MATHS 2106 - Differential Equations for Engineers II
North Terrace Campus - Semester 1 - 2024
General Course Information
Course Code MATHS 2106 Course Differential Equations for Engineers II Coordinating Unit 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: Associate Professor Ben Binder
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
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s)
Attribute 1: Deep discipline knowledge and intellectual breadth
Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.
Attribute 2: Creative and critical thinking, and problem solving
Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.
Attribute 7: Digital capabilities
Graduates are well prepared for living, learning and working in a digital society.
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 course 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 ModesThis course relies on instructional videos and workshops to guide students through the material, tutorial classes for peer and tutor support, and a sequence of written and online assignments that provide opportunities for students to practise techniques and develop their understanding of the course.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Course videos 60 Workshops 12 12 Tutorials 11 22 Midsemester test 1 7 Written assignments 5 25 Online assignments 10 30 TOTALS 156
Learning Activities Summary
Schedule Week 1 Differential equations and applications
Ordinary differential equations (ODEs), directional fields
Separable and linear first-order ODEs, substitution
Week 2 Exact first-order ODEs
Existence and uniqueness of solutions of first-order ODEs
Homogeneous ODEs, superposition, linear independence, Wronskian
Reduction of order
Week 3 Constant-coefficient homogenous ODEs
Modelling of mass-spring-dashpot systems, free oscillations
Nonhomogeneous ODEs, method of undetermined coefficients
Forced oscillations, electrical circuits
Week 4 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
Week 5 Ordinary and singular points, Legendre's equation
Frobenius method, Bessel's equation
Week 6 Laplace transform
Inverse Laplace transform, partial fractions, s-shifting
Laplace transform of derivatives, application to ODEs
Week 7 Convolution
Unit step function, t-shifting, Dirac delta function
Week 8 Complex form of Fourier series, energy spectrum, convergence
Fourier sine and cosine series, half-range expansions
Week 9 Partial differential equations (PDEs)
Wave equation, D’Alembert’s solution
Separation of variables in 1D
Week 10 Heat equation
Laplace transform solution of PDEs
Week 11 Fourier transform, Fourier integral, Fourier sine and cosine transforms
Fourier transform solution of PDEs
Week 12 Discrete Fourier transform
Fast Fourier transform
Tutorials will be held each week, commencing from week 2. Tutorials cover material from the previous lectures.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Task Type Weighting Learning Outcomes Written assignments Formative and Summative 12.5 % All Mobius (online) assignments Formative and Summative 12.5 % All except 2 Midsemester test Summative 15 % 1,2,3,4,5 Examination Summative 60 % All
Assessment Related RequirementsTo pass the course the student must attain:
- an aggregate score of 50%, and
- at least 40% on the final examination.
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.
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.
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.
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