MX4557: COMPLEX ANALYSIS (2020-2021)

Last modified: 05 Aug 2021 13:04

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	Aberdeen	Sustained Study	No
Co-ordinators	Dr Zur Izhakian

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

MA1005 Calculus 1 (Passed)
Either Programme Level 3 or Programme Level 4
Any Undergraduate Programme (Studied)
Either Mathematics (MA) or Mathematical Sciences (MX)
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?

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

3 x standard course assessments - 30%, 30% and 40%

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge Level	Thinking Skill	Outcome

Factual	Remember	ILO’s for this course are available in the course guide.