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
- Semester 2 - 2021
This course replaces the following course(s): MATH3242. Students who have successfully completed MATH3242 are not eligible to enrol in MATH2242.
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.
- 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
This course replaces MATH3242. Students who have successfully completed MATH3242 cannot enrol in MATH2242.
Written Assignment: Written Assignments
Quiz: In-class quiz
Formal Examination: Formal exam
Face to Face On Campus 3 hour(s) per Week for Full Term
Tutorial work will be integrated with the lecture material.
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