Students
ACST604 – Mathematical Modelling
2014 – S1 Day
General Information
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| Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
Christopher Gordon
Contact via chris.gordon@mq.edu.au
Unit Convenor
Rod Yager
Contact via rod.yager@mq.edu.au
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|---|---|
| Credit points |
Credit points
4
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| Prerequisites |
Prerequisites
Admission to MActPrac or MCom or MAcc(Prof)MCom or MBioTechMCom
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| Corequisites |
Corequisites
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| Co-badged status |
Co-badged status
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| Unit description |
Unit description
This unit covers algebra and calculus. The algebra content discusses linearity and applications to geometry. Algebraic techniques involving matrices and determinants are developed and used to study geometrical problems. Linearity is then developed via the notion of vector spaces and used to study systems of linear equations. The notion of a limit is developed and used to study the differential and integral calculus involving functions of one real variable. This is then extended to functions of two real variables. The notion of a limit is enhanced by the study of sequences and series. Numerical techniques for integration are also discussed.
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Important Academic Dates
Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
Learning Outcomes
On successful completion of this unit, you will be able to:
- Development of a range of algebraic skills and proficiency in algebraic techniques applicable to Economics and Finance
- Systematic understanding of linear equations and the properties of linear models applicable to Economics and Finance
- Apply a wide range of techniques and ideas from differential and integral calculus to the analyse business,economic and financial data.
- Investigate a range of optimisation problems using the techniques of calculus
- Formulate models of a variety of real world situations using techniques from differential equations.
Assessment Tasks
| Name | Weighting | Due |
|---|---|---|
| Assessed Coursework | 30% | Fortnightly - see iLearn site |
| Class Test | 20% | 1 May |
| Creative Production | 10% | 30 May |
| Final examination | 40% | 13 June |
Assessed Coursework
Due: Fortnightly - see iLearn site
Weighting: 30%
A selection of exercises related to topics currently being studied. These are to be handed in during class time on the due date. Consult the lecturers for alternative submission arrangements if you are unable to attend on the due date.
No extensions will be granted. Students who have not submitted the task prior to the deadline for that component will be awarded a mark of 0, except for cases in which an application for special consideration is made and approved.
On successful completion you will be able to:
- Development of a range of algebraic skills and proficiency in algebraic techniques applicable to Economics and Finance
- Systematic understanding of linear equations and the properties of linear models applicable to Economics and Finance
- Apply a wide range of techniques and ideas from differential and integral calculus to the analyse business,economic and financial data.
- Investigate a range of optimisation problems using the techniques of calculus
- Formulate models of a variety of real world situations using techniques from differential equations.
Class Test
Due: 1 May
Weighting: 20%
1 hour in class exam on topics covered in Weeks 1-6
On successful completion you will be able to:
- Development of a range of algebraic skills and proficiency in algebraic techniques applicable to Economics and Finance
- Systematic understanding of linear equations and the properties of linear models applicable to Economics and Finance
- Apply a wide range of techniques and ideas from differential and integral calculus to the analyse business,economic and financial data.
Creative Production
Due: 30 May
Weighting: 10%
Groups of 2-4 students are required to produce a short video (5-10 minutes) in which they demonstrate how some of the ideas and techniques developed in this unit can be applied to provide significant insight into a problem of economic or financial interest. The active participation of all members of the group must be evident in the video.
(see iLearn for further details)
No extensions will be granted. Students who have not submitted the task prior to the deadline for that component will be awarded a mark of 0, except for cases in which an application for special consideration is made and approved.
On successful completion you will be able to:
- Development of a range of algebraic skills and proficiency in algebraic techniques applicable to Economics and Finance
- Systematic understanding of linear equations and the properties of linear models applicable to Economics and Finance
- Apply a wide range of techniques and ideas from differential and integral calculus to the analyse business,economic and financial data.
- Investigate a range of optimisation problems using the techniques of calculus
- Formulate models of a variety of real world situations using techniques from differential equations.
Final examination
Due: 13 June
Weighting: 40%
2 hour in class exam with emphasis on topics covered in Weeks 7-12.
On successful completion you will be able to:
- Development of a range of algebraic skills and proficiency in algebraic techniques applicable to Economics and Finance
- Systematic understanding of linear equations and the properties of linear models applicable to Economics and Finance
- Apply a wide range of techniques and ideas from differential and integral calculus to the analyse business,economic and financial data.
- Investigate a range of optimisation problems using the techniques of calculus
- Formulate models of a variety of real world situations using techniques from differential equations.
Delivery and Resources
Classes
• There are 5 hours of face-to-face teaching per week consisting of 1 x 3 hour lectorial on Mondays and 1 x 2 hour lectorial on Tuesdays. These sessions will present material in a mix of lecture and tutorial styles.
• Students are required to attend all classes.
• The timetable for classes can be found on the University web site at: http://www.timetables.mq.edu.au/
Required and Recommended Texts and/or Materials
Detailed notes for the topics covered in ACST604 can be found in the following online resources
▪ Elementary Mathematics by Chen and Duong
▪ Calculus for MATH123 by C. Cooper
▪ First Year Calculus by W.W.L Chen
▪ Linear Algebra by W.W.L Chen
▪ Miscellaneous Topics in First Year Mathematics by W.W.L Chen
These can be downloaded from the links found at http://maths.science.mq.edu.au/ACST604s113/texts.html
The same material is covered in many texts. You should try several of these, adopting one which suits your personal style of learning. The following texts are recommended for this unit, and are available from the
CO-OP Bookshop on campus, and are in the reference section of the Library.
▪ Jacques; Mathematics for Economics and Business, 6th edition
▪ Stewart, Redlin and Watson; Precalculus: mathematics for calculus, 5th edition
▪ Hughes-Hallett and Gleason; Calculus: single and multivariable, 4th edition
▪ Stewart; Calculus
▪ Trim: Calculus
▪ Anton: Linear Algebra and its Applications
▪ David C. Lay; Linear Algebra and its Applications,
Other similar texts are available in the Library, and for reference in the
Numeracy Centre (C5A 225).
What has changed
The nature and weighting of the assessment tasks has been changed, so that the assessment is more directly aligned to the development of good mathematical modelling practice.
A creative production task has been added to provide students with an opportunity to demonstrate their ability to communicate mathematical ideas in a way appropriate to their audience.
A requirement of satisfactory performance in the class tests has been added to address a concern that arose from a student who did not take the final class test seriously.
Technology requirements
• Students will require a computer with internet access to obtain copies of assignments and other material. A calculator with a range of mathematical functions will also be needed.
• Students will require access to a smart phone or similar device to record their video production.
• Course material is available on the learning management system (iLearn)
• All required material for this unit can also be accessed on the unit web-site at
http://maths.science.mq.edu.au/ACST604s114/
Unit Schedule
|
Week |
Calculus |
Linear Algebra |
|
1 |
Functions of a real variable, inverse functions: exponentials and logarithms |
Polynomials, degree, polynomial equations, factors and roots, iterative methods for finding roots |
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2 |
The derivative; curve sketching, rates of growth in some simple functions, optimization, relative error, linearization, Newton's method |
Binomial theorem |
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3 |
Applications of the derivative in finance |
Linear equations; application to network flow, economics |
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4 |
Integrals as areas; Techniques of integration; application to separable differential equations |
Gauss-Jordan elimination |
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5 |
Application of the integral to modelling in finance; Gamma and Beta functions |
Matrices and matrix transformations; application to economics |
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6 |
Functions of two variables: partial derivatives, total derivative, linearization of the derivative, tangent planes and normals, stationary points, change of variables, constrained optimization |
Determinants |
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7 |
Integration of a real valued function of two variables over simple regions of the plane (rectangles mainly); evaluation by Fubini's theorem; change of variables (simple examples e.g. linear transformation) |
Vectors; application to geometry in 3-space |
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Mid session break |
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8 |
Numerical integration rules: trapezoidal, Simpson |
n-dimensional real vector spaces, subspaces, linear combination, linear independence, basis and dimension |
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9 |
Real sequences, recurrence relations, series, relationship with integrals, power series, Taylor and Maclaurin series |
Row space, column space, nullspace, rank of a matrix |
|
10 |
Introduction to differential equations; modelling with differential equations |
Eigenvalues and eigenvectors, diagonalization of matrices; applications |
|
11 |
First order ordinary differential equations: separable equations, linear equation; applications |
Least squares solution of anoverdetermined system of linear equations |
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12 |
Systems of first order differential equations (2 equations only) |
Modelling with matrices in finance: stochastic matrices, symmetric matrices |
| 13 | Revision and class test | Revision and class test |
Learning and Teaching Activities
Lectorials
Policies and Procedures
Macquarie University policies and procedures are accessible from Policy Central. Students should be aware of the following policies in particular with regard to Learning and Teaching:
Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html
Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
Grading Policy http://mq.edu.au/policy/docs/grading/policy.html
Grade Appeal Policy http://mq.edu.au/policy/docs/gradeappeal/policy.html
Grievance Management Policy http://mq.edu.au/policy/docs/grievance_management/policy.html
Disruption to Studies Policy http://www.mq.edu.au/policy/docs/disruption_studies/policy.html The Disruption to Studies Policy is effective from March 3 2014 and replaces the Special Consideration Policy.
In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.
Student Code of Conduct
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/
Supplementary Exams
Further information regarding supplementary exams, including dates, is available here http://www.businessandeconomics.mq.edu.au/current_students/undergraduate/how_do_i/special_consideration
Student Support
Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/
Learning Skills
Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.
Student Services and Support
Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.
Student Enquiries
For all student enquiries, visit Student Connect at ask.mq.edu.au
IT Help
For help with University computer systems and technology, visit http://informatics.mq.edu.au/help/.
When using the University's IT, you must adhere to the Acceptable Use Policy. The policy applies to all who connect to the MQ network including students.
Compulsory requirements
In order to obtain a passing grade in this unit, students must provide a satisfactory demonstration of the attainment of the learning outcomes in the class test and final examination.
Research and Practice
The development of appropriate mathematical models, and and understanding of their properties, together with an appreciation of the underlying assumptions and the impact that any discrepancy between these assumptions and reality may have on the results are key aspects of practice and research in Actuarial science.
This unit focuses on equipping students with these skills and providing opportunities for students to develop and demonstrate these skills through the exploration of a range of case studies. While many of these will be contrived to reduce the complexity to a level that can be analysed with the limited range of tools that can be developed in a one-semester gateway unit, there will be an emphasis on real world problems and the development of good research and professional practice.
Changes since First Published
| Date | Description |
|---|---|
| 11/02/2014 | The Prerequisites was updated. |