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  6. MX4557: COMPLEX ANALYSIS

MX4557: COMPLEX ANALYSIS (2017-2018)

Last modified: 26 Feb 2018 20:09


Course Overview

This course asks what happens when concepts such as convergence of sequences and series, continuity and differentiability, are applied in the complex plane? The results are much more beautiful, and often, surprisingly, simpler, than over the real numbers. This course also covers contour integration of complex functions, which has important applications in Physics and Engineering.





Course Details

Study Type Undergraduate Level 4
Term Second Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Zur Izhakian

Qualification Prerequisites

None.

What courses & programmes must have been taken before this course?

  • Either Mathematics (MA) or Mathematical Sciences (MX)
  • Any Undergraduate Programme (Studied)
  • Either Programme Level 3 or Programme Level 4
  • MA1005 Calculus 1 (Passed)
  • MA1508 Calculus II (Passed)
  • MA2009 Analysis I (Passed)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

  • MX3522 Complex Analysis (Studied)

Are there a limited number of places available?

No

Course Description

  • Revision of complex numbers, roots of unity, polynomials.
  • Elementary functions, differentiation, Cauchy-Riemann equations.
  • Path integrals, Cauchy's Theorem and Cauchy's Integral Formulae.
  • Liouville's Theorem and the Fundamental Theorem of Algebra.
  • Taylor Series, Laurent Series, Cauchy's Residue Theorem and applications to real integrals.

 

Syllabus

  • Complex numbers and complex plane.
  • Complex sequences and complex series.
  • Complex functions.
  • Sets, limits, and continuous functions.
  • Derivatives
  • Power series.
  • Integration
  • Cauchy’s theorem.
  • Taylor series.
  • Laurent series.
  • Residues.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour examination (maximum of 100% resit and 80% resit with 20% in-course assessment).

Only the marks obtained on first sitting can be used for Honours classification.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinators for feedback on the final examination.

Course Learning Outcomes

None.
 

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