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MAT3103 Mathematical Modelling and Dynamical Systems

Semester 2, 2020 On-campus Toowoomba
Short Description: Math Model & Dynamics Systems
Units : 1
Faculty or Section : Faculty of Health, Engineering and Sciences
School or Department : School of Sciences
Student contribution band : Band 2
ASCED code : 010101 - Mathematics
Grading basis : Graded

Staffing

Examiner:

Requisites

Pre-requisite: MAT2100 or MAT2500 or ENM2600

Rationale

Mathematical modelling is a process of fundamental importance to the practising researcher. Differential equations and an understanding of their qualitative behaviour provide a structure for the analysis of a wide variety of practical problems. This course uses mathematical tools developed so far and introduces dimensional analysis, the phase-plane concept, elements of bifurcation theory and theory of catastrophe, the calculus of variations and other contemporary methods to explore many problems of practical applications.

Synopsis

The course uses mathematical tools introduced in pre-requisite studies to model a variety of realistic phenomena surrounding us in everyday life and introduces calculus of variations for optimisation problems. The course emphasises the importance of the dimensional analysis and demonstrates the close connection between phase-plane concept and qualitative analysis of solutions of ODE. The basics of technical communication in the mathematical sciences are developed throughout the course. The oncampus offering of this course is normally available only in even-numbered years. The external offering of this course is available yearly.

Objectives

On completion of this course students will be able to:

  1. solve systems of linear differential equations
  2. analyse the dynamics of systems of differential equations to determine stability of solutions
  3. illustrate solutions by sketching phase portraits; deduce qualitative conclusions
  4. apply mathematical equations, modelling processes and principles to a range of authentic and real-life problems

Topics

Description Weighting(%)
1. Systems of differential equations: solution of linear ODE's, the conversion of higher-order linear ODE's to first-order systems; fixed points and phase portraits for second order ODEs, qualitative solution of nonlinear ODE in the vicinity of critical points. 15.00
2. Potentials, bifurcations, catastrophes. 15.00
3. Dimensions, scaling, dimensional analysis. 10.00
4. Growth and relaxation: exponential growth and decay, autoregulation. 10.00
5. Vibrations in complex systems: free vibrations, mechanical vibrations, nonlinear oscillations, forced vibrations, linear response, resonance, nonlinear response; coupled oscillators. 25.00
6. Dynamic and chaotic oscillations and waves. Simple and strange attractors. Auto-oscillations and auto-waves. 10.00
7. Calculus of variations: challenge problems and functionals; Euler-Lagrange equation, comparison functions, fundamental lemma; special cases; straight lines minimise arc length; geodesics; brachistochrone; the Lagrangian of dynamical systems. 15.00

Text and materials required to be purchased or accessed

ALL textbooks and materials available to be purchased can be sourced from (unless otherwise stated). (https://omnia.usq.edu.au/textbooks/?year=2020&sem=02&subject1=MAT3103)

Please for alternative purchase options from USQ Bookshop. (https://omnia.usq.edu.au/info/contact/)

Introductory Book (current year), Course MAT3103, Mathematical Modelling for Dynamics, USQ Distance and e-Learning Centre, Toowoomba.
(Available on course 精东传媒appDesk.)
精东传媒app Book (current year), Course MAT3103, Mathematical Modelling for Dynamics, USQ Distance and e-Learning Centre, Toowoomba.
(Available on course 精东传媒appDesk.)
Access to any graphical package to visualise solutions.
Access to computer or internet facilities for mathematical typesetting.

Reference materials

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.
Fabrikant, A.L., Stepanyants, Yu.A 1998, Propagation of Waves in Shear Flows, World Scientific, Singapore.
Higham, NJ 1998, Handbook of writing for the mathematical sciences, 2nd edn, SIAM, Philadelphia.
Kreyszig, E 2011, Advanced Engineering Mathematics, 10th edn, Wiley, New York.
Svobodny, T 1998, Mathematical Modeling for Industry and Engineering, Prentice Hall, Upper Saddle River N.J.
Weinstock, R 1974, Calculus of variations: with applications to physics and engineering, Dover Publications, New York.

Student workload expectations

Activity Hours
Assessments 42.00
Online Lectures 26.00
Private 精东传媒app 78.00
Tutorials 26.00

Assessment details

Description Marks out of Wtg (%) Due Date Notes
ASSIGNMENT 1 200 20 18 Aug 2020
ASSIGNMENT 2 200 20 22 Sep 2020
ASSIGNMENT 3 200 20 13 Oct 2020
ASSIGNMENT 4 400 40 23 Oct 2020 (see note 1)

Notes
  1. The assignment date or written assessment will be available via UConnect when the Alternative Assessment Schedule has been released. Students will be provided further instruction regarding the assignment by their course examiner via 精东传媒appDesk.

Important assessment information

  1. Attendance requirements:
    It is the students' responsibility to participate appropriately in all activities and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.

  2. Requirements for students to complete each assessment item satisfactorily:
    Due to COVID-19 the requirements for S2 2020 are:
    To satisfactorily complete an individual assessment item a student must achieve at least 50% of the marks for that item.

    Requirements after S2 2020:
    To satisfactorily complete an assessment item a student must achieve at least 50% of the marks or a grade of at least C-. Students do not have to satisfactorily complete each assessment item to be awarded a passing grade in this course. Refer to Statement 4 below for the requirements to receive a passing grade in this course.

  3. Penalties for late submission of required work:
    Students should refer to the Assessment Procedure (point 4.2.4)

  4. Requirements for student to be awarded a passing grade in the course:
    Due to COVID-19 the requirements for S2 2020 are:
    To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.

    Requirements after S2 2020:
    To be assured of receiving a passing grade a student must obtain at least 50% of the total weighted marks available for the course (i.e. the Primary Hurdle), and have satisfied the Secondary Hurdle (Supervised), i.e. the end of semester examination by achieving at least 40% of the weighted marks available for that assessment item.

    Supplementary assessment may be offered where a student has undertaken all of the required summative assessment items and has passed the Primary Hurdle but failed to satisfy the Secondary Hurdle (Supervised), or has satisfied the Secondary Hurdle (Supervised) but failed to achieve a passing Final Grade by 5% or less of the total weighted Marks.

    To be awarded a passing grade for a supplementary assessment item (if applicable), a student must achieve at least 50% of the available marks for the supplementary assessment item as per the Assessment Procedure (point 4.4.2).

  5. Method used to combine assessment results to attain final grade:
    The final grades for students will be assigned on the basis of the aggregate of the weighted marks /grades obtained for each of the summative assessment items in the course.

  6. Examination information:
    Due to COVID-19 the requirements for S2 2020 are: There is no examination in this course.

    Requirements after S2 2020:
    In a Restricted Examination, candidates are allowed access only to specific materials. The only materials that candidates may use in the restricted examination for this course are: writing materials (non-electronic and free from material which could give the student an unfair advantage in the examination); calculators which do not hold textual information (students must indicate on their examination paper the make and model of any calculator(s) they use during the examination). One A4 sheet of paper, written or typed on one or both sides with any material the student wishes to include. Students whose first language is not English, may take an appropriate unmarked non-electronic translation dictionary (but not technical dictionary) into the examination. Dictionaries with any handwritten notes will not be permitted. Translation dictionaries will be subject to perusal and may be removed from the candidate's possession until appropriate disciplinary action is completed if found to contain material that could give the candidate an unfair advantage.

  7. Examination period when Deferred/Supplementary examinations will be held:
    Due to COVID-19 the requirements for S2 2020 are:
    There is no examination in this course, there will be no deferred or supplementary examinations.

    Requirements after S2 2020:
    Any supplementary or deferred examinations for this course will be held during the next examination period.

  8. 精东传媒app Student Policies:
    Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene 精东传媒app policies and practices. These policies can be found at .

Assessment notes

  1. Exam paper presentation: All exam papers should be presented in accurate and clear writing by blue or black pen. Pencil writing is not acceptable.

  2. Assignments can be presented using any word processor such as Word or Latex, or can be neatly written by blue or black pen (but not by pencil).

Other requirements

  1. Computer, e-mail and Internet access:
    Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at .

  2. Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.

Date printed 6 November 2020