MATHS 2106 - Differential Equations for Engineers II

North Terrace Campus - Semester 1 - 2021

Mathematical models are used to understand, predict and optimise engineering systems. Many of these systems are deterministic and are modelled using differential equations. This course provides an introduction to differential equations and their applications in engineering. The following topics are covered: Linear ordinary differential equations of second and higher order, series solutions, Fourier series, Laplace transforms, partial differential equations, Fourier transforms.

  • General Course Information
    Course Details
    Course Code MATHS 2106
    Course Differential Equations for Engineers II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 5 hours per week.
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1012
    Incompatible MATHS 2102, MATHS 2201
    Assumed Knowledge Basic Matlab programming skills such as would be obtained from ENG 1002 or ENG 1003 or COMP SCI 1012 or COMP SCI 1101 or COMP SCI 1102 or COMP SCI 1201 or MECH ENG 1100 or MECH ENG 1102 or MECH ENG 1103 or MECH ENG 1104 or MECH ENG 1105 or C&ENVENG 1012
    Restrictions Available to Bachelor of Engineering students only.
    Course Description Mathematical models are used to understand, predict and optimise engineering
    systems. Many of these systems are deterministic and are modelled using differential equations. This course provides an introduction to differential equations and their applications in engineering. The following topics are covered: Linear ordinary differential equations of second and higher order, series solutions, Fourier series, Laplace transforms, partial differential equations, Fourier transforms.
    Course Staff

    Course Coordinator: Dr Trent Mattner

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    Students who successfully complete the course will be able to:
    1. Derive mathematical models of physical systems.
    2. Present mathematical solutions in a concise and informative manner.
    3. Recognise ODEs that can be solved analytically and apply appropriate solution methods.
    4. Solve more difficult ODEs using power series.
    5. Know key properties of some special functions.
    6. Express functions using Fourier series.
    7. Solve certain ODEs and PDEs using Fourier and Laplace transforms.
    8. Solve problems numerically via the fast Fourier transform using Matlab.
    9. Solve standard PDEs (wave and heat equations) using appropriate methods.
    10. Evaluate and represent solutions of differential equations using Matlab.
    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)
    All
    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
    All
  • Learning Resources
    Required Resources
    Course notes will be available in electronic form on MyUni.
    Recommended Resources
    Kreyszig, E., Advanced Engineering Mathematics, 10th edition, Wiley.
    Online Learning
    This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes, assignment and tutorial questions, and worked solutions. Students should make appropriate use of these resources. MyUni can be accessed here: https://myuni.adelaide.edu.au/

    This course also makes use of online assessment software for mathematics called Mobius, which we use to provide students with instantaneous formative feedback. Further details about using Mobius will be provided on MyUni.

    Students are also reminded that they need to check their University email on a daily basis. Sometimes important and time-critical information might be sent by email and students are expected to have read it. Any problems with accessing or managing student email accounts should be directed to Technology Services.
  • Learning & Teaching Activities
    Learning & Teaching Modes

    No information currently available.

    Workload

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

    Activity Quantity Workload hours
    Lectures 34 68
    Tutorials 11 22
    Midsemester test 1 9
    Written assignments 6 24
    Online assignments 11 33
    TOTALS 156
    Learning Activities Summary
    Lecture outline

    1. Differential equations and applications
    2. Ordinary differential equations (ODEs), directional fields
    3. Separable, linear and exact first-order ODEs, substitution
    4. Existence and uniqueness of solutions of first-order ODEs
    5. Homogeneous ODEs, superposition, linear independence, Wronskian
    6. Reduction of order, constant-coefficient homogenous ODEs
    7. Modelling of mass-spring-dashpot systems, free oscillations
    8. Nonhomogeneous ODEs, method of undetermined coefficients
    9. Forced oscillations, electrical circuits
    10. Variation of parameters
    11. Systems of first-order ODEs and applications
    12. Constant-coefficient homogeneous linear systems of ODEs
    13. Variable-coefficient homogeneous ODEs, Euler-Cauchy equation, power series method
    14. Ordinary and singular points, Legendre's equation
    15. Frobenius method, Bessel's equation
    16. Bessel functions
    17. Laplace transform
    18. Inverse Laplace transform, partial fractions, s-shifting
    19. Laplace transform of derivatives, application to ODEs
    20. Convolution
    21. Unit step function, t-shifting, Dirac delta function
    22. Fourier series
    23. Complex form of Fourier series, energy spectrum, convergence
    24. Fourier sine and cosine series, half-range expansions
    25. Partial differential equations (PDEs), wave equation, D’Alembert’s solution
    26. Separation of variables in 1D
    27. Separation of variables in 2D
    28. Heat equation
    29. Laplace equation
    30. Laplace transform solution of PDEs
    31. Fourier transform, Fourier integral, Fourier sine and cosine transforms
    32. Fourier transform solution of PDEs
    33. Discrete Fourier transform
    34. Fast Fourier transform

    Tutorials

    Tutorials will be held each week, commencing from week 2.  Tutorials cover material from the previous lectures.
  • 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
    Assessment
    Task Type Weighting Learning Outcomes
    Written assignments Formative and Summative 10 % All
    Mobius (online) assignments Formative and Summative 10 % All except 2
    Tutorial participation Formative 5 % All
    Midsemester test Summative 10 % 1,2,3,4,5
    Examination Summative 65 % All

    Due to the current COVID-19 situation modified arrangements have been made to assessments to facilitate remote learning and teaching. Assessment details provided here reflect recent updates.

    The new assessment for this course is:
    Assignments 35% (Written 17.5%, Mobius 17.5%),
    Midsemester Test 15%,
    Online Exam 50%.
    Assessment Related Requirements
    To pass the course the student must attain
    1. an aggregate score of 50%, and
    2. an exam score of at least 45%.
    Assessment Detail
    Written assignments are due every fortnight. The first written assignment will be released in Week 2 and due in Week 4.

    Mobius (online) assignments are due every week. The first Mobius assignment will be released in Week 2 and due in Week 4.

    The midsemester test will be held in Week 8.  Further details, including test dates, times and venues, will be provided by email and MyUni.
    Submission
    Assignments must be submitted according to the policies and procedures published on the Differential Equations for Engineers II MyUni site.
    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.

  • Student Support
  • Policies & Guidelines
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