Module Details |
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
Title | MATH201 - Ordinary Differential Equations | ||
Code | MATH201 | ||
Coordinator |
Dr O Selsil Mathematical Sciences Oselsil@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2024-25 | Level 5 FHEQ | First Semester | 15 |
Aims |
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•To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations. •To illustrate the breadth of applications of ODEs and fundamental importance of related concepts. |
Learning Outcomes |
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(LO1) To understand the basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions. |
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(LO2) To know the elementary techniques for the solution of ODEs. |
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(LO3) To understand the idea of reducing a complex ODE to a simpler one. |
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(LO4) To be able to solve linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix. |
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(LO5) To understand a range of applications of ODE. |
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(S1) Problem solving skills |
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(S2) Numeracy |
Syllabus |
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Introduction, Important ODEs and their analytic solutions. Initial value problem. Fundamental properties of ODE. Picard theorem. Second order linear ODE with constant and non-constant coefficients. Solution of second order linear ODE in series. Introduction to Sturm-Liouville theory. Orthogonal functions. Matrix methods for solving homogeneous and non-homogeneous linear systems with constant coefficients. Eigensystem. PDEs solved by separation of variables and ODEs. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH102 CALCULUS II; MATH101 Calculus I; MATH103 Introduction to Linear Algebra |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Class Test 2: 25% Open book and remote Around 60-90 minutes refers to the submission window | 0 | 25 | ||||
Class Test worth 25%, open book and remote Around 60-90 minutes submission window | 150 | 25 | ||||
Project component worth 50% of final mark Project is remote | 0 | 50 |