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Session: 2022/23
Last modified: 16/05/2022 16:39:53
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Title of Module: Advanced Calculus |
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Code: MATH09002 |
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: | Kenneth
C.
Nisbet |
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| Summary of Module |
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This module considers Fourier analysis and further ordinary differential equations, and their application to applied problems.
The construction of Fourier series will be discussed, together with their properties. Use of Fourier series to solve certain ODEs will be introduced. Mention will be made of Fourier transforms.
Other methods of solution of first order differential equations will be considered, e.g. exact equations. Qualitative analysis of autonomous nonlinear equations will be considered.
Building on the ideas of solution of linear equations with constant coefficients, equations such as those of Euler-Cauchy type will be considered. Further, series solution methods, including the method of Frobenius and an introduction to special functions, will be studied.
Systems: Both quantitative and qualitative methods in the study of linear and nonlinear first order systems will be considered. This will include the use of Laplace transforms and eigenvalue/eigenvector methods.
The Graduate Attributes relevant to this module are given below:
- Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Autonomous; Incisive; Innovative.
- 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.
Use a range of techniques in the solution and qualitative analysis of ordinary differential equations.
L2.
Use eigenvalues and eigenvectors in the analysis of systems of differential equations.
L3.
Use the methods of Laplace transforms or Fourier analysis in a range of problems.
L4.
Implement series solution methods in ordinary differential equations and investigate special functions. |
| 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.
Understanding some of the techniques used to solve ordinary differential equations.
Demonstrating awareness of established techniques of enquiry in the use of ordinary differential equations in applications.
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| Practice: Applied Knowledge and Understanding |
SCQF Level 9.
Using a range of mathematical techniques to obtain Ussolutions of problems.
Using a range of specialised techniques to solve ordinary differential equations.
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| Generic Cognitive skills |
SCQF Level 9.
Demonstrate a critical understanding of fundamental mathematical concepts.
Demonstrate a critical understanding of the validity and limitations of mathematical techniques.
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| Communication, ICT and Numeracy Skills |
SCQF Level 9.
Presenting reports describing investigations in mathematics.
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| Autonomy, Accountability and Working with others |
SCQF Level 9.
Collaborating in a small team to investigate and solve problems in mathematics.
Producing reports describing the solution of problems in mathematics.
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| Pre-requisites: |
Before undertaking this module the student should have
undertaken the following:
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Module Code:
MATH08002
| Module Title:
Differential Equations
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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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| The material will be presented through lectures and directed reading and the students will test their understanding of the material through tutorials. |
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 |
| Independent Study | 164 |
| 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:
“Advanced Calculus” class notes as published on the University VLE.
"Differential Equations", FR Giordano and MD Weir.
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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 | 2.10 |
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| Assessment: (also refer to Assessment Outcomes Grids below) |
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Assignment: a series of coursework tasks, 30% of the final mark.
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| Examination: 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 stated pre-requisite.
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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