MATHS 2102 - Differential Equations II

North Terrace Campus - Semester 1 - 2021

Most "real life" systems that are described mathematically, be they physical, biological, financial or economic, are described by means of differential equations. Our ability to predict the way in which these systems evolve or behave is determined by our ability to model these systems and find solutions of the equations explicitly or approximately. Every application and differential equation presents its own challenges, but there are various classes of differential equations, and for some of these there are established approaches and methods for solving them. Topics covered are: first order ordinary differential equations (ODEs), higher order ODEs, systems of ODEs, series solutions of ODEs, interpretation of solutions, Fourier analysis and solution of linear partial differential equations using the method of separation of variables.

  • General Course Information
    Course Details
    Course Code MATHS 2102
    Course Differential Equations II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3.5 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1012
    Incompatible MATHS 2201, MATHS 2106
    Course Description Most "real life" systems that are described mathematically, be they physical, biological, financial or economic, are described by means of differential equations. Our ability to predict the way in which these systems evolve or behave is determined by our ability to model these systems and find solutions of the equations explicitly or approximately. Every application and differential equation presents its own challenges, but there are various classes of differential equations, and for some of these there are established approaches and methods for solving them.

    Topics covered are: first order ordinary differential equations (ODEs), higher order ODEs, systems of ODEs, series solutions of ODEs, interpretation of solutions, Fourier analysis and solution of linear partial differential equations using the method of separation of variables.
    Course Staff

    Course Coordinator: Michael Chen

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    1. understand that physical systems can be described by differential equations
    2. understand the practical importance of solving differential equations
    3. understand the differences between initial value and boundary value problems (IVPs and BVPs)
    4. appreciate the importance of establishing the existence and uniqueness of solutions
    5. recognise an appropriate solution method for a given problem
    6. classify differential equations
    7. analytically solve a wide range of ordinary differential equations  (ODEs)
    8. obtain approximate solutions of ODEs using graphical and  numerical techniques
    9. use Fourier analysis in differential equation solution  methods  
    10. solve classical linear partial differential equations (PDEs)
    11. solve differential equations using computer software  
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    1-11
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    1-11
    Career and leadership readiness
    • technology savvy
    • professional and, where relevant, fully accredited
    • forward thinking and well informed
    • tested and validated by work based experiences
    11
  • Learning Resources
    Required Resources
    • Course notes: Differential Equations II, various authors, University of Adelaide (2021).
    • Instructional videos covering the material in the course notes
    Both these primary learning resources will be made available to enrolled students via the course's MyUni page.
    Recommended Resources
    Kreyszig, E. (2011), Advanced engineering mathematics, 10th edn, Wiley.

    Strogatz, S. (2000), Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, Perseus Publishing. [electronic copy from UoA library available here]
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as the textbook, videoed lectures, tutorial questions, assignments, sample solutions, quizzes (for self-testing) discussion boards, sample test/examination etc. Students must make appropriate use of all these resources to succeed in this course.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    Course delivery will occur on a weekly timetable. Each week typically consists of a variety of learning activities. All asynchronous activities/resources will be released at the beginning of each week, to enable students to personalise their schedules. Weekly tasks include:

    • Reading the relevant sections of the textbook
    • Viewing instructional videos
    • Participation in a synchronous scheduled (face-to-face or remote) tutorial session, which is designed for active learning
    • Completing online quizzes to strengthen understanding of the relevant weekly material
    • Review released solutions from the previous week's tutorial questions
    • Attend the online consulting sessions as necessary, particularly if the student is having difficulty in achieving the learning outcomes
    These Weekly Tasks are designed to provide complementary activities which carefully work with each other in helping students achieve the learning outcomes for the relevant sections for each week. The design ensures that each student has the opportunity to take responsibility for their own learning.
    Workload

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
    ActivityQuantityWorkload Hours
    Watching instructional videos 30
    Tutorials 12 24
    Quizzes 24
    Assignments 5 20
    Short projects 3 12
    Major project 1 24
    Other study/test revision 22
    Total 156
    Learning Activities Summary
    The course will explore and develop the following.
    1. First-order ordinary differential equations
    2. One-dimensional autonomous ODE models
    3. Second- and higher-order ODEs
    4. Partial differential equations
    5. Representing periodic functions by Fourier series
    6. Series solutions of ODEs
    7. More partial differential equations
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    ComponentWeightingObjective assessed
    Exam 30% all
    Test 1 5% all
    Test 2 5% all
    Assignments 20% all
    Weekly quizzes 10% all
    Tutorials/participation 10% all
    Short projects 9% all
    Major project 11% all

    Assessment Related Requirements
    An aggregate score of at least 50% is required to pass the course.
    Assessment Detail
    Assessment itemDistributedDue dateWeighting
    Exam - - 30%
    Test 1 - week 5 5%
    Test 2 - week 9 5%
    Weekly quizzes weekly weekly 10%
    Tutorial/participation quizzes weekly weekly 10%
    Assignment 1 week 1 week 2 4%
    Assignment 2 week 2 week 4 4%
    Assignment 3 week 6 week 8 4%
    Assignment 4 week 8 week 10 4%
    Assignment 5 week 10 week 12 4%
    Short project 1 week 1 week 3 3%
    Short project 2 week 4 week 6 3%
    Short project 3 week 6 week 7 3%
    Major project week 7 week 13 11%
    Submission
       
    1. All written assignments are to be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached, or submitted as pdf via MyUni.   
    2. Late assignments will not be accepted without a medical certificate.  
    3. Assignments normally have a two week turn-around time for feedback to students.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

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  • Policies & Guidelines
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