Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title COMPLEX FUNCTIONS
Code MATH243
Coordinator Dr D Meyer
Mathematical Sciences
Daniel.Meyer@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2023-24 Level 5 FHEQ First Semester 15

Aims

To introduce the student to a surprising, very beautiful theory having intimate connections with other areas of mathematics and physical sciences, for instance ordinary and partial differential equations and potential theory.

Learning Outcomes

(LO1) Understand the central role of complex numbers in mathematics.

(LO2) Develop the knowledge and understanding of all the classical holomorphic functions.

(LO3) Compute Taylor and Laurent series of standard holomorphic functions.

(LO4) Understand various Cauchy formulae and theorems and their applications.

(LO5) Be able to reduce a real definite integral to a contour integral.

(LO6) Be competent at computing contour integrals.

(S1) Problem solving skills

(S2) Numeracy

Syllabus
 

Reminder of complex arithmetic and algebra.

Holomorphicity, power series, radius of convergence.

Elementary functions, solving basic equations.

Contour integration and Cauchy theorem.

Taylor and Laurent series.

Poles and essential isolated singularities.

The Residue Theorem.

Evaluation of real integrals by means of contour integration.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
written exam  120    70       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 1 online (Moebius)  0    10       
Homework 2 online (Moebius)  0    10       
Homework 3 online (Moebius)  0    10