Available in 2021
Course code

MATH2242

Units

10 units

Level

2000 level

Course handbook

Description

Complex analysis forms a basis for not only advanced mathematical topics, including differential equations, number theory, operator theory and other 3000 and higher level courses, but also for special functions of mathematical and quantum physics. Through this, complex functions make a significant contribution to the understanding of the world in which we live. This course covers fundamental knowledge in the theory of analytical functions with applications to definite integration and culminates with study of harmonic and special functions.


Availability2021 Course Timetables

Callaghan

  • Semester 2 - 2021

Replacing course(s)

This course replaces the following course(s): MATH3242. Students who have successfully completed MATH3242 are not eligible to enrol in MATH2242.


Learning outcomes

On successful completion of the course students will be able to:

1. Calculate and manipulate series expansions for analytical complex-valued functions.

2. Manipulate and evaluate contour integrals in the complex plane.

3. Evaluate definite integrals using Cauchy’s residue theorem.

4. Relate the algebraic and geometric properties of conformal mappings, and apply these to determine the properties of analytic functions.

5. Apply the theory and methods of complex analysis to determine the properties of special functions.


Content

  • Functions of complex variable
  • Differentiation of functions of complex variables
  • Cauchy's integral theorem
  • The calculus of residues
  • Series expansions
  • Contour integration
  • Conformal mappings and further results on analytic functions
  • Harmonic functions
  • Entire functions and infinite products
  • Special functions

Requisite

This course replaces MATH3242. Students who have successfully completed MATH3242 cannot enrol in MATH2242.


Assumed knowledge

MATH2310


Assessment items

Written Assignment: Written Assignments

Quiz: In-class quiz

Formal Examination: Formal exam


Contact hours

Callaghan

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term

Tutorial work will be integrated with the lecture material.

The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.