## MATHS 2106 - Differential Equations for Engineers II

### North Terrace Campus - Semester 1 - 2023

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 Differential Equations for Engineers II Mathematical Sciences Semester 1 Undergraduate North Terrace Campus 3 Up to 5 hours per week. Y MATHS 1012 MATHS 2102, MATHS 2201 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 Available to Bachelor of Engineering students only. Ongoing assessment, examination.
##### 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)

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.

All

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.

All

Attribute 7: Digital capabilities

Graduates are well prepared for living, learning and working in a digital society.

7,10
• 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 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 Modes
This 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.
##### Workload

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
 Week 1 Differential equations and applicationsOrdinary differential equations (ODEs), directional fieldsSeparable and linear first-order ODEs, substitution Week 2 Exact first-order ODEsExistence and uniqueness of solutions of first-order ODEsHomogeneous ODEs, superposition, linear independence, WronskianReduction of order Week 3 Constant-coefficient homogenous ODEsModelling of mass-spring-dashpot systems, free oscillationsNonhomogeneous ODEs, method of undetermined coefficientsForced oscillations, electrical circuits Week 4 Variation of parametersSystems of first-order ODEs and applicationsConstant-coefficient homogeneous linear systems of ODEsVariable-coefficient homogeneous ODEs, Euler-Cauchy equation, power series method Week 5 Ordinary and singular points, Legendre's equationFrobenius method, Bessel's equationBessel functions Week 6 Laplace transformInverse Laplace transform, partial fractions, s-shiftingLaplace transform of derivatives, application to ODEs Week 7 ConvolutionUnit step function, t-shifting, Dirac delta functionFourier series Week 8 Complex form of Fourier series, energy spectrum, convergenceFourier sine and cosine series, half-range expansions Week 9 Partial differential equations (PDEs)Wave equation, D’Alembert’s solutionSeparation of variables in 1D Week 10 Heat equationLaplace equationLaplace transform solution of PDEs Week 11 Fourier transform, Fourier integral, Fourier sine and cosine transformsFourier transform solution of PDEs Week 12 Discrete Fourier transformFast Fourier transform

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
 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 Requirements
To pass the course the student must attain:
1. an aggregate score of 50%, and
2. at least 40% on the final examination.
##### 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
• Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

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