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MA32045: Complex analysis

[Page last updated: 22 May 2025]

Academic Year: 2025/26
Owning Department/School: Department of Mathematical Sciences
Credits: 5 [equivalent to 10 CATS credits]
Notional Study Hours: 100
Level: Honours (FHEQ level 6)
Period:
Semester 2
Assessment Summary: EXCB 100%
Assessment Detail:
  • Examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA12003 OR take MA12011 OR take MA10236
In taking this module you cannot take MA20219
Learning Outcomes: By the end of the unit, you should be able to:
  • demonstrate a good knowledge and understanding of the principal tools of complex analysis;
  • calculate and justify complex derivatives, contour integrals, power series, and Laurent series;
  • apply the theory to simple examples.



Synopsis: You will study functions of complex (as opposed to real) variables. These functions have surprising and often beautiful properties; for example, a striking result is the following: the definition of the derivative of a function of a complex variable is the same as the one for functions of a real variable (which you encountered in Year 1); however, if a function of a complex variable is once differentiable, then it is actually infinitely differentiable (which is not the case for real functions).

Content: The complex plane. Functions of a complex variable. Continuity, complex derivative. Contour integrals. The Cauchy-Riemann equations. Cauchy's theorem. Cauchy integral formulae. Power series and analytic functions. Liouville's theorem. Isolated zeroes. Laurent expansions. Isolated singularities. Cauchy's residue theorem. Applications to real definite integrals.

Course availability:

MA32045 is Optional on the following courses:

Department of Mathematical Sciences
  • 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-AFB30 : 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-AFB32 : 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)
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 3)
  • USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 4)
  • USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 4)
  • USMA-AFM30 : MMath(Hons) Mathematics (Year 3)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
Department of Physics
  • USPH-AFB26 : 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)
  • USPH-AFM26 : 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)

Notes:

  • This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
  • 好色tv and units are subject to change in accordance with normal University procedures.
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  • Find out more about these and other important University terms and conditions here.