University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 9

Semester: 1

Planned timetable: 12.00 noon Mon (odd weeks), Wed and Fri

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-requisite(s): Before taking this module you must pass MT2502 or pass MT2503

Learning and teaching methods and delivery

Weekly contact: 2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours: 35

Guided independent study hours: 116

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 90%, Coursework = 10%

As defined by QAA
Written examinations : 90%
Practical examinations : 0%
Coursework: 10%

Re-assessment: Oral examination = 100%

Personnel

Module coordinator: Dr J N Reinaud
Module coordinator email jnr1@st-andrews.ac.uk

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