MT3503 Complex Analysis

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 9

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

12.00 noon Mon (odd weeks), Wed and Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr J N Reinaud

Dr J N Reinaud
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module aims to introduce students to analytic function theory and applications. The topics covered include: analytic functions; Cauchy-Riemann equations; harmonic functions; multivalued functions and the cut plane; singularities; Cauchy's theorem; Laurent series; evaluation of contour integrals; fundamental theorem of algebra; Argument Principle; Rouche's Theorem.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2502 OR PASS MT2503

Assessment pattern

2-hour Written Examination = 90%, Coursework = 10%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

116

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • State what it means for a function to be holomorphic, be able to determine where complex-valued functions are holomorphic, and state and use the Cauchy-Riemann equations
  • Verify that a real-valued function to be harmonic and to be able to find the harmonic conjugate
  • Be able to state and use theorems concerning contour integration including Cauchy's Theorem, Cauchy's Integral Formula, Cauchy's Formula for Derivatives and Cauchy's Residue Theorem
  • Use properties of holomorphic functions including results such as Liouville's Theorem, the Fundamental Theorem of Algebra and Taylor's Theorem
  • Be able to classify singularities of a complex-valued function and to calculate the residue using the Laurent series and other standard methods
  • Apply the methods of complex analysis to calculate real integrals, determine the value of infinite sums, and to count the number of zeros of a function in appropriate regions in the complex plane