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MX4557: COMPLEX ANALYSIS (2021-2022)

Last modified: 31 May 2022 13:05


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
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Markus Upmeier

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?

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.

Details for second half-session courses, including assessments, may be subject to change until 23 December 2022.

Contact Teaching Time

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

Teaching Breakdown

  • 2 Lectures during University weeks 26 - 30, 32 - 35, 39 - 40
  • 1 Tutorial during University weeks 27 - 30, 32 - 35, 39 - 40

More Information about Week Numbers


Details for second half-session courses, including assessments, may be subject to change until 23 December 2022.

Summative Assessments

1st Attempt

3 x Standard Assignments - 30%, 30% and 40%

Alternative Resit Arrangements

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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