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  6. MX4557: Complex Analysis

MX4557: COMPLEX ANALYSIS (2025-2026)

Last modified: 14 Nov 2025 13:46


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
  • Professor Benjamin Martin

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.

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 31 August 2025 for 1st Term courses and 19 December 2025 for 2nd Term courses.

Summative Assessments

Exam

Assessment Type Summative Weighting 70
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Students will be invited to contact Course Coordinators for feedback on the final examination.

Duration: 2 hours
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseAbility to prove results about complex numbers and complex functions.
ConceptualApplyAbility to apply the important consequences of Cauchy’s theorem: Cauchy’s integral formulae, Liouville’s Theorem and Taylor Series.
ConceptualUnderstandUnderstand the necessary background and development of Cauchy’s theorem.
ConceptualUnderstandUnderstand the Cauchy residue theorem and some of its applications.
ConceptualUnderstandUnderstand Laurent Series and the classification of isolated singularities.
FactualUnderstandUnderstand the concept of analyticity and be familiar with the Cauchy-Riemann equations.
ProceduralApplyAbility to perform routine calculations with complex functions.

Problem Sheets

Assessment Type Summative Weighting 15
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseAbility to prove results about complex numbers and complex functions.
ConceptualApplyAbility to apply the important consequences of Cauchy’s theorem: Cauchy’s integral formulae, Liouville’s Theorem and Taylor Series.
ConceptualUnderstandUnderstand the Cauchy residue theorem and some of its applications.
ConceptualUnderstandUnderstand Laurent Series and the classification of isolated singularities.

Problem Sheets

Assessment Type Summative Weighting 15
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseAbility to prove results about complex numbers and complex functions.
ConceptualUnderstandUnderstand the necessary background and development of Cauchy’s theorem.
FactualUnderstandUnderstand the concept of analyticity and be familiar with the Cauchy-Riemann equations.
ProceduralApplyAbility to perform routine calculations with complex functions.

Formative Assessment

There are no assessments for this course.

Resit Assessments

Exam

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Best of (resit exam mark) or (resit exam mark with carried forward CA marks).

Duration: 2 hours
Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
ConceptualApplyAbility to apply the important consequences of Cauchy’s theorem: Cauchy’s integral formulae, Liouville’s Theorem and Taylor Series.
ProceduralApplyAbility to perform routine calculations with complex functions.
ConceptualUnderstandUnderstand the necessary background and development of Cauchy’s theorem.
ConceptualUnderstandUnderstand Laurent Series and the classification of isolated singularities.
ConceptualAnalyseAbility to prove results about complex numbers and complex functions.
FactualUnderstandUnderstand the concept of analyticity and be familiar with the Cauchy-Riemann equations.
ConceptualUnderstandUnderstand the Cauchy residue theorem and some of its applications.
 

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