MA202-5-AU-CO:
Ordinary Differential Equations
PLEASE NOTE: This module is inactive. Visit the Module Directory to view modules and variants offered during the current academic year.
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Inactive
Thursday 05 October 2023
Friday 15 December 2023
15
03 January 2024
Requisites for this module
MA101 and MA114
(none)
(none)
(none)
MA222, MA225, MA307, MA323
This module provides an overview of standard methods for solving single ordinary differential equations and systems of ordinary differential equations, with an introduction to the underlying theory. The first part is devoted to basic theory and methods for solving scalar ODEs. The second part of the module is devoted to the study of Systems of linear ODEs.
The subject of ordinary differential equations is a very important branch of Mathematical Analysis and has deep conections with Applied Mathematics. Many phenomena from Physics, Biology, Engineering, Chemistry, Finance, among others, may be described using ordinary differential equations. To understand the underlying processes, we have to find and interpret the solutions to these equations.
The aims of this module are:
- To introduce students to the basic theory of ordinary differential equations.
- To give a competence in solving ordinary differential equations by using analytical methods.
By the end of the module, students will be expected to:
- Use some of the standard methods to solve first order ODEs;
- Use some of the standard methods to solve second order ODEs;
- Be familiar with the basic theory and be able to solve higher order linear ODEs;
- Be familiar with the basic theory and be able to solve systems of first order linear ODEs;
- Be aware of the implications of existence and uniqueness theorems.
Indicative syllabus:
1. Introduction, Classification of Differential Equations, First order differential equations: Linear Equations with Variable Coefficients, Separable Equations.
2. First order differential equations: Differences Between Linear and Nonlinear Equations, Exact Equations and Integrating Factors, (Euler) homogeneous equations, The Existence and Uniqueness Theorem.
3. Second Order Linear Equations: Homogeneous Equations with Constant Coefficients, Fundamental Solutions of Linear Homogeneous Equations, Linear Independence and the Wronskian, Complex Roots of the Characteristic Equation, Repeated Roots; Reduction of Order; The Existence and Uniqueness Theorem.
4. Second Order Linear Equations: ODEs with missing variables, Non-homogeneous Equations, Method of Undetermined Coefficients, Variation of Parameters.
5. Higher Order Linear Equations: General Theory of nth Order Linear Equations, Homogeneous Equations with Constant Coefficients, The Method of Undetermined Coefficients, The Method of Variation of Parameters.
6. Systems of First Order Linear Equations: Basic Theory of Systems of First Order Linear Equations including Linear Systems with Constant Coefficients.
Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.
The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's
reading list.
Assessment items, weightings and deadlines
Coursework / exam |
Description |
Deadline |
Coursework weighting |
Exam |
Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period)
|
Exam |
Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Georgios Papamikos, email: g.papamikos@essex.ac.uk.
Dr Georgios Papamikos
g.papamikos@essex.ac.uk
No
No
No
Prof Stephen Langdon
Brunel University London
Professor
Available via Moodle
No lecture recording information available for this module.
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