MATHS 7102 - Differential Equations
North Terrace Campus - Semester 1 - 2020
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General Course Information
Course Details
Course Code MATHS 7102 Course Differential Equations Coordinating Unit Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y Assumed Knowledge MATHS 1012 Assessment Ongoing assessment, exam Course Staff
Course Coordinator: Dr Raymond Vozzo
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
On successful completion of this course students will be able to:- understand that physical systems can be described by differential equations
- understand the practical importance of solving differential equations
- understand the differences between initial value and boundary value problems (IVPs and BVPs)
- appreciate the importance of establishing the existence and uniqueness of solutions
- recognise an appropriate solution method for a given problem
- classify differential equations
- analytically solve a wide range of ordinary differential equations (ODEs)
- obtain approximate solutions of ODEs using graphical and numerical techniques
- use Fourier analysis in differential equation solution methods
- solve classical linear partial differential equations (PDEs)
- solve differential equations using computer software
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) 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 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
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Learning Resources
Required Resources
Access to the internet.Recommended Resources
Kreyszig, E. (2011), Advanced engineering mathematics, 10th edn, Wiley.Online Learning
This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/ -
Learning & Teaching Activities
Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides the assessment opportunities for students to gauge their progress and understanding.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures 36 90 Tutorials 6 24 Assignments 6 42 Total 156 Learning Activities Summary
The course will explore and develop the following.- Basic definitions; Physical examples; Classification of types ODEs
- Basic definitions; IVPs; 1st order ODEs; Separable, Linear, Exact
- Graphical and numerical methods; directional fields and Eulers method
- Existence and Uniqueness for 1st order ODEs; Picard's Method and Theorem
- Existence and Uniqueness of IVPs for n-th order linear ODEs; Wronskian test
- n-th order homogenous linear constant coefficient ODEs
- Reduction of order
- Non-homogenous n-th order linear constant coeffs; Method of undetermined coefficients
- Variation of parameters
- Modelling and interpretation
- Linear ODEs with variable coefficients; Euler-Cauchy equation
- Power Series, via computer algebra
- Legendre equation and polynomials
- Frobenius series solution and Bessels equation
- Frobenius series solution---classification of solutions.
- Systems ODES; modelling, eigenvalues and eigenvectors
- Systems ODES; algebraic and geometric multiplicity
- Periodic and odd/even functions; Generalised Fourier series
- Piecewise continous functions
- Fourier sine, cosine and complex Fourier series
- Fourier Integral and Transform
- Introduction to PDEs; modelling conservation of material
- Wave Equation and D'Alemberts solution; car traffic; shocks
- Separation of variables; Wave, Heat, Laplace equation
- Vibrating Drum; Fourier Bessel series; interpretation
- Temperature field in a sphere; Fourier Legendre Series; interpretation
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Assessment
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 Summary
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.
Component Weighting Objective assessed Assignments x5 20% all Projects x4 20% all online quizzes 10% all Exam 50% all
20% online projects (released throughout semester)
4 projects - 5% each
Projects 1 & 2 due Friday 8 May
Projects 3 & 4 due Friday 12 June
5 assignment 4% each
Assignment 1 due 19 March
Assignment 2 due 9 April (originally 2 April)
Assignment 3 due 30 April
Assignment 4 due 14 May
Assignment 5 due 28 May
Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.Assessment Detail
No information currently available.
Submission
- 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.
- Late assignments will not be accepted without a medical certificate.
- Assignments normally have a two week turn-around time for feedback to students.
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 .
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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.
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Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
- Careers Services
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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