MATHS 7102 - Differential Equations

North Terrace Campus - Semester 1 - 2022

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: 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
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)

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.

1-11

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.

1-11

Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.

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
This course relies on course videos, online quizzes and workshops to guide students through the material, tutorial classes for peer and tutor support, and a sequence of written 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 and quizzes 72 Workshops 12 12 Tutorials 11 22 Test 1 10 Assignments 6 40 TOTALS 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
 Task Type Weighting Learning Outcomes Quizzes Formative and Summative 6 % All Assignments Formative and Summative 24 % All Test Summative 10 % All Exam Summative 60 % All
Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
Assessment Detail
 Assessment Item Distributed Due Date Weighting Quizzes Weekly Weekly 6 % Assignment 1 Week 2 Week 4 4 % Assignment 2 Week 4 Week 6 4 % Assignment 3 Week 6 Week 8 4 % Assignment 4 Week 8 Week 10 4 % Assignment 5 Week 10 Week 12 4 % Assignment 6 Week 12 Week 13 4 % Test Week 8 10 % Exam Exam period 60 %
Submission
Assignments must be submitted according to the policies and procedures published on the MyUni course site.

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

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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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