MA202-5-AU-CO:
Ordinary Differential Equations
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
ReassessmentOnly
Thursday 07 October 2021
Friday 17 December 2021
15
03 August 2020
Requisites for this module
MA101
(none)
(none)
(none)
MA222, MA225, MA307, MA323
The subject of ordinary differential equations is a very important branch of 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 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 aim of the module is to introduce the students to the basic theory of ordinary differential equations and give a competence in solving ordinary differential equations by using analytical methods.
At the end of this module students should be able to:
1. use some of the standard methods to solve first order ODEs;
2. use some of the standard methods to solve second order ODEs;
3. be familiar with the basic theory and be able to solve higher order linear ODEs;
4. be familiar with the basic theory and be able to solve systems of first order linear ODEs.
5. be aware of the implications of existence and uniqueness theorems.
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 will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Exam |
Reassessment Main exam: 180 minutes during January
|
| Exam |
Reassessment Main exam: 180 minutes during Summer (Main 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 Murat Akman, email: murat.akman@essex.ac.uk.
Dr Murat Akman & Dr Georgios Papamikos
Dr Murat Akman (murat.akman@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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