MATHS 2102 - Differential Equations II
North Terrace Campus - Semester 1 - 2018
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 Code MATHS 2102 Course Differential Equations II Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y 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:Dr Barry Cox
The full timetable of all activities for this course can be accessed from Course Planner.
- Learning Outcomes
Course Learning Outcomes
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
- 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
- Learning Resources
Kreyszig, E. (2011), Advanced engineering mathematics, 10th edn, Wiley.
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 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.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 DAlemberts 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.
Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
Grades for your performance in this course will be awarded in accordance with the following 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.
Component Weighting Objective assessed Assignments 20% all Exam 70% all Quizzes 10% all 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 within 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.
- Student Feedback
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One of the modules for Further Maths (MEI) is Differential Equations (DE), within which there is an element of coursework. The task of my class is to model the landing of an aircraft. However, I am finding this most challenging, mostly due to the fact that we have no guide or template to follow!
Is there anybody in the same position as me, or currently undertaking Differential Equations Coursework?
Thank you very much.
- (Original post by hello calum)
I'm not doing this myself, but I think you can write a differential equation taking friction and air resistance into account.
so if R=mg