MATHS 7102 - Differential Equations
North Terrace Campus - Semester 1 - 2014
General Course Information
Course Code MATHS 7102 Course Differential Equations Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Prerequisites MATHS 1012 Incompatible MATHS 2201 Course Description 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 Coordinator: Professor Anthony Roberts
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesOn 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) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. all An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. all Skills of a high order in interpersonal understanding, teamwork and communication. all A proficiency in the appropriate use of contemporary technologies. all A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. all
Required ResourcesAccess to the internet.
Recommended ResourcesKreyszig, E. (2011), Advanced engineering mathematics, 10th edn, Wiley.
Online LearningThis 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 ModesThis 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.
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 SummaryThe 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
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.
Component Weighting Objective assessed Assignments 30% all Exam 70% all
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
Assessment item Distributed Due date Weighting Continuous assessment TBA TBA 10% Assignment 1 week 2 week 3 4% Assignment 2 week 4 week 5 4% Assignment 3 week 6 week 7 4% Assignment 4 week 8 week 9 4% Assignment 5 week 10 week 11 4%
- 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.
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.
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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