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MX3522: COMPLEX ANALYSIS (2015-2016)

Last modified: 25 Mar 2016 11:35


Course Overview

This course builds on the courses Introduction to Analysis (MA2005) and Further Real Analysis (MX3021), and 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 3
Session Second Sub Session 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?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

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.

Degree Programmes for which this Course is Prescribed

  • BSc Education (Secondary) - Mathematics
  • Mathematics Major

Contact Teaching Time

54 hours

This is the total time spent in lectures, tutorials and other class teaching.

Teaching Breakdown


Assessment

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.

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