 Academic Year: |
2014/5 |
| Owning Department/School: |
Department of Mathematical Sciences |
| Credits: |
6 |
| Level: |
Honours (FHEQ level 6) |
| Period: |
Semester 2
|
| Assessment Summary: |
EX 100% |
| Assessment Detail: | |
| Supplementary Assessment: |
MA30056 Mandatory Extra Work (where allowed by programme regulations)
|
| Requisites: |
Before taking this unit you must take MA20218 and take MA20219 |
| Description: |
Aims & Learning Objectives:
Aims:
The aim of this course is to cover the standard introductory material in the theory of functions of a complex variable and to cover complex function theory up to Cauchy's Residue Theorem and its applications.
Objectives:
Students should end up familiar with the theory of functions of a complex variable and be capable of calculating and justifying power series, Laurent series, contour integrals and applying them.
Content:
Topics will be chosen from the following:
Functions of a complex variable. Continuity. Complex series and power series. Circle of convergence. The complex plane. Regions, paths, simple and closed paths. Path-connectedness. Analyticity and the Cauchy-Riemann equations. Harmonic functions. Cauchy's theorem. Cauchy's Integral Formulae and its application to power series. Isolated zeros. Differentiability of an analytic function. Liouville's Theorem. Zeros, poles and essential singularities. Laurent expansions. Cauchy's Residue Theorem and contour integration. Applications to real definite integrals.
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| Programme availability: |
MA30056 is Optional on the following programmes:
Department of Computer Science
- USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
- USCM-AAB14 : BSc(Hons) Computer Science with Mathematics with Study year abroad (Year 4)
- USCM-AKB14 : BSc(Hons) Computer Science with Mathematics with Year long work placement (Year 4)
- USCM-AFB01 : BSc Computing (Year 3)
- USCM-AKB01 : BSc Computing with Year long work placement (Year 4)
Department of Mathematical Sciences
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- TSMA-AFM09 : MSc Mathematical Sciences
- TSMA-APM09 : MSc Mathematical Sciences
- USMA-AFB05 : BSc(Hons) Statistics (Year 3)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)
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