35511 Linear Dynamical Systems
Warning: The information on this page is indicative. The subject outline for a
particular session, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2019 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
There are course requisites for this subject. See access conditions.
Description
Analysing the effects of interest rate changes, ecological change and many other realworld problems requires the development of sophisticated quantitative skills for modelling complex dynamical systems. This subject develops the conceptual framework for modelling such systems based on the foundations provided by linear algebra, difference equations and differential equations. Topics covered include the formulation and solution of linear systems of algebraic equations; series solutions of differential equations; methods of integration; the algebraic eigenvalue problem and its application to the solution of linear systems of differential equations. Computational work is conducted using the mathematical software platform. Students participate in an extension seminar focusing on the creative integration of learned technical skills, and their ability to articulate the relevance of the mathematics being studied to their career.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
1.  understand and apply the properties of the elementary functions of calculus 

2.  apply the principles and techniques of elementary calculus, solve linear systems of algebraic equations, calculate the eigenvalues and eigenvectors of a real square matrix and solve simple linear systems of first order differential equations 
3.  Understand and relate the interplay between linear algebra and differential equations 
4.  use the computer system Mathematica to perform calculations and explore mathematical ideas relevant to the subject content 
5.  apply the subject matter covered in lectures, tutorials and laboratories to previously unseen problems 
6.  articulate the role that the specialist techniques (pertaining in particular to static and dynamic linear models) learnt in the subject play in a range of complex applications that arise in a professional workplace or a broader social context 
7.  effectively communicate to others, including nonspecialist audiences, the contribution made by the specialist mathematical techniques learnt in the subject to the solution of a complex problem arising in a professional workplace or a broader social context 
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
 Disciplinary knowledge and its appropriate application (1.0)
 An Enquiryoriented approach (2.0)
 Professional skills and their appropriate application (3.0)
 Engagement with the needs of society (5.0)
 Communication skills (6.0)
Contribution to the development of graduate attributes
Graduate Attributes (Faculty of Science)
The Faculty of Science has determined that its courses will aim to develop the following attributes in students at the completion of their course of study. Each subject will contribute to the development of these attributes in ways appropriate to the subject and the stage of progression, thus not all attributes are expected to be addressed in all subjects.
1. Disciplinary knowledge and its appropriate application
The lectures/tutorials and laboratory classes and exercises communicate knowledge and skills and demonstrate how to apply both the knowledge and the skills to a variety of problems. This graduate attribute is measured in assessment tasks 1 to 4.
2. An inquiryoriented approach
The lectures discuss various ways to address a particular question, and students will develop skills in determining the correct approach themselves in the laboratory classes. This graduate attribute is measured in assessment tasks 1 to 4.
3. Professional skills and their appropriate application
The ability to work effectively and responsibly in a group is emphasised in the group work components of the inclass assessments. Interpretation of numerical and graphical outputs of Mathematica software.
5. Engagement with the needs of society
Assessment task 1 introduces to the students a problem (physical sciences, life sciences, and/or engineering and business), presented in every day (nonmathematical) manner. Students are expected to apply the knowledge gained during lectures and tutorials to formulate and model a solution for the problem. These problems will be taken from current research themes and industrial practice.
6. Communication skills
Presentation of written and oral solutions to problems using appropriate professional language is emphasised in the inclass assessments.
Course Intended Learning Outcomes (Graduate Certificate in Mathematics)
In the Graduate Certificate in Mathematics these attributes are expressed in the following Course Intended Learning Outcomes (CILOs):
CILO 1: specialised knowledge of techniques and principles in an area of the mathematical sciences, providing a pathway for further learning. (GA1: Disciplinary knowledge and its appropriate application)
CILO 2: the ability to present a valid argument to draw conclusions from quantitative and qualitative information. (GA 2: An Inquiryoriented approach)
CILO 3: the ability to: formulate problems in mathematical terms; to structure information; to interpret information, and to generate and transmit solutions to complex problems. (GA 3: Professional skills and their appropriate application)
CILO 4: skills in finding reliable information independently, then critically evaluating, and applying the information that they find. (GA 4: Ability and motivation for continued intellectual development)
CILO 5: an appreciation for the wide variety of applications for mathematical methods. Applications to real world problems will be introduced through practical tasks and in assignments. (GA 5: Engagement with the needs of society)
CILO 6: the ability to appropriately formulate a mathematical model and develop a solution (or solutions). This includes the ability to: gain meaning from written and verbal instructions or problem statements; ask questions to clarify the problem; clearly and accurately communicate knowledge, skills and ideas to others, including an audience which is not expert in mathematics. By the end of the program, graduates will have advanced communications skills for use with peers, managers, and clients. (GA 6: Communication skills)
CILO 7: the ability to apply their knowledge to unfamiliar problems. This includes the mathematical formulation of realworld problems, the application of different techniques to solve them and the testing of assumptions on which a solution lies. (GA 7: Initiative and innovative ability)
This subject introduces students to the fundamentals of linear algebra and calculus that underpin more advanced applications of the mathematical sciences and gives some insight into the nature, practice and application of this type of mathematics. Homework questions are designed to help students develop skills in problemsolving and critical thinking and regular weekly learning tasks are designed to encourage the development of personal organisational skills and time management skills in addition to the practical skills of this subject. Students are introduced to the specialised notation used in mathematical discourse and develop skills in reading and writing mathematics using this notation; computer laboratory activities are designed to aid visualisation and concept development.
This subject introduces practical skills in mathematics that will provide a good foundation for other subjects in the course program, particularly 35512 Modelling Change, 35212 Computational Linear Algebra and 35241 Optimisation in Quantitative Management. Students will participate in an extension seminar focusing on the creative integration of learned technical skills, the critical analysis of complex ideas, and their ability to articulate for a variety of audiences the relevance of the mathematics being studied to their career and to the solution of complex problems arising in the broader social context.
Specific contribution of Subject Learning Outcomes (35511 Linear Dynamical Systems) to Graduate Attributes and Course Intended Learning Outcomes
This subject contributes to the graduate attributes and course intended learning outcomes in the following ways:
 SLOs 1, 2, 3 contribute to CILO 1 by developing essential disciplinary knowledge.
 SLOs 4, 5 contribute to CILO 2 by developing students’ computational expertise along with an understanding of how this expertise enables the solution of certain mathematical problems.
 SLO 6 contributes to CILOs 3, 4, 5 by developing students’ ability to identify mathematical techniques that are relevant to particular problems arising in a broader societal context.
 SLOs 6, 7 contribute to CILO 6 by developing students’ ability to articulate technically complex ideas and communicate these effectively to a broad audience.
 SLOs 6, 7 contribute to CILO 7 by developing students’ ability to formulate appropriate mathematical descriptions of complex problems, including the assumptions made during model formulation.
 SLO 8 contributes to CILO 4 by developing student’s understanding of the critical evaluation and ethical use of information.
Teaching and learning strategies
Weekly on campus: Two 1.5 hr lectures, 1 hr tutorial, 1 hr laboratory. Facetoface classes will incorporate a range of teaching and learning strategies including short presentations, discussion of readings and student group work. The five hours of classes each week are supported by at least five hours per week of individual or group study, developing and practising skills by doing many textbook questions, etc. UTSonline will be used as the official medium to disseminate learning materials. Students will need to prepare before the classroom using these learning resources such as readings and lectures handouts. The knowledge acquired in this preparation will be used in the classroom for active learning activities and group discussion. Additionally, students may use the online resources available at http://www.coursecompass.com/ for selected homework questions with links to “Help me solve this”, “View an example” as well as “textbook”, “video” and “animation”; UTSOnline will display links to other interactive websites that provide further insight.
In the extension seminar component, students will be required to identify at least two key areas of activity in a professional workplace or a broader social context in which mathematical techniques play a critical role in the solution of complex problems. For each chosen area, students will be required to describe:
 The nature of a specific complex business/social problem or task whose solution relies on advanced mathematical techniques, and the significance of that problem or task in the broader social or commercial context;
 How the mathematical techniques employed in the solution of the problem are related to the mathematical content of the subject, in terms accessible to a lay (nonexpert in mathematics) audience.
These competencies will be established by the completion of two assignments, completed independently.
In order to help students develop the skills and insights required to produce these outputs, they will
 Have regular contact (at least once every two weeks) with the subject coordinator to monitor and discuss progress on the learning tasks;
 Have access to, and be expected to contribute to, a collection of webbased resources focused on industry engagement and communication of mathematics;
 Be encouraged to attend occasional seminars focused on the engagement of mathematical sciences in industry.
Study Advice: Take advantage of all the help available to you through the Mathematics Study Centre CB04.03.331
Feedback will be provided to the students from week 1 during facetoface classrooms and tutorials across the entire semester. Verbal and in written feedback will be provided by tutors and also peers during the tutorials and laboratory component.
Content (topics)
Systems of linear equations, and their occurrence in everyday problems; methods for solving these equations using matrices and determinants; solution of differential equations by series; methods of integration; eigenvalues, eigenvectors, matrix exponentials and their use in the solution of systems of differential equations. The computer algebra system Mathematica is used for symbolic, graphical and numerical computations. The extension seminar will focus on the creative integration of technical skills drawn from the subject, and on articulating the relevance of the mathematics being studied to a career.
Assessment
Assessment task 1: In class tests (week 5 and week 9)
Intent:  To assess progress in learning during the previous 34 weeks of learning. Allows students to 

Objective(s):  This assessment task addresses subject learning objective(s): 1, 2, 3, 4, 5, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0, 3.0, 5.0 and 6.0 
Type:  Quiz/test 
Groupwork:  Individual 
Weight:  20% 
Length:  Each test is 60 minutes. There will be 2 tests in total. 
Criteria:  Students will be assessed on:

Assessment task 2: Individual learning task 1
Intent:  This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an inquiryoriented approach 3. professional skills and their appropriate application 6. communication skills 

Objective(s):  This assessment task addresses subject learning objective(s): 3, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0, 3.0 and 6.0 
Type:  Report 
Groupwork:  Individual 
Weight:  15% 
Criteria: 

Assessment task 3: Individual learning task 2
Intent:  This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an inquiryoriented approach 3. professional skills and their appropriate application 6. communication skills 

Objective(s):  This assessment task addresses subject learning objective(s): 3, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0, 3.0 and 6.0 
Type:  Presentation 
Groupwork:  Individual 
Weight:  20% 
Length:  Task 3A  Group critical review of 1  2 pages long 
Criteria: 

Assessment task 4: Final examination
Intent:  This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an inquiryoriented approach 3. professional skills and their appropriate application 6. communication skills 

Objective(s):  This assessment task addresses subject learning objective(s): 1, 2, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0, 3.0 and 6.0 
Type:  Examination 
Groupwork:  Individual 
Weight:  45% 
Criteria:  Students will be assessed on:

Minimum requirements
In order to pass this subject, a student must achieve a final result of 50% or more and must achieve both 40% or more of the combined marks available for the two individual learning tasks, and 40% or more on the final examination. The final mark is simply the sum of the marks gained in each piece of assessment. Students who obtain 50 marks or more but fail to score either 40% or more of the combined marks available for the two individual learning tasks, or 40% or more on the final examination, will be given an X grade (fail).
Recommended texts
As for 37131 Introduction to Linear Dynamical Systems.
References
As for 37131 Introduction to Linear Dynamical Systems.