Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH219
Module Title: Complex Functions
Module Level: Level 2
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: MTH118
   
Aims
To introduce the student to a theory having intimate connections with other areas of mathematics and physical sciences, for instance, ordinary and partial differential equations and potential theory.
Learning outcomes 
A. Appreciate the central role of complex numbers in mathematics.

B. Be familiar with classical holomorphic functions.

C. Compute Taylor and Laurent series of such functions.

D. Understand the content and relevance of relevant Cauchy formulae and theorems.

E. Be familiar with the reduction of real definite integrals to contour integrals.

Method of teaching and learning 
Students will be expected to attend formal lectures and supervised tutorials in a typical week.
Syllabus 
Review of complex arithmetic and algebra.

Limit, Continuity, Derivative and Holomorphicity (Analyticity).

Elementary functions, Solving basic equations.

Cauchy Theorem (without proof), Taylor and Laurent series (short exposure), Poles and essential isolated singularities.

The Residue Theorem, and evaluation of real integrals by means of contour integration.
Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 

Assessment

Sequence Method % of Final Mark
1 Final Exam 80.00
2 Coursework 1 10.00
3 Coursework 2 10.00

Module Catalogue generated from SITS CUT-OFF: 12/16/2019 8:02:41 AM