MATHS 2102 - Differential Equations II

North Terrace Campus - Semester 1 - 2019

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
    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

    No information currently available.

    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
    Access to the internet.
    Recommended Resources
    Kreyszig, E. (2011), Advanced engineering mathematics, 10th edn, Wiley.
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions.  Students should make appropriate use of these resources.  Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures as the primary delivery mechanism for the material.  Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures.  A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.
    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
    Lectures 36 90
    Tutorials 6 24
    Assignments 6 42
    Total 156
    Learning Activities Summary
    The course will explore and develop the following.
    1. Basic definitions; Physical examples; Classification of types ODEs
    2. Basic definitions; IVPs; 1st order ODEs; Separable, Linear, Exact
    3. Graphical and numerical methods; directional fields and Eulers method
    4. Existence and Uniqueness for 1st order ODEs; Picard's Method and Theorem
    5. Existence and Uniqueness of IVPs for n-th order linear ODEs; Wronskian test
    6. n-th order homogenous linear constant coefficient ODEs
    7. Reduction of order
    8. Non-homogenous n-th order linear constant coeffs; Method of undetermined coefficients
    9. Variation of parameters
    10. Modelling and interpretation
    11. Linear ODEs with variable coefficients; Euler-Cauchy equation
    12. Power series, via computer algebra
    13. Legendre equation and polynomials
    14. Frobenius series solution and Bessels equation
    15. Frobenius series solution---classification of solutions.
    16. Systems ODES; modelling, eigenvalues and eigenvectors
    17. Systems ODES; algebraic and geometric multiplicity
    18. Periodic and odd/even functions; Generalised Fourier series
    19. Piecewise continous functions
    20. Fourier sine, cosine and complex Fourier series
    21. Fourier Integral and Transform
    22. Introduction to PDEs; modelling conservation of material
    23. Wave Equation and DAlemberts solution; car traffic; shocks
    24. Separation of variables; Wave, Heat, Laplace equation
    25. Vibrating Drum; Fourier Bessel series; interpretation
    26. Temperature field in a sphere; Fourier Legendre Series; interpretation  
  • 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
    Assignments 20% all
    Exam 70% all
    Quizzes 10% all
    Assessment Related Requirements
    An aggregate score of at least 50% is required to pass the course.
    Assessment Detail
                            
    Assessment itemDistributedDue dateWeighting
    Continuous assessment TBA TBA 10%
    Assignment 1 week 2 week 3 4%
    Assignment 2 week 4 week 5 4%
    Assignment 3 week 6 week 7 4%
    Assignment 4 week 8 week 9 4%
    Assignment 5 week 10 week 11 4%
    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

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    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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