## MATHS 7102 - Differential Equations

### North Terrace Campus - Semester 1 - 2021

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 7102 Differential Equations School of Mathematical Sciences Semester 1 Postgraduate Coursework North Terrace Campus 3 Up to 3.5 hours per week Y MATHS 1012 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

Course Coordinator: Michael Chen

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
On successful completion of this course students will be able to:
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

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
• 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
• Course notes: Differential Equations II, various authors, University of Adelaide (2021).
• Instructional videos covering the material in the course notes
Both these primary learning resources will be made available to enrolled students via the course's MyUni page.
##### Recommended Resources
Kreyszig, E. (2011), Advanced engineering mathematics, 10th edn, Wiley.

Strogatz, S. (2000), Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, Perseus Publishing. [electronic copy from UoA library available here]
##### Online Learning
This course uses MyUni exclusively for providing electronic resources, such as the textbook, videoed lectures, tutorial questions, assignments, sample solutions, quizzes (for self-testing) discussion boards, sample test/examination etc. Students must make appropriate use of all these resources to succeed in this course.
• Learning & Teaching Activities
##### Learning & Teaching Modes
Course delivery will occur on a weekly timetable. Each week typically consists of a variety of learning activities. All asynchronous activities/resources will be released at the beginning of each week, to enable students to personalise their schedules. Weekly tasks include:

• Reading the relevant sections of the textbook
• Viewing instructional videos
• Participation in a synchronous scheduled (face-to-face or remote) tutorial session, which is designed for active learning
• Completing online quizzes to strengthen understanding of the relevant weekly material
• Review released solutions from the previous week's tutorial questions
• Attend the online consulting sessions as necessary, particularly if the student is having difficulty in achieving the learning outcomes
These Weekly Tasks are designed to provide complementary activities which carefully work with each other in helping students achieve the learning outcomes for the relevant sections for each week. The design ensures that each student has the opportunity to take responsibility for their own learning.

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.
Watching instructional videos 30
Tutorials 12 24
Quizzes 24
Assignments 5 20
Short projects 3 12
Major project 1 24
Other study/test revision 22
Total 156
##### Learning Activities Summary
The course will explore and develop the following.
1. First-order ordinary differential equations
2. One-dimensional autonomous ODE models
3. Second- and higher-order ODEs
4. Partial differential equations
5. Representing periodic functions by Fourier series
6. Series solutions of ODEs
7. More partial differential equations
• 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
Exam 30% all
Test 1 5% all
Test 2 5% all
Assignments 20% all
Weekly quizzes 10% all
Tutorials/participation 10% all
Short projects 9% all
Major project 11% all

##### Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
##### Assessment Detail
Assessment itemDistributedDue dateWeighting
Exam - - 30%
Test 1 - week 5 5%
Test 2 - week 9 5%
Weekly quizzes weekly weekly 10%
Tutorial/participation quizzes weekly weekly 10%
Assignment 1 week 1 week 2 4%
Assignment 2 week 2 week 4 4%
Assignment 3 week 6 week 8 4%
Assignment 4 week 8 week 10 4%
Assignment 5 week 10 week 12 4%
Short project 1 week 1 week 3 3%
Short project 2 week 4 week 6 3%
Short project 3 week 6 week 7 3%
Major project week 7 week 13 11%
##### Submission

1. All written assignments are to be submitted to the designated hand-in boxes in 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.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
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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