assignments will receive NO marks if submitted after the solutions are released.
- Critically analyse and apply integral calculus to problems of calculating areas, volumes, lengths, average values and other applications in physics and engineering
- Model problems with differential equations with a particular focus on exponential and logistic models
- Solve first order differential equations using direction fields and Euler’s method, or using methods for separable equations
- Use mathematical software to visualise, analyse, and solve problems in single variable integral calculus and linear algebra.
- Communication
- Problem Solving
- Critical Thinking
- Information Literacy
- Information Technology Competence
- Ethical practice
3 Take Home Exam
Due to uncertainties of recovery post the COVID-19 pandemic, the Standard Examination for Term 2 of 2020 MATH12224 is temporarily replaced by a Take Home Exam. You are given 24 hours to work on the Take Home Exam. During the 24-hour timeframe, you will need to download the exam from the unit’s Moodle website, complete it and upload it back. Detailed instructions for the Take Home Exam will be communicated near the end of Term 2.
The Take Home Exam will be scheduled during the Exam Week.
The results will be made available on Certification of Grades day. Like a regular exam, your marked answer script will not be returned to you, unless you apply to see it as part of the first step of the review of grade process.
This assessment task is open book. You can reference all notes and study materials. Any submission after the deadline will not be accepted. You are required to do your own work, maintaining academic integrity with all honesty. Your submission may be subject to additional verification in the form of an oral defence through interview with the Unit Coordinator (or nominee). Students unable to satisfactorily answer questions about their submitted solution(s) will receive no marks for the question(s).
Answered 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.
- Assess and apply the fundamental theorem of calculus
- Evaluate definite and indefinite integrals using the substitution rule, integration by parts, trigonometric substitution and other numerical approximations
- Critically analyse and apply integral calculus to problems of calculating areas, volumes, lengths, average values and other applications in physics and engineering
- Model problems with differential equations with a particular focus on exponential and logistic models
- Solve first order differential equations using direction fields and Euler’s method, or using methods for separable equations
- Use the determinant of a matrix to solve a system of linear equations
- Analyse the convergence and divergence of infinite sequences or series with particular focus on power series
- Calculate a Taylor or Maclaurin series representation of a function and use it to integrate or differentiate a function
- Communication
- Problem Solving
- Critical Thinking
- Information Literacy
- Ethical practice
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?
