MTH3020 Complex analysis and integral transforms

When you finish this unit, you should be able to:

1. 1

   Understand the basic properties of complex numbers and functions, including differentiability;

2. 2

   Evaluate line integrals in the complex plane;

3. 3

   Understand Cauchy's integral theorem and its consequences;

4. 4

   Determine and work with Laurent and Taylor series;

5. 5

   Understand the method of Laplace transforms and evaluate the inverse transform;

6. 6

   Appreciate the importance of complex analysis for other mathematical units, as well as for physics and engineering, through seeing applications of the theory;

7. 7

   Use a computer algebra package to assist in the application of complex analysis.