MA1DE1NU-Differential Equations I

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:4
Terms in which taught: Autumn term module
Pre-requisites:
Non-modular pre-requisites: Some basic knowledge for programming with Matlab, R, Excel or similar.
Co-requisites:
Modules excluded:
Current from: 2020/1

Module Convenor: Dr Nick Biggs

Email: n.r.t.biggs@reading.ac.uk

Type of module:

Summary module description:

In this module, we consider the topics related to ODEs including solving first-order, higher- order differential equations and systems of differential equations introduce some fundamental theory of ODEs including existence and uniqueness of solutions and stability. ÌýThen we consider more advanced topics such as ODEs with non-constant coefficients, integral and series solutions, Fourier series and the theory of boundary value problems.

The Module lead at NUIST is Dr Jian Ding.

Aims:

To introduce and develop the study of ordinary differential equations

Assessable learning outcomes:

By the end of this module students are expected to be able to:

• Solve a range of ordinary differential equations including first-order and high-order ordinary differential equations, and systems of first-order linear equations;


• Construct and use Green's function to solve appropriate ODEs problems;


• Use series solution techniques for ODEs;


• Use integral transform techniques to solve IVPs for ODEs;


• Derive the Fourier series of a function;


• Use eigenfunction expansions to solve appropriate BVPs for ODEs

Additional outcomes:

By the end of the module, the student will also achieve an improved understanding of the issues of existence and uniqueness of solutions and stability of solutions.

Outline content:

Week 1 ÌýÌýÌýÌý Differential Equation Models, General Concepts and Definitions, The Method of Separation of Variables, and the Method of Transformation of VariablesÌýÌýÌýÌýÌý

Week 2 ÌýÌýÌý First-Order Linear Equations: Method of Variation of Parameters, Bernoulli Differential Equations, Riccati Equations.

Week 3 ÌýÌýÌý Exact Differential Equations and Integrating Factors, First-Order Implicit Differential Equa tion

Week 4ÌýÌýÌýÌý The Existence-uniqueness Theorem, Extension of Solutions, Dependence of solutions on initial conditions

Week 5ÌýÌýÌýÌý Quiz1

Week 6ÌýÌýÌýÌý General Theory of High-order Linear Equations, Homogeneous Equations with Constant Coefficients

Week 7ÌýÌýÌýÌý Homogeneous Equations with Constant Coefficients, Non-homogeneous Equations with Constant Coefficients

We ek 8ÌýÌýÌýÌý Non-homogeneous Equations and Variation of Parameters, Some Simple High-order Differential Equations (reduction of order method)

Week 9ÌýÌýÌýÌý Quiz2

Week 10ÌýÌý First-order Systems, Review of Matrices and Linear Algebraic Systems, Basic Theory of Systems of First-order Linear Equations

Week 11ÌýÌý Homogeneous Linear Systems with Constant Coefficients–Distinct Eigenvalues, Homogeneous Linear Sy stems with Constant Coefficients– Repeated Eigenvalues

Week 12ÌýÌý Nonhomogeneous Linear Systems, Quiz3

Week 13ÌýÌý Green’s Functions for ODEs

Week 14ÌýÌý The Laplace Transform for ODEs

Week 15ÌýÌýÌý Successive approximations (Picard) including existence & uniqueness, series solutions for a regular point, Fourier Series

Week 16ÌýÌý ODE Boundary Value Problems, Sturm-Liouville P roblems

Brief description of teaching and learning methods:

Lectures supported by problem sheets and weekly tutorials.

Contact hours:

Ìý	Autumn	Spring	Summer
Lectures	48
Tutorials	16
Guided independent study:	Ìý	Ìý	Ìý
Ìý Ìý Wider reading (independent)	20
Ìý Ìý Wider reading (directed)	6
Ìý Ìý Exam revision/preparation	10
Ìý	Ìý	Ìý	Ìý
Total hours by term		0	0
Ìý	Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written exam	70
Written assignment including essay	30

Summative assessment- Examinations:

2 Hours

Summative assessment- Coursework and in-class tests:

One examination and a number of assignments.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Module Convenor will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day[1] (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at:
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

40% to pass the module academically.

Reassessment arrangements:

One re-examination paper of 2 hours duration in August - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (70% exam, 30% coursework).

Additional Costs (specified where applicable):

Last updated: 24 August 2020