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Session: 2022/23
Last modified: 10/01/2023 11:15:18
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Title of Module: Partial Differential Equations |
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Code: MATH10003 |
SCQF Level: 10
(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: | Kenneth
C.
Nisbet |
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| Summary of Module |
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The module covers the solution of first and second order partial differential equations, and their application in commonly occurring problems in science and engineering.
For first order equations, the use of direct integration, separation of variables, Laplace transforms and the method of characteristics as methods of solution are studied, with application in problems involving, for example, advection processes.
For second order equations, the focus of the study is on the main analytic method of solution, i.e. separation of variables. The theory of Fourier series is revisited in this context. Applications to problems involving such as conduction, diffusion and wave propagation are discussed.
In addition to these analytic processes, numerical methods of solution, such as finite difference methods, are discussed together with application in problems such as advection processes.
The Graduate Attributes relevant to this module are given below:
- Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Digitally literate; Autonomous.
- Personal: Motivated, Creative; Resilient.
- Professional: Research-minded; 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.
Demonstrate detailed knowledge and understanding of analytic solution methods for first order partial differential equations.
L2.
Demonstrate detailed knowledge and understanding of analytic solution methods for second order partial differential equations.
L3.
Implement mathematical software to solve partial differential equations in applications, and to interpret the solutions. |
| 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 10.
Demonstrating a detailed knowledge and understanding of important techniques used in solving partial differential equations.
Demonstrating critical awareness of established techniques of enquiry in common applications of partial differential equations.
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| Practice: Applied Knowledge and Understanding |
SCQF Level 10.
Using a range of standard techniques to solve problems at advanced levels, and sometimes in non-routine contexts.
Carrying out defined investigative problems within a mathematically based subject. |
| Generic Cognitive skills |
SCQF Level 10.
Conceptualising and analysing problems informed by professional and research issues. |
| Communication, ICT and Numeracy Skills |
SCQF Level 10.
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 10.
Exercising independence and initiative in carrying out complex activities.
Identifying learning needs through reflection based on self, tutor and peer evaluation of work.
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| Pre-requisites: |
Before undertaking this module the student should have
undertaken the following:
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Module Code:
MATH09002
| Module Title:
Advanced Calculus
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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 | 18 |
| Tutorial/Synchronous Support Activity | 18 |
| Laboratory/Practical Demonstration/Workshop | 12 |
| Independent Study | 152 |
| 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:
“Partial Differential Equations” class notes as published on the University VLE.
Suitable mathematical software, e.g. Octave and/or generic software such as Microsoft EXCEL.
"Applied Partial Differential Equations", J Ockendon
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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 | C Macdonald |
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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: an individual coursework task, 20% of the final mark |
| Examination: a final, closed book assessment, 80% 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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