Module Specification
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.
1. Module Title COMPLEX FUNCTIONS
2. Module Code MATH243
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 5 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr D Meyer Mathematical Sciences Daniel.Meyer@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr D Marti-Pete Mathematical Sciences David.Marti-Pete@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 24

   24

       48
17.

Private Study

 102
18.

TOTAL HOURS

 150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:
25. Programme(s) (including Year of Study) to which this module is available on a required basis:
26. Programme(s) (including Year of Study) to which this module is available on an optional basis:
27. 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.
 
28. 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
 
29. Teaching and Learning Strategies
 

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of 2 hours of active learning sessions and 2 hours of supported study/drop-in sessions.
 
30. 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.
 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment
32. EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  written exam 120 70
33. 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