35101 Introduction to Linear Dynamical Systems

Warning: The information on this page is indicative. The subject outline for a particular semester, 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.

Handbook description

Problems as diverse as analysing the effects of interest rates or ecological change involve the study of systems that evolve in various ways. This subject provides an introduction to the modelling of change through difference and differential equations and allows students to see something of the power of mathematics through the interplay between linear algebra and differential equations. Topics include 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.

Subject objectives/outcomes

Students who successfully complete this subject should be able to:

1. understand the way in which mathematics can provide useful tools and resources to model real world problems – in particular, static and dynamic linear models
2. appreciate the interplay between linear algebra and differential equations
3. use formal and informal language to demonstrate understanding of the underlying concepts and their application
4. communicate the above knowledge clearly, logically and critically
5. use the computer system Mathematica to perform calculations and explore mathematical ideas relevant to the subject content
6. apply the subject matter covered in lectures, tutorials, laboratories and assignments to previously unseen problems
7. respond ethically and appropriately to the completion of learning activities and assessment tasks.
   

Contribution to course aims and graduate attributes

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
2. An inquiry-oriented approach
3. Professional skills and their appropriate application
4. The ability to be a lifelong learner
5. Engagement with the needs of society
6. Communication skills
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 problem solving and critical thinking whilst the regular weekly assessment 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 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 later subjects in the degree program, particularly 35102 Introduction to Analysis and Multivariable Calculus, 35212 Computational Linear Algebra and 35241 Optimisation in Quantitative Management.

Teaching and learning strategies

Weekly on campus: Two 1.5 hr lectures, 1 hr tutorial, 1 hr laboratory

Face-to-face classes will incorporate a range of teaching and learning strategies including short presentations, discussion of readings and student groupwork. 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. 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.

Study Advice: Take advantage of all the help available to you through the Mathematics Study Centre CB01.16.15!!

Content

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.

Assessment

Assessment Item 1: Weekly Learning Activities

Assessment Item 2: Class Test

Assessment Item 3: Final Examination

Minimum requirements

In order to pass this subject, a student must achieve a final result of 50% or more and achieve 40% or more on the final examination. The final result is simply the sum of all the marks gained in each piece of assessment. Students who obtain 50 marks or more but fail to score 40% or more on the final examination will be given an X grade (fail).

Recommended texts

McLelland, G. J. An Introduction to Linear Dynamical Systems, UTS, CN4632

[Available for $18 at UTS Union Shop, Level 3, Tower Building, Broadway; when sold out,
orders are taken on a prepaid basis only. A copy is also kept in UTS Library Closed Reserve.]

References

• Hass, J., Weir, M. D. & Thomas, G. B. University Calculus (Alternate Edition), Pearson Education, 2008. (ISBN9780321500977) – also used in 35102 Introduction to Analysis & Multivariable Calculus and 35232 Advanced Calculus
• Lay, D. C. Linear Algebra and its Applications, 4th edition, Pearson Education, 2010. (ISBN9780321623355) – also used in 35212 Computational Linear Algebra

If you want to purchase both books, then you can save money by asking the Coop Bookshop to order the combined value-pack (ISBN9314994248463). Members of the Coop Bookshop receive a further 9% discount off this price.

• O’Neil, P. V. Advanced Engineering Mathematics, 6th edition, Thomson Publishing, 2007. (ISBN053455208 )