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Session: 2022/23
Last modified: 10/01/2023 11:10:57
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Title of Module: Numerical Solution of ODEs |
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Code: MATH09011 |
SCQF Level: 9
(Scottish Credit and Qualifications Framework) |
Credit Points: 20 |
ECTS: 10
(European Credit Transfer Scheme) |
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| School: | School of Computing, Engineering and Physical Sciences |
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| Module Co-ordinator: | Wan
R
Mekwi |
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| Summary of Module |
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This module builds on the concept of an ordinary differential equation as introduced in MATH08009 Numerical Analysis. The ethos of the approach taken is underpinned by the fact that most ordinary differential equations cannot be solved analytically in terms of standard functions, thereby leading to the study of numerical methods of solution.
The basic idea of numerical solution of first order equations is introduced using Euler’s method, and extended to cover a range of other methods, including Modified and Improved Euler’s methods, Runge-Kutta methods. Multistep methods will be discussed briefly.
Finite difference methods for initial and boundary value problems will be discussed.
Issues of consistency and convergence are investigated across the range of numerical methods discussed above. A treatment of error analysis in such problems will be given.
The implementation of these solution methods will be supported by suitable mathematical software.
The Graduate Attributes relevant to this module are given below:
- Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Digitally literate; Autonomous.
- Personal: Motivated; Resilient
- Professional: Ambitious; Driven.
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| Module Delivery Method |
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| Face-To-Face | Blended | Fully Online | HybridC | HybridO | Work-based Learning |
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Face-To-Face
Term used to describe the traditional classroom environment where the students and the lecturer meet synchronously in the same room for the whole provision.
Blended
A mode of delivery of a module or a programme that involves online and face-to-face delivery of learning, teaching and assessment activities, student support and feedback. A programme may be considered “blended” if it includes a combination of face-to-face, online and blended modules. If an online programme has any compulsory face-to-face and campus elements it must be described as blended with clearly articulated delivery information to manage student expectations
Fully Online
Instruction that is solely delivered by web-based or internet-based technologies. This term is used to describe the previously used terms distance learning and e learning.
HybridC
Online with mandatory face-to-face learning on Campus
HybridO
Online with optional face-to-face learning on Campus
Work-based Learning
Learning activities where the main location for the learning experience is in the workplace.
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| Term(s) for Module Delivery |
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(Provided viable student numbers permit).
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| Term 1 | | Term 2 | | Term 3 | |
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| Learning Outcomes: (maximum of 5 statements) |
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On successful completion of this module the student will be able to:
L1.
Implement numerical solution methods for ordinary differential equations.
L2.
Perform error analysis, stability, consistency and convergence of numerical methods.
L3.
Apply finite difference methods to solve initial and boundary value problems. |
| Employability Skills and Personal Development Planning (PDP) Skills |
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| SCQF Headings |
During completion of this module, there will be an opportunity to achieve
core skills in:
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| Knowledge and Understanding (K and U) |
SCQF Level 9.
Demonstrating a detailed knowledge and understanding of important techniques necessary in the analysis of numerical methods for solving ordinary differential equations.
Demonstrating critical awareness of established techniques in solving ordinary differential equations numerically. |
| Practice: Applied Knowledge and Understanding |
SCQF Level 9.
Using a range of standard techniques to solve problems at an advanced level, sometimes in non-routine contexts.
Carrying out defined investigative problems within a mathematically based subject. |
| Generic Cognitive skills |
SCQF Level 9.
Conceptualising and analysing problems informed by professional and research issues. |
| Communication, ICT and Numeracy Skills |
SCQF Level 9.
Implementing and interpreting suitable mathematical software.
Making formal written presentation(s) based on the output from an investigative problem.
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| Autonomy, Accountability and Working with others |
SCQF Level 9.
Exercising independence and initiative in carrying out a range of activities.
Identifying learning needs through reflection based on self, tutor and peer evaluation of work. |
| Pre-requisites: |
Before undertaking this module the student should have
undertaken the following:
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Module Code:
MATH08009
MATH08007
| Module Title:
Numerical Analysis
Linear Algebra
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| Other: | or equivalent. |
| Co-requisites | Module Code:
| Module Title:
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* Indicates that module descriptor is not published.
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| Learning and Teaching |
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Learning Activities
During completion of this module, the learning activities undertaken to
achieve the module learning outcomes are stated below:
| Student Learning Hours
(Normally totalling 200 hours):
(Note: Learning hours include both contact hours and hours spent on other learning activities) |
| Lecture/Core Content Delivery | 24 |
| Tutorial/Synchronous Support Activity | 12 |
| Laboratory/Practical Demonstration/Workshop | 12 |
| Independent Study | 146 |
| Personal Development Plan | 6 |
| 200
Hours Total
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**Indicative Resources: (eg. Core text, journals, internet
access)
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The following materials form essential underpinning for the module content
and ultimately for the learning outcomes:
“Numerical Solution of ODEs" class notes as published on the University VLE.
Suitable mathematical software, such as Octave, and generic software such as Microsoft Word.
"Numerical Analysis", RL Burden and JD Faires
"A Friendly Introduction to Numerical Analysis", B Bradie
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(**N.B. Although reading lists should include current publications,
students are advised (particularly for material marked with an asterisk*) to
wait until the start of session for confirmation of the most up-to-date
material)
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| Engagement Requirements |
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In line with the Academic Engagement Procedure, Students are defined as academically engaged if they are regularly engaged with timetabled teaching sessions, course-related learning resources including those in the Library and on the relevant learning platform, and complete assessments and submit these on time. Please refer to the Academic Engagement Procedure at the following link: Academic engagement procedure |
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Supplemental Information
| Programme Board | Physical Sciences |
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| Assessment Results (Pass/Fail) |
No
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| Subject Panel | Physical Sciences |
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| Moderator | Dr Alan J Walker |
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| External Examiner | P Wilson |
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| Accreditation Details | |
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| Version Number | 1.06 |
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| Assessment: (also refer to Assessment Outcomes Grids below) |
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| Assignment: Series of coursework assignments, 30% of final mark |
| Examination: a final, closed book assessment, 70% of the final mark |
(N.B. (i) Assessment Outcomes Grids for the module
(one for each component) can be found below which clearly demonstrate how the learning outcomes of the module
will be assessed.
(ii) An indicative schedule listing approximate times
within the academic calendar when assessment is likely to feature will be
provided within the Student Handbook.)
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Assessment Outcome Grids (Footnote A.)
Footnotes
A. Referred to within Assessment Section above
B. Identified in the Learning Outcome Section above
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Note(s):
- More than one assessment method can be used to assess individual learning outcomes.
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Schools are responsible for determining student contact hours. Please refer to University Policy on contact hours (extract contained within section 10 of the Module Descriptor guidance note).
This will normally be variable across Schools, dependent on Programmes &/or Professional requirements.
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| Equality and Diversity |
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The module is suitable for any student satisfying the pre-requisites.
UWS Equality and Diversity Policy |
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(N.B. Every effort
will be made by the University to accommodate any equality and diversity issues
brought to the attention of the School)
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