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Module Descriptors

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Session: 2022/23

Last modified: 16/05/2022 12:54:21

Title of Module: Complex Analysis

Code: MATH09009 SCQF Level: 9
(Scottish Credit and Qualifications Framework)		 Credit Points: 20 ECTS: 10
(European Credit Transfer Scheme)
School:School of Computing, Engineering and Physical Sciences
Module Co-ordinator:Alan  J.  Walker

Summary of Module

This module extends the material on complex numbers encountered in prior study to discuss complex functions, and their use in geometry and calculus.

Complex functions will be discussed, including power, trigonometric, exponential, logarithmic, and the Gamma and Beta functions. Rational complex functions will be used to motivate a discussion of Mobius transformations.

Mappings, branches, branch cuts and points and branch planes will be introduced as well as their application to boundary value problems in physics and engineering.

The idea of limits and differentiability, including reference to the Cauchy-Riemann equations, will be introduced, as will the idea of analyticity. Taylor and Laurent series will also be discussed.

Integrals of complex functions will be introduced, and will extend to cover contour integrals and the residue theorem, for which a discussion of poles will be necessary.

Some important results in complex analysis will also be covered, such as the Poisson Integral formula, Rouché’s Theorem, and the Schwarz-Christoffel transformation.

The Graduate Attributes relevant to this module are given below:

  • Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Autonomous.
  • Personal: Motivated; Resilient
  • Professional: Ambitious; Driven.

Module Delivery Method
Face-To-FaceBlendedFully OnlineHybridCHybridOWork-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.


Campus(es) for Module Delivery
The module will normally be offered on the following campuses / or by Distance/Online Learning: (Provided viable student numbers permit)
Paisley:Ayr:Dumfries:Lanarkshire:London:Distance/Online Learning:Other:
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Term(s) for Module Delivery
(Provided viable student numbers permit).
Term 1check markTerm 2

 

Term 3

 

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Learning Outcomes: (maximum of 5 statements)

On successful completion of this module the student will be able to:

L1. Demonstrate a detailed knowledge and understanding of complex functions.

L2. Use a range of differentiation techniques for complex functions, and their applications.

L3. Use a range of integration techniques for complex functions, and their applications.

L4. Use complex variables in the analysis of improper real integrals.

Employability Skills and Personal Development Planning (PDP) Skills
SCQF Headings During completion of this module, there will be an opportunity to achieve core skills in:
Knowledge and Understanding (K and U) SCQF Level 9.

Demonstrating a detailed knowledge and understanding of important techniques necessary in the use of complex functions.

Demonstrating critical awareness of established techniques of enquiry in common applications of complex functions.

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.

Formally presenting standard topics in the field of complex analysis to a range of audiences.

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:
Module Code:
MATH08008
Module Title:
Multivariable Calculus
Other:or equivalent.
Co-requisitesModule Code:
Module Title:

* Indicates that module descriptor is not published.

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Learning and Teaching
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 Delivery36
Tutorial/Synchronous Support Activity0
Independent Study164
200 Hours Total

**Indicative Resources: (eg. Core text, journals, internet access)

The following materials form essential underpinning for the module content and ultimately for the learning outcomes:

“Complex Analysis” class notes as published on the University VLE.

“Complex Analysis”, IN Stewart and DO Tall.

“Complex Variables”, M Spiegel.

(**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)

Engagement Requirements

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 BoardPhysical Sciences
Assessment Results (Pass/Fail) No
Subject PanelPhysical Sciences
ModeratorDr Kenneth C. Nisbet
External ExaminerC Macdonald
Accreditation Details
Version Number

1.05

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Assessment: (also refer to Assessment Outcomes Grids below)
Assignment: a series of short coursework assignments, 30% of the 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.)

Assessment Outcome Grids (Footnote A.)

Component 1
Assessment Type (Footnote B.) Learning Outcome (1) Learning Outcome (2) Learning Outcome (3) Learning Outcome (4) Weighting (%) of Assessment ElementTimetabled Contact Hours
Unseen closed book (standard)check markcheck markcheck markcheck mark702

Component 2
Assessment Type (Footnote B.) Learning Outcome (1) Learning Outcome (2) Learning Outcome (3) Learning Outcome (4) Weighting (%) of Assessment ElementTimetabled Contact Hours
Class test (practical)check markcheck markcheck mark 306
Combined Total For All Components100% 8 hours

Footnotes
A. Referred to within Assessment Section above
B. Identified in the Learning Outcome Section above

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Note(s):
  1. More than one assessment method can be used to assess individual learning outcomes.
  2. 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.

Equality and Diversity
The module is suitable for any student satisfying the pre-requisites.
UWS Equality and Diversity Policy
(N.B. Every effort will be made by the University to accommodate any equality and diversity issues brought to the attention of the School)

2014 University of the West of Scotland

University of the West of Scotland is a Registered Scottish Charity.

Charity number SC002520.

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