MATHS 2106 - Differential Equations for Engineers II
North Terrace Campus - Semester 1 - 2021
General Course Information
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 Coordinator: Dr Trent Mattner
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesStudents who successfully complete the course will be able to:
- Derive mathematical models of physical systems.
- Present mathematical solutions in a concise and informative manner.
- Recognise ODEs that can be solved analytically and apply appropriate solution methods.
- Solve more difficult ODEs using power series.
- Know key properties of some special functions.
- Express functions using Fourier series.
- Solve certain ODEs and PDEs using Fourier and Laplace transforms.
- Solve problems numerically via the fast Fourier transform using Matlab.
- Solve standard PDEs (wave and heat equations) using appropriate methods.
- Evaluate and represent solutions of differential equations using Matlab.
University Graduate Attributes
University Graduate Attribute Course Learning Outcome(s)
- 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)
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
Required ResourcesCourse notes will be available in electronic form on MyUni.
Recommended ResourcesKreyszig, E., Advanced Engineering Mathematics, 10th edition, Wiley.
Online LearningThis 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.
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 SummaryLecture outline
- Differential equations and applications
- Ordinary differential equations (ODEs), directional fields
- Separable, linear and exact first-order ODEs, substitution
- Existence and uniqueness of solutions of first-order ODEs
- Homogeneous ODEs, superposition, linear independence, Wronskian
- Reduction of order, constant-coefficient homogenous ODEs
- Modelling of mass-spring-dashpot systems, free oscillations
- Nonhomogeneous ODEs, method of undetermined coefficients
- Forced oscillations, electrical circuits
- Variation of parameters
- Systems of first-order ODEs and applications
- Constant-coefficient homogeneous linear systems of ODEs
- Variable-coefficient homogeneous ODEs, Euler-Cauchy equation, power series method
- Ordinary and singular points, Legendre's equation
- Frobenius method, Bessel's equation
- Bessel functions
- Laplace transform
- Inverse Laplace transform, partial fractions, s-shifting
- Laplace transform of derivatives, application to ODEs
- Unit step function, t-shifting, Dirac delta function
- Fourier series
- Complex form of Fourier series, energy spectrum, convergence
- Fourier sine and cosine series, half-range expansions
- Partial differential equations (PDEs), wave equation, D’Alembert’s solution
- Separation of variables in 1D
- Separation of variables in 2D
- Heat equation
- Laplace equation
- Laplace transform solution of PDEs
- Fourier transform, Fourier integral, Fourier sine and cosine transforms
- Fourier transform solution of PDEs
- Discrete Fourier transform
- Fast Fourier transform
Tutorials will be held each week, commencing from week 2. Tutorials cover material from the previous lectures.
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment must maintain academic standards.
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 RequirementsTo pass the course the student must attain
- an aggregate score of 50%, and
- an exam score of at least 45%.
Assessment DetailWritten 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.
SubmissionAssignments must be submitted according to the policies and procedures published on the Differential Equations for Engineers II MyUni site.
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.
Final results for this course will be made available through Access Adelaide.
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